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REVIEW 3 major objections 5 minor 124 references

Anomalous slow-down of the bound state dynamics in a non-locally coupled quantum circuit

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Adding a next-nearest-neighbor hopping channel can freeze, rather than speed up, a repulsively bound pair of magnons.

desk verdict Solid observation, incomplete explanation: the ED slow-down near J2 ~ 1/Jz is real, but the second-order effective Hamiltonian in Eq. (3) predicts a bandwidth twenty times larger than the ED result, so the paper overclaims its quantitative mechanism. read the letter →

arxiv 2506.09818 v1 pith:L7JPXHSB submitted 2025-06-11 cond-mat.quant-gas cond-mat.otherquant-ph

Biswajit Paul , Suman Mondal , Tapan Mishra This is my paper · ORCID
classification cond-mat.quant-gascond-mat.otherquant-ph
keywords magnonboundstatesquantumwalknext-nearest-neighborhoppingquasi-flatbandquenchdynamicsedgelocalizationeffectiveHamiltoniandigitalsimulation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper claims that adding next-nearest-neighbor hopping to a one-dimensional spin chain can suppress, rather than accelerate, the motion of a repulsively bound pair of spin excitations (a magnon pair). The slowdown happens at a magic NNN coupling $J_2 = J_1^2/J_z$, where the effective hopping of the bound pair vanishes because the direct NNN hop and a second-order virtual process interfere destructively. At that point the two-magnon bound-state band becomes quasi-flat, the pair stays almost frozen in the bulk, and a pair created at the edge remains localized there. The authors establish this with exact diagonalization, a perturbative effective-Hamiltonian calculation, and short-time digital quantum simulation, and they extend the same argument to a three-magnon bound state. If correct, this supplies a simple, disorder-free way to freeze or release bound pairs in quantum simulators.

What carries the argument

The load-bearing object is the effective two-magnon Hamiltonian obtained by treating $J_z$ as the unperturbed energy and $J_1,J_2$ as perturbations, then projecting onto the nearest-neighbor bound-pair subspace. In this effective description the bound pair behaves as a single particle moving with hopping amplitude $-J_2 + J_1^2/J_z$ (Eq. 3), and the magic condition is the destructive-interference zero of this amplitude. The same machinery, carried to third order for three adjacent magnons, yields the slowdown condition $-2J_2 + J_1^2/J_z = 0$. The paper also uses the boundary variant of the projection: an edge dimer has an on-site potential that is half the bulk value, which produces the complete edge-localization effect.

What would settle it

Measure the two-magnon band width and quench dynamics for $J_z=10$, $J_1=1$ as $J_2$ is swept through $0.09808$: if the band width does not dip below its $J_2=0$ value, or if the occupation fidelity at the supposed magic coupling decays on a timescale comparable to $J_2=0$, the central claim fails. A direct experiment could prepare two adjacent magnons in a chain with tunable NNN hopping and look for the predicted dip in the RMSD around $J_2=J_1^2/J_z$; observing no such dip, or a dip that does not move as $1/J_z$, would falsify the mechanism. For the edge claim, diagonalizing the open chain and checking whether a state with IPR close to one exists at $J_2 \approx 0.1$ for significantly larger $L$ would settle the edge-localization prediction.

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Extended reading notes

Core claim

The paper's central claim is that a repulsively bound pair of nearest-neighbor magnons on a ferromagnetic spin-$1/2$ chain with both NN and NNN transverse couplings moves slowest when the NNN coupling satisfies $J_2 \simeq J_1^2/J_z$, because the second-order effective Hamiltonian for the two-magnon bound state is $$ \hat $H^{{(2)}}$_{\rm eff} = \left(-J_2 + \frac{$J_1^{2}$}{J_z}\right)\sum_i (\hat B_i^\dagger \hat B_{i+1} + \mathrm{H.c.}) + \cdots, $$ with $\hat B_i = \hat\sigma^-_i \hat\sigma^-_{i+1}$. The coefficient in front of the nearest-neighbor pair-hopping term is the sum of two competing amplitudes: the direct NNN transverse coupling $-J_2$ and a virtual second-order process $+J_1^2/J_z$ in which the pair breaks apart and re-binds. At the magic coupling these cancel, the bound-state band becomes quasi-flat, and the quantum walk of the pair is almost frozen; at the open boundary the effective on-site energy is half the bulk value, so the pair is fully localized at the edge. Exact diagonalization places the band-width minimum at $J_2 = 0.09808$ for $J_z=10$, close to $1/J_z$, and quench dynamics show the occupation fidelity stays near one for long times. A third-order calculation gives an analogous slowdown for three magnons at $-2J_2 + J_1^2/J_z = 0$.

Load-bearing premise

The load-bearing premise is that the large interaction $J_z$ lets one treat the two hopping terms as a small correction, so that the bound pair's motion is fully described by the first nontrivial step of that approximation; at $J_z=10$ the exact band-width minimum already sits at $0.09808$ rather than the predicted $0.1$, so the claimed flat band and long-lived suppression depend on that approximation being good.

