Quantum dynamics of a spin model with an extensive degeneracy

Diptiman Sen; Krishanu Ghosh; K. Sengupta

REVIEW 3 major objections 5 minor 63 references

Quantum dynamics of a spin model with an extensive degeneracy

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

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Passage through an extensively degenerate point deletes Kibble-Zurek scaling and creates an emergent U(1) symmetry.

desk verdict The Floquet section is analytically solid and worth refereeing; the ramp section has a clean finite-size result but its exponential-gap explanation does not match the observed crossover scale, so the thermodynamic-limit claim needs repair or scaling back. read the letter →

arxiv 2502.07609 v1 pith:XK3QHCBY submitted 2025-02-11 quant-ph cond-mat.str-el

Krishanu Ghosh , Diptiman Sen , K. Sengupta This is my paper · ORCID

classification quant-phcond-mat.str-el

keywords extensivedegeneracyKibble-ZurekscalingLandau-ZenercrossoverFloquetHamiltonianemergentU(1)symmetryStückelbergoscillationsRydbergatomchaindynamicrestoration

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 argues that a one-dimensional spin model with an exponentially large degenerate manifold at $h=0$ behaves differently under ramps and periodic drives than systems with a quantum critical point. For a linear ramp through the degenerate point, the residual energy $Q(\tau)$ is independent of system size and switches directly from Landau-Zener scaling ($Q\sim\tau^{-2}$) at slow ramps to a plateau at fast ramps, with no Kibble-Zurek regime. A double passage through the degenerate point suppresses Stückelberg oscillations because the dynamics averages over exponentially many relative phases. Under square-pulse driving at frequencies $\omega_D = h_0/(p\hbar)$, the first-order Floquet Hamiltonian acquires an approximate $U(1)$ symmetry that pins certain correlators to zero and restores symmetry from symmetry-broken initial states up to a prethermal timescale. The results matter because they identify extensive degeneracy itself as a distinct dynamical mechanism, with proposed tests in Rydberg atom chains.

What carries the argument

The load-bearing object is the extensively degenerate ground-state manifold at $h=0$, whose size $N(L)=\varphi^L+(-1/\varphi)^L$ grows exponentially, so a wave function passing through the point acquires overlap with an exponentially large set of states and the many-body gaps become exponentially small. This explains the ramp phenomenology: the state spreads so strongly that $Q(\tau)$ saturates into a plateau and loses its dependence on $L$, eliminating the Kibble-Zurek scaling window. For the driven system, the machinery is first-order Floquet perturbation theory for a square pulse: at $h_0 T=2\pi p$, the first-order Floquet Hamiltonian $H_F^{(1)}$ reduces to a $U(1)$-symmetric XY chain commuting with $\sum_j\sigma^x_j$. The third-order Floquet correction breaks this symmetry, so the symmetry is approximate but still controls the dynamics up to a long prethermal timescale.

What would settle it

Simulate the same ramp on larger systems (e.g., $L=18,20$) or with different boundary conditions, and look at $Q(\tau)/(V_0L)$ versus $\hbar/(\tau V_0)$: if an intermediate $\tau^{-1}$ Kibble-Zurek regime appears as $L$ grows, or if the plateau moves with $L$, the no-Kibble-Zurek claim fails. For the drive, measure $\Delta C(mT)$ at $\omega_D=h_0/\hbar$ on a longer chain or for longer times than studied; if $\Delta C$ drifts away from zero before the expected prethermal time scale, the emergent symmetry is not in control.

Watch

Extended reading notes

Core claim

The paper's central discovery is that an extensively degenerate point acts as a qualitatively different dynamical object from a quantum critical point. The degenerate manifold at $h=0$ consists of all Fock states with no two neighboring up spins, and its number grows as $N(L)=\varphi^L+(-1/\varphi)^L$ with $\varphi$ the golden ratio. Passing through this point spreads the wave function over an exponentially large number of near-degenerate eigenstates with typical gaps $\sim e^{-L}$, so for the ramp $h(t)=h_0(2t/\tau-1)$ the residual energy obeys $Q(\tau)/(V_0 L)$ independent of $L$, showing a direct crossover between a Landau-Zener regime $Q\sim\tau^{-2}$ and a plateau, and never Kibble-Zurek scaling. For the square-pulse drive, Floquet perturbation theory gives $H_F^{(1)} = (V_0/4)\sum_j [1+\tfrac12(\sigma^z_j\sigma^z_{j+1}+\sigma^y_j\sigma^y_{j+1})]$ at $\omega_D=h_0/(p\hbar)$, a $U(1)$-symmetric XY Hamiltonian commuting with $\sum_j\sigma^x_j$; the third-order term breaks this symmetry, making it approximate. The paper demonstrates numerically that correlators $\Delta C=\langle C_{zz}-C_{yy}\rangle$ remain pinned to zero and that symmetry-broken initial states undergo dynamic symmetry restoration at these frequencies.

Load-bearing premise

The load-bearing premise is that behavior seen in exact diagonalization on chains up to $L=16$ persists in the thermodynamic limit and that the first-order Floquet Hamiltonian controls the dynamics over the observed timescales, assumptions validated only numerically.

Editorial extensions

If this is right

A slow ramp through an extensively degenerate point leaves the system with a residual energy that is independent of system size and falls as $Q\sim\tau^{-2}$ until a plateau sets in, so adiabaticity is never restored in a Kibble-Zurek manner.
Double passage through the degenerate point suppresses Stückelberg oscillations in the residual energy, because the return amplitude averages over an exponentially large number of relative phases.
At drive frequencies $\omega_D=h_0/(p\hbar)$ with $h_0\gg V_0$, the stroboscopic dynamics is governed by an approximate $U(1)$-symmetric Hamiltonian, so the correlator $\Delta C=\langle C_{zz}-C_{yy}\rangle$ remains at zero for symmetric initial states.
Starting from an initial state that breaks the emergent $U(1)$, the long-time value of $\Delta C$ vanishes at these special frequencies, demonstrating dynamic symmetry restoration.
Reducing the drive amplitude makes higher-order Floquet terms break the symmetry and $\Delta C$ deviates from zero, providing a diagnostic of the approximation's breakdown.

Reading between the lines

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

Inference: any model with an exponentially large degenerate manifold at an isolated parameter value, not just this spin chain, should show the same $L$-independent ramp plateau, making the ramp protocol a general probe of constraint-induced degeneracy.
Inference: the special frequencies $\omega_D=h_0/(p\hbar)$ act as a form of dynamical localization in the interaction picture, so a direct two-point correlation measurement in a Rydberg chain should see $\Delta C$ dip sharply to zero at every integer $p$.
Inference: the finite-size crossover between plateau and Landau-Zener scaling should occur at a ramp time set by the exponentially small typical gap, roughly $\tau\sim e^{L}$; checking this scaling with larger $L$ would either confirm or falsify the thermodynamic-limit claim.
Inference: the third-order Floquet correction's noncommuting terms suggest that at longer times or lower amplitude the correlator should recover a nonzero value, and the crossover time as a function of $V_0/h_0$ could be extracted and compared with a prethermal estimate.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Here is my take. The genuinely new piece is the Floquet analysis: for the square-pulse drive at h0 = p*hbar*omega_D, the first-order Floquet Hamiltonian is an XY-type model with an emergent U(1) symmetry, the second-order term vanishes, and the third-order symmetry-breaking term is exhibited explicitly. That is real, checkable perturbation theory, and the numerics for L up to 18 showing Delta C pinned near zero and dynamic symmetry restoration support it. That section deserves a serious referee and should survive with modest revision.

The ramp section is the soft spot, and I think the stress-test note lands. The data collapse of Q(tau)/(V0 L) for L = 10-16 and the direct crossover from a tau^-2 scaling to a plateau are clean and worth reporting. But the paper's explanation via "typical gaps ~ e^{-L}" does not survive contact with the data. At h = 0 the degeneracy is exact; there are not exponentially small gaps, and a Landau-Zener estimate with Delta ~ e^{-L} would put the crossover at tau ~ e^{2L}, not at tau ~ 100. The observed crossover implies O(V0) energy scales. So the mechanism text in Sec. III needs to be rewritten, and with it the claim that the absence of Kibble-Zurek scaling is established for L to infinity. What is actually shown is a finite-size statement for L <= 16; that is valuable but should be labeled as such.