Editorial extensions

If this is right

  • A longer-range hopping channel is not always a speed-up knob: for repulsively bound pairs it provides a control point at which transport nearly stops, so slow and fast dynamics can be engineered by tuning $J_2$ alone.
  • The magic coupling scales as $J_1^2/J_z$, so the freezing point is set by the interaction strength; varying $J_z$ shifts the slowest dynamics and can be used to probe the interacting regime.
  • At an open boundary the same tuning fully pins the pair at the edge, offering a disorder-free way to store or hold a bound state and to study boundary effects in quantum walks.
  • The phenomenon persists for a three-magnon bound state with its own magic condition, suggesting that few-body bound states of any size in such chains will show analogous freezing points.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The destructive-interference mechanism should generalize to longer-range hopping: any additional direct hop of range $r$ contributes an amplitude $-J_r$, and virtual second-order processes contribute positive amplitudes, so multiple magic couplings may exist where the total pair-hopping amplitude vanishes.
  • The edge-localization effect can be viewed as an effective impurity potential of half the bulk value; this suggests similar pinning could be induced deliberately by local modifications of $J_z$ or $J_1$ at a chosen site, not only by the chain boundary.
  • A direct optical-lattice experiment with tunable NNN tunnelling should see the bound-pair RMSD dip at $J_2 = J_1^2/J_z$; because higher-order corrections shift the dip from $0.1$ to $0.09808$ at $J_z=10$, high-precision data could also map the breakdown of second-order perturbation theory.
  • For quantum simulation hardware, the frozen pair is a favorable regime: since the dynamics is suppressed, short-time Trotter errors are less consequential, so this parameter region may be easier to verify on current noisy devices than fast-spreading regimes.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The manuscript studies the quench dynamics of two nearest-neighbor spin excitations on a ferromagnetic spin-1/2 chain with both nearest-neighbor (J1) and next-nearest-neighbor (J2) transverse couplings, plus a strong longitudinal interaction Jz. Exact diagonalization shows that as J2 increases, the spreading of the bound magnon pair first slows down, reaches a minimum near J2 ~ 0.1 (for Jz = 10), and then speeds up again. The authors attribute this anomalous slowdown to a quasi-flat band of the bound state, which they interpret via a second-order perturbative effective Hamiltonian: the bound-pair hopping amplitude is -J2 + J1^2/Jz, so it nearly vanishes at J2 = J1^2/Jz. They also report a complete suppression of edge-initiated dynamics, interpret it as edge localization due to a reduced boundary on-site potential, and support the bulk results with digital quantum simulations on an IBM device using Trotterization, circuit recompilation, post-selection, and zero-noise extrapolation.

Significance. The reported effect is conceptually interesting: an additional hopping channel can suppress, rather than accelerate, the motion of a repulsively bound pair. If the explanation is correct, the mechanism is simple and potentially observable in cold-atom or superconducting-circuit platforms. The paper includes transparent exact diagonalization data, a clear scaling prediction J2 ∝ 1/Jz, and a plausible perturbative framework. The NISQ demonstration is a useful proof-of-principle, although the hardware data are significantly noisier than the exact results. The main weakness is that the quantitative flatness of the bound-state band is not actually captured by the retained second-order perturbation theory, so the central explanatory claim needs strengthening.

major comments (3)
  1. [Results, Eq. (3) and Fig. 4] The paper claims that the second-order effective Hamiltonian, Eq. (3), explains the slowdown via the vanishing of the leading pair-hopping amplitude -J2 + J1^2/Jz. At the numerical bandwidth minimum J2 = 0.09808, Jz = 10, Eq. (3) gives t = -J2 + J1^2/Jz = 0.00192 and t' = J2^2/Jz = 0.00096, corresponding to an effective bandwidth of about 0.0077. The exact diagonalization bandwidth shown in Fig. 4(b) is plotted on a vertical scale of only 0.0004, i.e., roughly an order of magnitude narrower. Thus the near-perfect flatness of the band at the magic coupling is not controlled by the terms retained in Eq. (3); higher-order processes must produce additional near-cancellations. The manuscript does not provide the third-order effective Hamiltonian for the two-magnon sector (it provides one only for three magnons, Supplementary Eq. 12), so the central quantitative claim that J2 = J1^2/Jz is the magic condition is not actually derived at the working parameters. I recommend either deriving the higher-order effective Hamiltonian or explicitly stating that the second-order calculation predicts only the approximate location of the minimum and that the observed quasi-flatness arises from higher-order cancellations.
  2. [Results, edge localization paragraph] The edge-localization argument rests on the statement that for a bound pair initialized at the edge of an open chain, the effective on-site potential is exactly half of the bulk value, (J1^2/Jz + J2^2/Jz) rather than 2(J1^2/Jz + J2^2/Jz). This assertion is not derived anywhere in the main text or the supplementary material. Since the explanation of the complete suppression of edge dynamics depends on this quantitative factor of two, the calculation should be provided explicitly or the claim should be softened to a numerical observation.
  3. [Results, Figs. 2(b) and 5(a)] The quantum computing data are presented as evidence that the anomalous slowdown is observable on a NISQ device. However, the hardware data in Fig. 2(b) do not reproduce the near-unity Fo at J2 = 0.1 seen in the ED data; the text acknowledges this deviation. The abstract's claim that 'we obtain such non-trivial signatures' is therefore too strong. Please specify more precisely which signatures are robustly obtained on the hardware and which are only visible after comparison with ED.
minor comments (5)
  1. [Introduction] In the introduction, 'approachs' is a typo for 'approaches'.
  2. [Model, Eq. (1)] The phrase 'the system is not domain-wall conserving' is unclear; the last term in Eq. (1) is a density-density interaction, not a domain-wall term, and the statement is not used in the analysis.
  3. [Supplementary, Eq. (17)] In the supplementary, Eq. (17) uses the symbol J2 both as the NNN coupling and as a summation index; please use a different index to avoid confusion.
  4. [References] Reference [109] is a duplicate of reference [100].
  5. [Fig. 2(d) caption] In Fig. 2(d), the hollow markers are described as quantum computing data, but the caption also states that the solid line is the perturbative relation; please clarify which curves correspond to ED and which to quantum computation in the main text.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the magic-coupling condition is derived from a parameter-free perturbative Hamiltonian and checked against ED, not fitted.