There is also a plain ambiguity: Sec. III says Q(tau) is independent of L, while Fig. 3 plots Q(tau)/(V0 L) and the collapse means Q scales with L. That needs fixing.

The comparison with PXP and the Stuckelberg suppression is suggestive but likewise rests on ED at L = 16; the "decoherence by many phases" argument is heuristic. I would not block publication on that, but I would want it framed as a finite-size observation plus heuristic.

Bottom line: the paper is honest and self-contained, and the Floquet part is analytically solid. The ramp part has a central explanation that appears inconsistent with its own data; the empirical ramp claim may still be right, but the authors need to either supply a controlled argument for the thermodynamic limit or scale back the claim. I would send it to peer review, because a good referee will catch exactly this and the paper is otherwise worth engaging with. No code or data is a minor inconvenience, not a fatal flaw.

Referee Report

3 major / 5 minor

Summary. The paper studies a one-dimensional spin chain (a nearest-neighbor Rydberg model) whose spectrum has an extensively degenerate manifold at h=0, with N≈φ^L zero-energy eigenstates. For a linear ramp through h=0 the authors compute fidelity F(t) and residual energy Q(t) by exact diagonalization for L≤16 and report that Q(τ)/(V0L) is L-independent and crosses directly from Landau-Zener τ^{-2} scaling to a plateau, with no Kibble-Zurek regime; for a double passage they report strong suppression of Stückelberg oscillations. For periodic square-pulse driving they compute the first-order Floquet Hamiltonian H_F^(1), show H_F^(2)=0, and show that at ω_D=h0/(pℏ) H_F^(1) has an emergent U(1) symmetry, while H_F^(3) breaks it; numerically, certain correlators remain zero or relax to zero at the special frequencies in the high-amplitude regime, which they call dynamic symmetry restoration. They propose a Rydberg-atom experiment to test the ramp predictions.

Significance. If substantiated, the ramp results would establish a qualitatively new dynamical signature of extensive degeneracy: unlike a quantum critical point, the degenerate manifold would eliminate Kibble-Zurek scaling and suppress Stückelberg oscillations. The Floquet section is the strongest part: H_F^(1) is derived by explicit integration, the vanishing of H_F^(2) is proven, and the symmetry-breaking H_F^(3) is exhibited, with an exact oddness-in-V0 argument that explains the structure. The numerical comparisons with the PXP critical-point model and the concrete Rydberg measurement proposal are useful. However, the thermodynamic-limit ramp claims currently rest on L≤16 ED and on a gap heuristic that is inconsistent with the data, so the significance of the ramp section is not yet established. The Floquet symmetry-restoration claim is credible but its 'prethermal' timescale is not quantified.

major comments (3)

[Sec. III, Eq. (2) and Fig. 3 left] The heuristic used to explain the absence of Kibble-Zurek scaling is quantitatively inconsistent with the data. The text states that at the degenerate point the wave function spreads over N≈φ^L states and that these have a typical gap Δε∼e^{-L}. Landau-Zener scaling then locates the nonadiabatic crossover at τ*∼(ℏ/Δ)^2. With N≈φ^L and Δ∼1/N, τ*∼φ^{2L}≈5×10^6 for L=16; with the text's e^{-L} estimate, τ*∼8×10^13. The data in Fig. 3 left show the crossover between the τ^{-2} regime and the plateau at ℏ/(τV0)≈0.01, i.e., τ≈100, corresponding to gaps of order 0.1V0. The mechanism invoked therefore does not explain the observed crossover scale and predicts a strong L dependence that is not seen. This needs a corrected computation of the instantaneous gap, or a different explanation of the crossover, since it is the only analytic support for the no-Kibble-Zurek claim.
[Sec. III, paragraph after Fig. 3] The assertion that Q(τ) is independent of L and that there is a direct crossover to a plateau with no Kibble-Zurek regime is stated as a thermodynamic-limit conclusion. The support, however, is the collapse of curves for L=10, 12, 14, and 16 in the left panel of Fig. 3, with no scaling analysis in L and no controlled extrapolation. In critical systems a Kibble-Zurek regime can appear at τ∼L^2, so collapse over an L-range of 10–16 does not by itself rule out such a regime. Because the gap heuristic of Sec. III is inconsistent with the observed crossover scale, the finite-size collapse cannot be interpreted via the degenerate manifold either. Please provide an analytic or numerically controlled statement about the thermodynamic limit, or explicitly restrict the no-Kibble-Zurek claim to the finite sizes studied.
[Sec. IV B and Sec. V] The claim that the emergent U(1) symmetry controls correlators 'up to a very large prethermal timescale' is not quantified. The numerical evidence is limited to L≤16 and m up to about 4×10^4 (Figs. 6 and 7), and the only analytic result is the first-order Floquet Hamiltonian; H_F^(3) is shown to break the symmetry but no bound on its effect is given. Please state the expected prethermal time, for example as a function of h0/V0, or explicitly describe the symmetry-controlled regime as a finite-time numerical observation.

minor comments (5)

[Appendix, Eq. (A.48)] As written, H_F(−V0)=−H_F(−V0) is inconsistent; it should presumably read H_F(−V0)=−H_F(V0).
[Sec. III and Fig. 3 caption] The text says Q(τ) is independent of L, but the plotted quantity is Q(τ)/(V0L); please state unambiguously that the L-independence applies to the normalized residual energy.
[Fig. 3 left] The fit Q∼a/τ^b with a=14.01 and b=2.04 needs the fitted τ range, the units (presumably ℏ=1), and uncertainties; otherwise the claimed plateau/power-law crossover cannot be assessed.
[Sec. I] The sentence 'This is followed by Sec. III where we discuss the ramp dynamics of the followed' is incomplete and should be corrected.
[Sec. IV B] The phrase 'spacial drive frequency' should read 'special drive frequency'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the Floquet Hamiltonian is obtained by explicit integration and the ramp scaling is extracted from numerics against external benchmarks; self-citations are contextual, not load-bearing.

full rationale

The paper's central derivations are self-contained rather than circular. The ramp claim that Q(τ)/(V0L) is independent of L with a direct crossover from Landau-Zener scaling to a plateau is presented as an exact-diagonalization result (Fig. 3) with a fitted power law Q(τ) ∼ a/τ^b; the exponent b=2.04 is extracted from the data, not imposed as an input, and no equation defines Q in terms of the claimed scaling. The explanatory heuristic about exponentially small instantaneous gaps and the absence of Kibble-Zurek scaling is an interpretation, and its possible lack of control for L→∞ is a correctness risk, not a circular reduction. The Floquet part is also non-circular: H_F^(1) in Eq. (18) follows from the explicit first-order integral in Eq. (13), H_F^(2)=0 is proven from the time-ordering identities in the Appendix, and H_F^(3) is computed explicitly and shown to break the special-frequency U(1) symmetry. The emergent symmetry is therefore a derived consequence of the perturbation theory, and the numerical correlator behavior independently verifies it. Citations to the authors' previous work (e.g., Refs. [19], [24-26], [57-59]) supply standard Floquet perturbation theory, Kibble-Zurek scaling, and PXP critical-point benchmarks; they are used as context and external comparisons, not as unverified inputs that force the conclusions. No uniqueness theorem, ansatz, or fitted parameter is imported from a self-citation to define the target results. Hence no circular step can be exhibited.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The paper's central claims rest on standard Floquet and Landau-Zener/Kibble-Zurek machinery plus a finite-size ED extrapolation. The main fitted quantity is the numerical scaling exponent for Q(τ). No new physical entities are postulated.

free parameters (2)

fit exponent b for Q(τ) = 2.04
Power-law fit to Q(τ)/(V0L) vs 1/τ in Fig. 3, used to claim Landau-Zener scaling Q ~ τ^{-2}; the theoretical exponent 2 is not derived for this model.
fit prefactor a for Q(τ) = 14.01
Fitted amplitude in Q(τ) ~ a/τ^b from the same Fig. 3 fit, in units of V0.