full rationale

The central claim—that the bound-pair slowdown occurs at J2 ≈ J1^2/Jz because the second-order effective pair hopping vanishes—is not circular. The paper derives Eq. (3) from an explicit second-order perturbative projection (Supplementary Eqs. 13–19) whose inputs are the original Hamiltonian and projection operators; no fitted parameter enters the condition −J2 + J1^2/Jz = 0. The ED bandwidth minimum is then used as an independent numerical check: the paper locates the minimum at J2 = 0.09808 (Fig. 4) and compares it with the perturbative value 0.1 (Figs. 2(d), 3), rather than using the ED minimum to define or fit the effective hopping. The quantum-computing data are likewise compared with ED, not used to set the magic coupling. Self-citations in the reference list (e.g., Refs. [76, 79, 81, 83–85]) concern earlier quantum-walk or doublon methods and are not load-bearing for the new flat-band prediction; the perturbative calculation cites external prescriptions [80, 122]. The reviewer-style concern that the second-order bandwidth at J2 = 0.09808 is wider than the exact ED bandwidth indicates that higher-order corrections are quantitatively important, but that is a correctness/accuracy issue, not a reduction of the prediction to its inputs. No step was found in which a fitted parameter is renamed as a prediction or in which Eq. (3) is equivalent by construction to the numerical band-structure data. Accordingly, the circularity score is 0.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

Free parameters: none. The couplings J1, J2, Jz are physical inputs; the magic condition J2 = J1^2/Jz is derived from perturbation theory and confirmed numerically. Axioms: the model Hamiltonian (Eq. 1), unitarity of time evolution, the large-Jz perturbative expansion, and the boundary-potential assumption for edge localization. Invented entities: none. The main ledger item is the perturbative truncation at second order, which is standard but carries the finite-Jz error seen in the 0.09808 vs 0.1 shift.

assumptions (4)
  • domain assumption The spin-1/2 Hamiltonian (Eq. 1) with Jz >> J1, J2 accurately models a hardcore-boson system where two NN magnons form a repulsively bound pair.
    This is the physical model under study, mapped to hardcore bosons via Holstein-Primakoff; used throughout the paper.
  • standard math Time evolution is unitary e^{-iHt} and the system is isolated during ED evolution.
    Standard quantum mechanics; the NISQ part explicitly adds noise and error mitigation, but the ED benchmark assumes closed-system dynamics.
  • domain assumption Second-order perturbation theory with Jz as the unperturbed part and J1, J2 as weak perturbations is valid for Jz=10.
    The central magic condition -J2 + J1^2/Jz = 0 and the effective Hamiltonian (Eq. 3) depend on this expansion; the numerical shift from 0.1 to 0.09808 highlights its finite-Jz limitation.
  • domain assumption For the edge localization study, the effective Hamiltonian applies to an open chain and the boundary on-site potential is exactly half the bulk value.
    The edge localization claim relies on this stated without derivation in the main text; it is not explicitly derived in the supplement.

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Cite this review

Pith. "Pith review of Anomalous slow-down of the bound state dynamics in a non-locally coupled quantum circuit." pith.science (2026). https://pith.science/paper/L7JPXHSB

@misc{pith2026250609818,
  author       = {Pith},
  title        = {Pith review of: Anomalous slow-down of the bound state dynamics in a non-locally coupled quantum circuit},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/L7JPXHSB}},
  note         = {Machine review of arXiv:2506.09818}
}
read the original abstract

Additional hopping channels in a tight-binding lattice is known to introduce faster dynamics of a quantum mechanical particle. However, we show that in the case of a repulsively bound state, the dynamics becomes abnormally slow when next-nearest neighbor (NNN) hopping is allowed for the particles. We show that such slowing down occurs for some magic strength of the NNN hopping at which the bound state band exhibits a quasi-flatband feature. We reveal this anomalous dynamical behavior by analyzing the quench dynamics of two nearest neighbor (NN) spin excitations (magnons) on a ferromagnetic chain by allowing both NN and NNN couplings. By implementing digital quantum computing simulations on a NISQ device, we obtain such non-trivial signatures and complement the results with exact numerical calculations. Moreover, through perturbative arguments, we reveal that the slowing down is due to the destructive interference between different paths associated to the bound state dynamics.

Figures

Figures reproduced from arXiv: 2506.09818 by the authors.

Figure 1
Figure 1. FIG. 1. (a-c) The quantum computing results of the time [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a-c) The band structure of two spin excitations are [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) and (b) Show the RMSD ( [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (a) The band width (∆ [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 6
Figure 6. Figure 6: FIG. 6. (a) The circuit diagram for a single Trotter step. (b) The recompiled circuit consisting of an alternative single-qubit [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. (a-c) The PS+ZNE mitigated data for the time [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 9
Figure 9. Figure 9: FIG. 9. (a-c) the time evolved expectation value of ˆσ [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]

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Works this paper leans on

124 extracted references · 65 canonical work pages

  1. [1]

    Dziarmaga, Dynamics of a quantum phase transition and relaxation to a steady state, Advances in Physics 59, 1063 (2010)

    J. Dziarmaga, Dynamics of a quantum phase transition and relaxation to a steady state, Advances in Physics 59, 1063 (2010)

    2010

  2. [2]

    Polkovnikov, K

    A. Polkovnikov, K. Sengupta, A. Silva, and M. Ven- galattore, Colloquium: Nonequilibrium dynamics of closed interacting quantum systems, Rev. Mod. Phys. 83, 863 (2011)

    2011

  3. [3]

    Dutta, G

    A. Dutta, G. Aeppli, B. K. Chakrabarti, U. Divakaran, T. F. Rosenbaum, and D. Sen, Quantum Phase Transi- tions in Transverse Field Spin Models: From Statistical Physics to Quantum Information (Cambridge Univer- sity Press, Cambridge, 2015)

    2015

  4. [4]

    A. K. Chandra, A. Das, and B. K. Chakrabarti, Quan- tum quenching, annealing and computation, Vol. 802 (Springer Science & Business Media, 2010)

    2010

  5. [5]

    Shevchenko, S

    S. Shevchenko, S. Ashhab, and F. Nori, Lan- dau–zener–st¨ uckelberg interferometry, Physics Reports 492, 1 (2010)

    2010

  6. [6]