assumptions (4)

domain assumption Floquet perturbation theory to first order is valid when drive amplitude and frequency are much larger than the interaction strength V0.
Invoked in Sec. IV A and the Appendix; if V0 is comparable to h0 or ω, H_F^(1) does not control the dynamics.
standard math The degenerate manifold at h = 0 consists of the φ^L Fock states with no adjacent up-spins, which are exactly zero-energy eigenstates of H1.
Sec. II, transfer matrix count Eq. (2); serves as the premise for the ramp dynamics.
standard math Kibble-Zurek and Landau-Zener scaling formulas apply to the finite-size comparisons.
Sec. III, used to interpret Q(τ) versus τ for both the degenerate model and the PXP model.
ad hoc to paper Finite-size exact diagonalization up to L = 16 captures the thermodynamic-limit behavior.
Sec. III, Fig. 2 and Fig. 3: the absence of Kibble-Zurek scaling and the L-independent Q(τ)/(V0L) are inferred from L ≤ 16 data without a controlled extrapolation.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Quantum dynamics of a spin model with an extensive degeneracy." pith.science (2026). https://pith.science/paper/XK3QHCBY

@misc{pith2026250207609,
  author       = {Pith},
  title        = {Pith review of: Quantum dynamics of a spin model with an extensive degeneracy},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XK3QHCBY}},
  note         = {Machine review of arXiv:2502.07609}
}

abstract

We study the role played by extensive degeneracy in shaping the nature of the quantum dynamics of a one-dimensional spin model for both ramp and periodic drive protocols. The model displays an extensive degenerate manifold of states for a specific value of one of the parameters of its Hamiltonian. We study a linear ramp which takes the spin model through this degenerate point and show that it leads to a deviation from the usual Kibble-Zurek behavior. We also study the St\"uckelberg oscillations in such a model for a ramp which passes twice through the degenerate point. Our study indicates that such oscillations are strongly suppressed leading to a distinct behavior compared to those arising from double passage through a quantum critical point. Finally, we study the periodic dynamics of the model and show, for a large drive amplitude, the existence of special drive frequencies at which the system exhibits an approximate emergent $U(1)$ symmetry. We study the effect of this emergent symmetry on the correlators of the driven system and demonstrate the existence of dynamic symmetry restoration at these frequencies. We study the fate of the emergent symmetry when the drive amplitude is decreased and discuss possible experiments to test our theory.

Figures

Figures reproduced from arXiv: 2502.07609 by the authors.

**Figure 2.** FIG. 2. Top left panel: Plot of [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** FIG. 3. Left panel: Plot of [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 5.** Figure 5: where the absence of such oscillations can be seen; the right panel shows an analogous plot for H′ where the system is ramped twice through the critical point by appropriate variation of λ(t) given by λ(t) = λc + λ0 cos(2πt/τ ), 0 ≤ t ≤ τ. (10) In this case, Q(t) shows…

**Figure 6.** Figure 6: FIG. 6. Top panel: Plot of ∆ [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]

**Figure 7.** Figure 7: FIG. 7. Top panel: Plot of ∆ [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

63 extracted references · 48 canonical work pages

[1]

and spin liquids [2]. For fractional quantum Hall sys- tems, a strong magnetic field in the kinetic term of the Hamiltonian of non-interacting electrons leads to an ex- tensive degeneracy; the mechanism of the lifting of this degeneracy by Coulomb interactions between the elec- trons is central to the realization of fractional quantum Hall states hosting ...

work page Pith review arXiv 2025
[2]

, (A.18) which is precisely cnm according to Eq. (A.15). Hence cmn = cnm. (A.19) We can prove another identity. From Eq. (A.15), we find that cmn + cnm = Z T 0 dt1 Z T 0 dt2 fm(t1) fn(t2), (A.20) where there is now no ordering of t1, t2 on the right hand side; so we just have two separate integrals. Doing the integrals explicitly and using Eq. (A.19), we ...

work page
[3]

We find that for large drive amplitudes, where H (1) F controls the dy- namics, ∆C remains pinned to zero as expected from the presence of the emergent symmetry. In contrast, for lower drive amplitudes, where higher order terms in HF which do not respect this symmetry become important, 7 0 20×103 40×103 0 0.4 0 500 1000 -0.5 0 0.5 1 m ΔC 0 20×103 40×103 0...