    L. D. Marin Bukov and A. Polkovnikov, Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to floquet engineering, Ad- vances in Physics 64, 139 (2015)

    2015

  7. [7]

    D’Alessio and A

    L. D’Alessio and A. Polkovnikov, Many-body energy lo- calization transition in periodically driven systems, An- nals of Physics 333, 19 (2013)

    2013

  8. [8]

    D’Alessio, Y

    L. D’Alessio, Y. Kafri, A. Polkovnikov, and M. Rigol, From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics, Advances in Physics 65, 239 (2016)

    2016

Show all 124 references
  1. [9]

    Oka and S

    T. Oka and S. Kitamura, Floquet engineering of quan- tum materials, Annual Review of Condensed Matter Physics 10, 387 (2019)

    2019

  2. [10]

    Blanes, F

    S. Blanes, F. Casas, J. Oteo, and J. Ros, The magnus expansion and some of its applications, Physics Reports 470, 151 (2009)

    2009

  3. [11]

    A. Sen, D. Sen, and K. Sengupta, Analytic approaches to periodically driven closed quantum systems: methods and applications, Journal of Physics: Condensed Matter 33, 443003 (2021)

    2021

  4. [12]

    Banerjee and K

    T. Banerjee and K. Sengupta, Emergent symmetries in prethermal phases of periodically driven quantum sys- tems, Journal of Physics: Condensed Matter 37, 133002 (2025)

    2025

  5. [13]

    Eckardt, Colloquium: Atomic quantum gases in pe- riodically driven optical lattices, Rev

    A. Eckardt, Colloquium: Atomic quantum gases in pe- riodically driven optical lattices, Rev. Mod. Phys. 89, 011004 (2017)

    2017

  6. [14]

    Bloch, J

    I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys. 80, 885 (2008)

    2008

  7. [15]

    D. A. Abanin, E. Altman, I. Bloch, and M. Serbyn, Col- loquium: Many-body localization, thermalization, and entanglement, Rev. Mod. Phys. 91, 021001 (2019)

    2019

  8. [16]

    Sierant, M

    P. Sierant, M. Lewenstein, A. Scardicchio, L. Vidmar, and J. Zakrzewski, Many-body localization in the age of classical computing*, Reports on Progress in Physics 88, 026502 (2025)

    2025

  9. [17]

    Pai and M

    S. Pai and M. Pretko, Dynamical scar states in driven fracton systems, Phys. Rev. Lett. 123, 136401 (2019)

    2019

  10. [18]

    Mukherjee, S

    B. Mukherjee, S. Nandy, A. Sen, D. Sen, and K. Sen- gupta, Collapse and revival of quantum many-body scars via floquet engineering, Phys. Rev. B 101, 245107 (2020)

    2020

  11. [19]

    Mizuta, K

    K. Mizuta, K. Takasan, and N. Kawakami, Exact flo- quet quantum many-body scars under rydberg block- ade, Phys. Rev. Res. 2, 033284 (2020)

    2020

  12. [20]

    Sugiura, T

    S. Sugiura, T. Kuwahara, and K. Saito, Many-body scar state intrinsic to periodically driven system, Phys. Rev. Res. 3, L012010 (2021)

    2021

  13. [21]

    Maskara, A

    N. Maskara, A. A. Michailidis, W. W. Ho, D. Bluvstein, S. Choi, M. D. Lukin, and M. Serbyn, Discrete time- crystalline order enabled by quantum many-body scars: Entanglement steering via periodic driving, Phys. Rev. Lett. 127, 090602 (2021)

    2021

  14. [22]

    Bernien, S

    H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Om- 6 ran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Probing many- body dynamics on a 51-atom quantum simulator, Na- ture 551, 579 (2017)

    2017

  15. [23]

    W. W. Ho, S. Choi, H. Pichler, and M. D. Lukin, Pe- riodic orbits, entanglement, and quantum many-body scars in constrained models: Matrix product state ap- proach, Phys. Rev. Lett. 122, 040603 (2019)

    2019

  16. [24]

    S. Choi, C. J. Turner, H. Pichler, W. W. Ho, A. A. Michailidis, Z. Papi´ c, M. Serbyn, M. D. Lukin, and D. A. Abanin, Emergent su(2) dynamics and perfect quantum many-body scars, Phys. Rev. Lett. 122, 220603 (2019)

    2019

  17. [25]

    Moudgalya, B

    S. Moudgalya, B. A. Bernevig, and N. Regnault, Quan- tum many-body scars and hilbert space fragmentation: a review of exact results, Reports on Progress in Physics 85, 086501 (2022)

    2022

  18. [26]

    Chandran, T

    A. Chandran, T. Iadecola, V. Khemani, and R. Moess- ner, Quantum many-body scars: A quasiparticle per- spective, Annual Review of Condensed Matter Physics 14, 443 (2023)

    2023

  19. [27]

    Scherg, T

    S. Scherg, T. Kohlert, P. Sala, F. Pollmann, B. Hebbe Madhusudhana, I. Bloch, and M. Aidels- burger, Observing non-ergodicity due to kinetic con- straints in tilted fermi-hubbard chains, Nature Commu- nications 12, 4490 (2021)

    2021

  20. [28]

    Kohlert, S

    T. Kohlert, S. Scherg, P. Sala, F. Pollmann, B. Hebbe Madhusudhana, I. Bloch, and M. Aidels- burger, Exploring the regime of fragmentation in strongly tilted fermi-hubbard chains, Phys. Rev. Lett. 130, 010201 (2023)

    2023

  21. [29]

    Ghosh, I

    S. Ghosh, I. Paul, and K. Sengupta, Prethermal frag- mentation in a periodically driven fermionic chain, Phys. Rev. Lett. 130, 120401 (2023)

    2023

  22. [30]

    Ghosh, K

    S. Ghosh, K. Sengupta, and I. Paul, Hilbert space frag- mentation imposed real spectrum of non-hermitian sys- tems, Phys. Rev. B 109, 045145 (2024)