work page 2020
[4]

In contrast to the ramp studied earlier where the system passes through the degenerate point only once, these features depend sensitively on τ

We find that the second passage through the degener- ate points leads to an enhancement of F and a reduction of Q. In contrast to the ramp studied earlier where the system passes through the degenerate point only once, these features depend sensitively on τ . For smaller val- ues of τ , both F (τ ) and Q(τ ) are found to attain values much closer to zero ...

work page
[5]

See, for example, H. L. Stormer, D. C. Tsui, and A. C. Gossard, Rev. Mod. Phys. 71, S298 (1999)

work page 1999
[6]

Kivelson and S

See, for example, S. Kivelson and S. L. Sondhi, Nature Rev. Phys. 5, 368 (2023)

work page 2023
[7]

R. B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983)

1983
[8]

J. K. Jain, Phys. Rev. Lett. 63, 199 (1989)

1989

Show all 63 references

[9]

Y. Zhou, K. Kanoda, and T.-K. Ng, Rev. Mod. Phys. 89, 025003 (2017); L. Savary and L. Balents, Rep. Prog. Phys. 80, 016502 (2017)

2017
[10]

Villain, R

J. Villain, R. Bidaux, J. P. Carton, and R. Conte, J. 12 Phys. 41, 1263 (1980); E. F. Shender, JETP 56, 178 (1982); E. F. Shender and P. C. W. Holdsworth,Order by Disorder and Topology in Frustrated Magnetic Systems , Pg 259-279 (Springer US, New York, 1996)

1980
[11]

J. T. Chalker, P. C. W. Holdsworth and E. F. Shender, Phys. Rev. Lett. 68, 855 (1992); C. L. Henley, Phys. Rev. Lett. 62, 2056 (1989)

1992
[12]

J. M. Hopkinson, S. V. Isakov, H.-Y. Kee, and Y. B. Kim, Phys. Rev. Lett. 99, 037201 (2007); M. Sarkar, M. Pal, A. Sen, and K. Sengupta, SciPost Phys. 14, 004 (2023)

2007
[13]

Dziarmaga, Adv

J. Dziarmaga, Adv. Phys. 59, 1063 (2010)

2010
[14]

Polkovnikov, K

A. Polkovnikov, K. Sengupta, A. Silva, and M. Vengalat- tore, Rev. Mod. Phys. 83, 863 (2011)

2011
[15]

Dutta, G

A. Dutta, G. Aeppli, B. K. Chakrabarti, U. Divakaran, T. F. Rosenbaum, and D. Sen, Quantum phase tran- sitions in transverse field spin models: from statistical physics to quantum information , (Cambridge University Press, Cambridge, 2015); Quantum Quenching, Anneal- ing and C...

2015
[16]

S. N. Shevchenko, S. Ashhab, and F. Nori, Physics Re- ports 492, 1 (2010)

2010
[17]

Bukov, L

M. Bukov, L. D’Alessio, and A. Polkovnikov, Adv. Phys. 64, 139 (2015)

2015
[18]

D’Alessio and A

L. D’Alessio and A. Polkovnikov, Ann. Phys. 333, 19 (2013)

2013
[19]

D’Alessio, Y

L. D’Alessio, Y. Kafri, A. Polokovnikov, and M. Rigol, Adv. Phys. 65, 239 (2016)

2016
[20]

Oka and S

T. Oka and S. Kitamura, Annu. Rev. Condens. Matter Phys. 10, 387 (2019)

2019
[21]

Blanes, F

S. Blanes, F. Casas, J. A. Oteo, and J. Ros, Physics Reports 470, 151 (2009)

2009
[22]

Eckardt, Rev

A. Eckardt, Rev. Mod. Phys. 89, 011004 (2017)

2017
[23]

A. Sen, D. Sen, and K. Sengupta, J. Phys. Cond. Mat. 33, 443003 (2021)

2021
[24]

Banerjee and K

T. Banerjee and K. Sengupta, J. Phys. Cond. Mat. 37 133002 (2025)

2025
[25]

T. W. B. Kibble, J. Phys. A 9, 1387 (1976)

1976
[26]