    2024

  23. [31]

    B. Paul, T. Mishra, and K. Sengupta, Floquet realiza- tion of prethermal meissner phase in a two-leg flux lad- der (2025), arXiv:2504.11017 [cond-mat.quant-gas]

    2025 arXiv

  24. [32]

    N. Y. Yao and C. Nayak, Time crystals in periodically driven systems, Physics Today 71, 40 (2018)

    2018

  25. [33]

    D. V. Else, C. Monroe, C. Nayak, and N. Y. Yao, Dis- crete time crystals, Annual Review of Condensed Matter Physics 11, 467 (2020)

    2020

  26. [34]

    M. P. Zaletel, M. Lukin, C. Monroe, C. Nayak, F. Wilczek, and N. Y. Yao, Colloquium: Quantum and classical discrete time crystals, Rev. Mod. Phys. 95, 031001 (2023)

    2023

  27. [35]

    Khemani, R

    V. Khemani, R. Moessner, and S. L. Sondhi, A brief history of time crystals (2019), arXiv:1910.10745 [cond- mat.str-el]

    2019 arXiv

  28. [36]

    Sacha and J

    K. Sacha and J. Zakrzewski, Time crystals: a review, Reports on Progress in Physics 81, 016401 (2017)

    2017

  29. [37]

    Khemani, A

    V. Khemani, A. Lazarides, R. Moessner, and S. L. Sondhi, Phase structure of driven quantum systems, Phys. Rev. Lett. 116, 250401 (2016)

    2016

  30. [38]

    C. W. von Keyserlingk, V. Khemani, and S. L. Sondhi, Absolute stability and spatiotemporal long-range order in floquet systems, Phys. Rev. B 94, 085112 (2016)

    2016

  31. [39]

    Moessner and S

    R. Moessner and S. L. Sondhi, Equilibration and or- der in quantum floquet matter, Nature Physics 13, 424 (2017)

    2017

  32. [40]

    D. V. Else, B. Bauer, and C. Nayak, Floquet time crys- tals, Phys. Rev. Lett. 117, 090402 (2016)

    2016

  33. [41]

    D. V. Else, B. Bauer, and C. Nayak, Prethermal phases of matter protected by time-translation symme- try, Phys. Rev. X 7, 011026 (2017)

    2017

  34. [42]

    N. Y. Yao, A. C. Potter, I.-D. Potirniche, and A. Vish- wanath, Discrete time crystals: Rigidity, criticality, and realizations, Phys. Rev. Lett. 118, 030401 (2017)

    2017

  35. [43]

    M. Heyl, A. Polkovnikov, and S. Kehrein, Dynamical quantum phase transitions in the transverse-field ising model, Phys. Rev. Lett. 110, 135704 (2013)

    2013

  36. [44]

    Heyl, Dynamical quantum phase transitions: a re- view, Reports on Progress in Physics 81, 054001 (2018)

    M. Heyl, Dynamical quantum phase transitions: a re- view, Reports on Progress in Physics 81, 054001 (2018)

    2018

  37. [45]

    Oka and H

    T. Oka and H. Aoki, Photovoltaic hall effect in graphene, Phys. Rev. B 79, 081406 (2009)

    2009

  38. [46]

    Kitagawa, T

    T. Kitagawa, T. Oka, A. Brataas, L. Fu, and E. Demler, Transport properties of nonequilibrium systems under the application of light: Photoinduced quantum hall in- sulators without landau levels, Phys. Rev. B 84, 235108 (2011)

    2011

  39. [47]

    Kundu, H

    A. Kundu, H. A. Fertig, and B. Seradjeh, Effective the- ory of floquet topological transitions, Phys. Rev. Lett. 113, 236803 (2014)

    2014

  40. [48]

    Kitagawa, E

    T. Kitagawa, E. Berg, M. Rudner, and E. Demler, Topo- logical characterization of periodically driven quantum systems, Phys. Rev. B 82, 235114 (2010)

    2010

  41. [49]

    N. H. Lindner, G. Refael, and V. Galitski, Floquet topo- logical insulator in semiconductor quantum wells, Na- ture Physics 7, 490 (2011)

    2011

  42. [50]

    Thakurathi, A

    M. Thakurathi, A. A. Patel, D. Sen, and A. Dutta, Flo- quet generation of majorana end modes and topological invariants, Phys. Rev. B 88, 155133 (2013)

    2013

  43. [51]

    Thakurathi, K

    M. Thakurathi, K. Sengupta, and D. Sen, Majorana edge modes in the kitaev model, Phys. Rev. B 89, 235434 (2014)

    2014

  44. [52]

    Nathan and M

    F. Nathan and M. S. Rudner, Topological singularities and the general classification of floquet–bloch systems, New Journal of Physics 17, 125014 (2015)

    2015

  45. [53]

    Mukherjee, A

    B. Mukherjee, A. Sen, D. Sen, and K. Sengupta, Sig- natures and conditions for phase band crossings in pe- riodically driven integrable systems, Phys. Rev. B 94, 155122 (2016)

    2016

  46. [54]

    Mukherjee, Floquet topological transition by unpo- larized light, Phys

    B. Mukherjee, Floquet topological transition by unpo- larized light, Phys. Rev. B 98, 235112 (2018)

    2018

  47. [55]

    Jangjan and M

    M. Jangjan and M. V. Hosseini, Floquet engineering of topological metal states and hybridization of edge states with bulk states in dimerized two-leg ladders, Scientific Reports 10, 14256 (2020)

    2020

  48. [56]

    Wintersperger, C

    K. Wintersperger, C. Braun, F. N. ¨Unal, A. Eckardt, M. D. Liberto, N. Goldman, I. Bloch, and M. Aidels- burger, Realization of an anomalous floquet topological system with ultracold atoms, Nature Physics 16, 1058 (2020)