W. H. Zurek, Nature (London) 317, 505 (1985)

1985
[27]

Polkovnikov, Phys

A. Polkovnikov, Phys. Rev. B 72, 161201(R) (2005); A. Polkovnikov and V. Gritsev, Nature Phys. 4, 477 (2008)

2005
[28]

Sengupta, S

K. Sengupta, S. Mondal, and D. Sen, Phys. Rev. Lett. 100, 077204 (2008)

2008
[29]

D. Sen, S. Mondal, and K. Sengupta, Phys. Rev. Lett. 101, 016806 (2008); R. Barankov and A. Polkovnikov, Phys. Rev. Lett. 101, 076801 (2008)

2008
[30]

Mukherjee, P

B. Mukherjee, P. Mohan, D. Sen, and K. Sengupta, Phys. Rev. B 97, 205415 (2018)

2018
[31]

Das, Phys

A. Das, Phys. Rev. B 82, 172402 (2010); S. Bhat- tacharyya, A. Das, and S. Dasgupta, Phys. Rev. B 86, 054410 (2012); S. S. Hegde, H. Katiyar, T. S. Mahesh, and A. Das, Phys. Rev. B 90, 174407 (2014)

2010
[32]

Mondal, D

S. Mondal, D. Pekker, and K. Sengupta, Europhys. Lett. 100, 60007 (2012); U Divakaran and K. Sengupta. Phys. Rev. B 90, 184303 (2014); S. Kar, B. Mukherjee, and K. Sengupta, Phys. Rev. B 94, 075130 (2016); S. Kar, Phys. Rev. B 95, 085141 (2017)

2012
[33]

H. Guo, R. Mukherjee, and D. Chowdhury, arXiv:2405.01627 (unpublished); A. Haldar, D. Sen, R. Moessner, and A. Das, Phys. Rev. X 11, 021008 (2021)

2021 arXiv
[34]

Camilo and D

G. Camilo and D. Texiera, Phys. Rev. B 102, 174304 (2020); B. Mukherjee, R. Melendrez, M. Szyniszewski, H. J. Changlani, and A. Pal, Phys. Rev. B 109, 064303 (2024)

2020
[35]

Agarwala and D

A. Agarwala and D. Sen, Phys. Rev. B95, 014305 (2017); S. Aditya and D. Sen, SciPost Phys. Core 6, 083 (2023)

2017
[36]

T. Nag, S. Roy, A. Dutta, and D. Sen, Phys. Rev. B 89, 165425 (2014); L. Tamang, T. Nag, and T. Biswas, Phys. Rev. B 104, 174308 (2021)

2014
[37]

Y. Baum, E. P. L. van Nieuwenburg, and G. Refael, Sci- Post Phys. 5, 017 (2018); D. J. Luitz, Y. Bar Lev, and A. Lazarides, SciPost Phys. 3, 029 (2017)

2018
[38]

M. Fava, R. Fazio, and A. Russomanno, Phys. Rev. B 101, 064302 (2020); A. Eckardt, C. Weiss, and M. Holthaus, Phys. Rev. Lett. 95, 260404 (2005)

2020
[39]

Ghosh, B

R. Ghosh, B. Mukherjee, and K. Sengupta, Phys. Rev. B 102, 235114 (2020); A. C. Keser, S. Ganeshan, G. Refael, and V. Galitski, Phys. Rev. B 94, 085120 (2016)

2020
[40]

Oka and H

T. Oka and H. Aoki, Phys. Rev. B 79, 081406(R) (2009); T. Kitagawa, T. Oka, A. Brataas, L. Fu, and E. Demler, Phys. Rev. B 84, 235108 (2011); A. Kundu, H. A. Fertig, and B. Seradjeh, Phys. Rev. Lett. 113, 236803 (2014)

2009
[41]

Kitagawa, E

T. Kitagawa, E. Berg, M. Rudner, and E. Demler, Phys. Rev. B 82, 235114 (2010); N. H. Lindner, G. Refael, and V. Galitski, Nature Phys. 7, 490 (2011)

2010
[42]