    2020

  49. [57]

    M. F. Mart ´ ınez and F. N. ¨Unal, Wave-packet dynam- ics and edge transport in anomalous floquet topological phases, Phys. Rev. A 108, 063314 (2023)

    2023

  50. [58]

    Yang, K.-Y

    X.-X. Yang, K.-Y. Shi, F. N. ¨Unal, and W. Zhang, Anomalous wave-packet transport on boundaries of flo- quet topological systems, Phys. Rev. Res. 7, 023077 (2025)

    2025

  51. [59]

    P. L. Knight, E. Rold´ an, and J. E. Sipe, Quantum walk on the line as an interference phenomenon, Phys. Rev. A 68, 020301 (2003)

    2003

  52. [60]

    Shenvi, J

    N. Shenvi, J. Kempe, and K. B. Whaley, Quantum random-walk search algorithm, Phys. Rev. A67, 052307 7 (2003)

    2003

  53. [61]

    A. M. Childs and J. Goldstone, Spatial search by quan- tum walk, Phys. Rev. A 70, 022314 (2004)

    2004

  54. [62]

    P. K. Pathak and G. S. Agarwal, Quantum random walk of two photons in separable and entangled states, Phys. Rev. A 75, 032351 (2007)

    2007

  55. [63]

    Tulsi, Faster quantum-walk algorithm for the two- dimensional spatial search, Phys

    A. Tulsi, Faster quantum-walk algorithm for the two- dimensional spatial search, Phys. Rev. A 78, 012310 (2008)

    2008

  56. [64]

    A. M. Childs, Universal computation by quantum walk, Phys. Rev. Lett. 102, 180501 (2009)

    2009

  57. [65]

    N. B. Lovett, S. Cooper, M. Everitt, M. Trevers, and V. Kendon, Universal quantum computation using the discrete-time quantum walk, Phys. Rev. A 81, 042330 (2010)

    2010

  58. [66]

    Peruzzo, M

    A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. W¨ orhoff, Y. Bromberg, Y. Silberberg, M. G. Thomp- son, and J. L. OBrien, Quantum walks of correlated photons, Science 329, 1500 (2010)

    2010

  59. [67]

    ˇStefaˇ n´ ak, S

    M. ˇStefaˇ n´ ak, S. M. Barnett, B. Koll´ ar, T. Kiss, and I. Jex, Directional correlations in quantum walks with two particles, New Journal of Physics13, 033029 (2011)

    2011

  60. [68]

    Lahini, M

    Y. Lahini, M. Verbin, S. D. Huber, Y. Bromberg, R. Pu- gatch, and Y. Silberberg, Quantum walk of two inter- acting bosons, Phys. Rev. A 86, 011603 (2012)

    2012

  61. [69]

    A. M. Childs, D. Gosset, and Z. Webb, Universal com- putation by multiparticle quantum walk, Science 339, 791 (2013)

    2013

  62. [70]

    Qiang, T

    X. Qiang, T. Loke, A. Montanaro, K. Aungskunsiri, X. Zhou, J. L. O’Brien, J. B. Wang, and J. C. F. Matthews, Efficient quantum walk on a quantum pro- cessor, Nature Communications 7, 11511 (2016)

    2016

  63. [71]

    Rigovacca and C

    L. Rigovacca and C. Di Franco, Two-walker discrete- time quantum walks on the line with percolation, Sci- entific Reports 6, 22052 (2016)

    2016

  64. [72]

    Caruso, Universally optimal noisy quantum walks on complex networks, New Journal of Physics 16, 055015 (2014)

    F. Caruso, Universally optimal noisy quantum walks on complex networks, New Journal of Physics 16, 055015 (2014)

    2014

  65. [73]

    P. M. Preiss, R. Ma, M. E. Tai, A. Lukin, M. Rispoli, P. Zupancic, Y. Lahini, R. Islam, and M. Greiner, Strongly correlated quantum walks in optical lattices, Science 347, 1229 (2015)

    2015

  66. [74]

    Chattaraj and R

    T. Chattaraj and R. V. Krems, Effects of long-range hopping and interactions on quantum walks in ordered and disordered lattices, Phys. Rev. A94, 023601 (2016)

    2016

  67. [75]

    P. C. S. Costa, F. de Melo, and R. Portugal, Multiparti- cle quantum walk with a gaslike interaction, Phys. Rev. A 100, 042320 (2019)

    2019

  68. [76]

    Mondal and T

    S. Mondal and T. Mishra, Quantum walks of interact- ing mott-insulator defects with three-body interactions, Phys. Rev. A 101, 052341 (2020)

    2020

  69. [77]

    Yan, Y.-R

    Z. Yan, Y.-R. Zhang, M. Gong, Y. Wu, Y. Zheng, S. Li, C. Wang, F. Liang, J. Lin, Y. Xu, et al., Strongly corre- lated quantum walks with a 12-qubit superconducting processor, Science 364, 753 (2019)

    2019

  70. [78]

    M. Gong, S. Wang, C. Zha, M.-C. Chen, H.-L. Huang, Y. Wu, Q. Zhu, Y. Zhao, S. Li, S. Guo, et al., Quantum walks on a programmable two-dimensional 62-qubit su- perconducting processor, Science 372, 948 (2021)

    2021

  71. [79]

    M. K. Giri, S. Mondal, B. P. Das, and T. Mishra, Two component quantum walk in one-dimensional lattice with hopping imbalance, Scientific Reports 11, 22056 (2021)

    2021

  72. [80]

    X. Cai, H. Yang, H.-L. Shi, C. Lee, N. Andrei, and X.- W. Guan, Multiparticle quantum walks and fisher in- formation in one-dimensional lattices, Phys. Rev. Lett. 127, 100406 (2021)

    2021

  73. [81]

    M. K. Giri, S. Mondal, B. P. Das, and T. Mishra, Sig- natures of nontrivial pairing in the quantum walk of two-component bosons, Phys. Rev. Lett. 129, 050601 (2022)

    2022

  74. [82]

    Ostahie, D

    B. Ostahie, D. Sticlet, C. u. u. u. u. P. m. c. Moca, B. D´ ora, M. A. Werner, J. K. Asb´ oth, and G. Zar´ and, Multiparticle quantum walk: A dynamical probe of topological many-body excitations, Phys. Rev. B 108, 035126 (2023)

    2023

  75. [83]

    M. K. Giri, B. Paul, and T. Mishra, Flux-induced reen- trant dynamics in the quantum walk of interacting bosons, Phys. Rev. A 108, 063319 (2023)

    2023

  76. [84]

    M. K. Giri, B. Paul, and T. Mishra, Flux-enhanced lo- calization and reentrant delocalization in the quench dynamics of two interacting bosons on a bose-hubbard ladder, Phys. Rev. A 109, 043308 (2024)

    2024

  77. [85]

    Paul and T

    B. Paul and T. Mishra, Realizing nontrivial doublon for- mation using a quantum computer, Phys. Rev. B 110, L020302 (2024)

    2024

  78. [86]

    Maity, B

    S. Maity, B. Paul, S. P. Sharma, and T. Mishra, Dy- namics of interacting particles on a rhombus chain: Aharonov-bohm caging and inverse anderson transition (2024), arXiv:2409.05853 [cond-mat.quant-gas]

    2024 arXiv

  79. [87]

    T. Chen, C. Huang, B. Gadway, and J. P. Covey, Quan- tum walks and correlated dynamics in an interacting synthetic rydberg lattice, Phys. Rev. Lett. 133, 120604 (2024)

    2024

  80. [88]

    Camacho, J

    G. Camacho, J. Meinecke, and J. Wolters, Quantum walk on a square lattice with identical particles, Phys. Rev. A 111, 052416 (2025)

    2025

  81. [89]

    Qiang, S

    X. Qiang, S. Ma, and H. Song, Quantum walk comput- ing: Theory, implementation, and application, Intelli- gent Computing 3, 0097 (2024)

    2024

  82. [90]

    Bethe, Zur theorie der metalle, Zeitschrift f¨ ur Physik 71, 205 (1931)

    H. Bethe, Zur theorie der metalle, Zeitschrift f¨ ur Physik 71, 205 (1931)

    1931

  83. [91]

    Hubbard and B

    J. Hubbard and B. H. Flowers, Electron correlations in narrow energy bands, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sci- ences 276, 238 (1963)

    1963

  84. [92]

    C. N. Yang, η pairing and off-diagonal long-range order in a hubbard model, Phys. Rev. Lett. 63, 2144 (1989)

    1989

  85. [93]

    Silberglitt and J

    R. Silberglitt and J. B. Torrance, Effect of single-ion anisotropy on two-spin-wave bound state in a heisenberg ferromagnet, Phys. Rev. B 2, 772 (1970)

    1970

  86. [94]

    T. Tonegawa, Two-Magnon Bound States in the Heisen- berg Ferromagnet with Anisotropic Exchange and Uni- axial Anisotropy Energies*), Progress of Theoretical Physics Supplement 46, 61 (1970)

    1970

  87. [95]

    Winkler, G

    K. Winkler, G. Thalhammer, F. Lang, R. Grimm, J. Hecker Denschlag, A. J. Daley, A. Kantian, H. P. B¨ uchler, and P. Zoller, Repulsively bound atom pairs in an optical lattice, Nature 441, 853 (2006)

    2006

  88. [96]

    Wang, C.-M

    Z. Wang, C.-M. Halati, J.-S. Bernier, A. Ponomaryov, D. I. Gorbunov, S. Niesen, O. Breunig, J. M. Klopf, S. Zvyagin, T. Lorenz, A. Loidl, and C. Kollath, Ex- perimental observation of repulsively bound magnons, Nature 631, 760 (2024)

    2024

  89. [97]

    Ganahl, E

    M. Ganahl, E. Rabel, F. H. L. Essler, and H. G. Ev- ertz, Observation of complex bound states in the spin- 1/2 heisenberg xxz chain using local quantum quenches, 8 Phys. Rev. Lett. 108, 077206 (2012)

    2012

  90. [98]

    Fukuhara, P

    T. Fukuhara, P. Schauß, M. Endres, S. Hild, M. Che- neau, I. Bloch, and C. Gross, Microscopic observation of magnon bound states and their dynamics, Nature 502, 76 (2013)

    2013

  91. [99]

    Corrielli, A

    G. Corrielli, A. Crespi, G. Della Valle, S. Longhi, and R. Osellame, Fractional bloch oscillations in photonic lattices, Nature Communications 4, 1555 (2013)

    2013

  92. [101]

    Morvan, T

    A. Morvan, T. I. Andersen, X. Mi, C. Neill, A. Petukhov, K. Kechedzhi, D. A. Abanin, A. Michai- lidis, R. Acharya, F. Arute, et al., Formation of robust bound states of interacting microwave photons, Nature 612, 240 (2022)

    2022

  93. [102]

    F. M. Surace and O. Motrunich, Robustness and even- tual slow decay of bound states of interacting microwave photons in the google quantum ai experiment, PRX Quantum 5, 010317 (2024)

    2024

  94. [103]

    Hudomal, R

    A. Hudomal, R. Smith, A. Hallam, and Z. Papi´ c, In- tegrability breaking and bound states in google’s deco- rated xxz circuits, PRX Quantum 5, 010316 (2024)

    2024

  95. [104]

    Holstein and H

    T. Holstein and H. Primakoff, Field dependence of the intrinsic domain magnetization of a ferromagnet, Phys. Rev. 58, 1098 (1940)

    1940

  96. [105]

    J. M. Koh, T. Tai, Y. H. Phee, W. E. Ng, and C. H. Lee, Stabilizing multiple topological fermions on a quantum computer, npj Quantum Information 8, 16 (2022)

    2022

  97. [106]

    Huang, P

    Y. Huang, P. Hosur, and H. K. Pal, Quasi-flat-band physics in a two-leg ladder model and its relation to magic-angle twisted bilayer graphene, Phys. Rev. B 102, 155429 (2020)

    2020

  98. [107]

    Park and J.-W

    J.-H. Park and J.-W. Rhim, Quasi-localization and wan- nier obstruction in partially flat bands, Communications Physics 7, 179 (2024)

    2024

  99. [108]

    G. A. Dom ´ ınguez-Castro and R. Paredes, The aubry–andr´ e model as a hobbyhorse for understand- ing the localization phenomenon, European Journal of Physics 40, 045403 (2019)

    2019

  100. [109]

    Kranzl, S

    F. Kranzl, S. Birnkammer, M. K. Joshi, A. Bastianello, R. Blatt, M. Knap, and C. F. Roos, Observation of magnon bound states in the long-range, anisotropic heisenberg model, Phys. Rev. X 13, 031017 (2023)

    2023

  101. [110]

    L. M. Sieberer, T. Olsacher, A. Elben, M. Heyl, P. Hauke, F. Haake, and P. Zoller, Digital quantum sim- ulation, trotter errors, and quantum chaos of the kicked top, npj Quantum Information 5, 78 (2019)

    2019

  102. [111]

    M. Heyl, P. Hauke, and P. Zoller, Quantum localization bounds trotter errors in digital quantum simulation, Sci- ence Advances 5, eaau8342 (2019)

    2019

  103. [112]

    Smith, M

    A. Smith, M. S. Kim, F. Pollmann, and J. Knolle, Simu- lating quantum many-body dynamics on a current dig- ital quantum computer, npj Quantum Information 5, 106 (2019)

    2019

  104. [113]

    Vatan and C

    F. Vatan and C. Williams, Optimal quantum circuits for general two-qubit gates, Phys. Rev. A 69, 032315 (2004)

    2004

  105. [114]

    Jones and S

    T. Jones and S. C. Benjamin, Robust quantum compi- lation and circuit optimisation via energy minimisation, Quantum 6, 628 (2022)

    2022

  106. [115]

    Khatri, R

    S. Khatri, R. LaRose, A. Poremba, L. Cincio, A. T. Sornborger, and P. J. Coles, Quantum-assisted quantum compiling, Quantum 3, 140 (2019)

    2019

  107. [116]

    K. Heya, Y. Suzuki, Y. Nakamura, and K. Fu- jii, Variational quantum gate optimization, (2018), arXiv:1810.12745 [quant-ph]

    2018 arXiv

  108. [117]

    Gray, quimb: A python package for quantum infor- mation and many-body calculations, Journal of Open Source Software, 3(29), 819 10.21105/joss.00819 (2018)

    J. Gray, quimb: A python package for quantum infor- mation and many-body calculations, Journal of Open Source Software, 3(29), 819 10.21105/joss.00819 (2018)

    2018 doi

  109. [118]

    Li and S

    Y. Li and S. C. Benjamin, Efficient variational quan- tum simulator incorporating active error minimization, Phys. Rev. X 7, 021050 (2017)

    2017

  110. [119]

    Temme, S

    K. Temme, S. Bravyi, and J. M. Gambetta, Error mit- igation for short-depth quantum circuits, Phys. Rev. Lett. 119, 180509 (2017)

    2017

  111. [120]

    LaRose, A

    R. LaRose, A. Mari, S. Kaiser, P. J. Karalekas, A. A. Alves, P. Czarnik, M. El Mandouh, M. H. Gordon, Y. Hindy, A. Robertson, et al., Mitiq: A software pack- age for error mitigation on noisy quantum computers, Quantum 6, 774 (2022)

    2022

  112. [121]

    Kandala, K

    A. Kandala, K. Temme, A. D. C´ orcoles, A. Mezzacapo, J. M. Chow, and J. M. Gambetta, Error mitigation ex- tends the computational reach of a noisy quantum pro- cessor, Nature 567, 491 (2019)

    2019

  113. [122]

    Anomalous slow-down of the bound state dynamics in a non-locally coupled quantum circuit

    M. Takahashi, Half-filled hubbard model at low tem- perature, Journal of Physics C: Solid State Physics 10, 1289 (1977). 9 Supplementary materials for “Anomalous slow-down of the bound state dynamics in a non-locally coupled quantum circuit” In this supplementary material, we ...

    1977

  114. [123]

    E0 = 2Jz, possible only when three excitations re- side at adjacent sites, and therefore correspond to the eigenstate |E(j) 0 ⟩ = |j, j + 1, j + 2⟩

  115. [124]

    Therefore, corresponding states are |E(j1j2) 1 ⟩ = |j1, j1 + 1, j2⟩, where j2 ̸= j1 − 1, j2 ̸= j1 + 2

    E1 = Jz, only two excitations at adjacent sites are possible. Therefore, corresponding states are |E(j1j2) 1 ⟩ = |j1, j1 + 1, j2⟩, where j2 ̸= j1 − 1, j2 ̸= j1 + 2

  116. [125]

    Therefore the eigenstates are |E(j1j2j3) 2 ⟩ = |j1, j2, j3⟩, where j1 ̸= j2 ± 1, j1 ̸= j3 ± 1 and j3 ̸= j2 ± 1

    E2 = 0, existaions at NN sites are prohab- ited. Therefore the eigenstates are |E(j1j2j3) 2 ⟩ = |j1, j2, j3⟩, where j1 ̸= j2 ± 1, j1 ̸= j3 ± 1 and j3 ̸= j2 ± 1. The projection operator to the three-excitation bound state subspace, P0 = X j |E(j) 0 ⟩⟨E(j) 0 |, (20) 13 and the p...

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