Thakurathi, A

M. Thakurathi, A. A. Patel, D. Sen, and A. Dutta, Phys. Rev. B 88, 155133 (2013); M. Thakurathi, K. Sengupta, and D. Sen, Phys. Rev. B 89, 235434 (2015)

2013
[43]

Nathan and M

F. Nathan and M. S. Rudner, New J. Phys. 17, 125014 (2015); B. Mukherjee, A. Sen, D. Sen, and K. Sengupta, Phys. Rev. B 94, 155122 (2016); B. Mukherjee, Phys. Rev. B 98, 235112 (2018)

2015
[44]

Pai and M

S. Pai and M. Pretko, Phys. Rev. Lett. 123, 136401 (2019); B. Mukherjee, S. Nandy, A. Sen, D. Sen, and K. Sengupta, Phys. Rev. B 101, 245107 (2020)

2019
[45]

Mizuta, K

K. Mizuta, K. Takasan, and N. Kawakami, Phys. Rev. Res 2, 033284 (2020); S. Sugiura, T. Kuwahara, and K. Saito, Phys. Rev. Research 3, L012010 (2021); N. Maskara, A. A. Michalidis, W. W. Ho, D. Bluvstein, S. Choi, M. D. Lukin, and M. Serbyn, Phys. Rev. Lett.127, 090602 (2021)

2020
[46]

Hudomal, J-Y Desaules, B

A. Hudomal, J-Y Desaules, B. Mukherjee, G.-X. Su, J. C. Halimeh, and Z. Papic, Phys. Rev. B 106, 104302 (2022); B. Huang, T.-H. Leung, D. M. Stamper-Kurn, and W. V. Liu, Phys. Rev. Lett. 129, 133001 (2022)

2022
[47]

Mukherjee, A

B. Mukherjee, A. Sen, D. Sen, and K. Sengupta, Phys. Rev. B 102, 075123 (2020); ibid, Phys. Rev. B 102, 014301 (2020)

2020
[48]

Ghosh, I

S. Ghosh, I. Paul, and K. Sengupta, Phys. Rev. Lett. 130, 120401 (2023); S. Ghosh, I. Paul, and K. Sengupta, Phys. Rev. B 109, 214304 (2024)

2023
[49]

C. M. Langlett and S. Xu, Phys. Rev. B 103, L220304 (2021); L. Zhang, Y. Ke, L. Lin, and C. Lee, Phys. Rev. B 109, 184313 (2024)

2021
[50]

N. Y. Yao and C. Nayak, Physics Today 71, 40 (2018); D. V. Else, C. Monroe, C. Nayak, and N. Y. Yao, Ann. Rev. Cond. Mat. 11, 467 (2020)

2018
[51]

M. P. Zaletel, M. Lukin, C. Monroe, C. Nayak, F. Wilczek, and N. Y. Yao, Rev. Mod. Phys. 95, 031001 (2023); V. Khemani, R. Moessner, and S. L. Sondhi, arXiv:1910.10745 (unpublished); K. Sacha and J. Za- krzewski, Rep. Prog. Phys. 81, 016401 (2018)

2023 arXiv
[52]

Khemani, A

V. Khemani, A. Lazarides, R. Moessner, and S. L. Sondhi, Phys. Rev. Lett. 116, 250401 (2016); C. W. von Keyserlingk, V. Khemani, and S. L. Sondhi, Phys. Rev. B 94, 085112 (2016); R. Moessner and S. L. Sondhi, Nature Phys. 13, 424 (2017). 13

2016
[53]

D. V. Else, B. Bauer, and C. Nayak, Phys. Rev. Lett. 117, 090402 (2016); ibid, Phys. Rev. X 7, 011026 (2017); N. Y. Yao, A. C. Potter, I.-D. Potirniche, and A. Vish- wanath, Phys. Rev. Lett. 118, 030401 (2017)

2016
[54]

F. Ares, S. Murciano, and P. Calabrese, Nature Comm. 14, 2036 (2023)

2023
[55]

L. K. Joshi, J. Franke, A. Rath, F. Ares, S. Murciano, F. Kranzl, R. Blatt, P. Zoller, B. Vermersch, P. Cal- abrese, C. F. Roos, and M. K. Joshi, Phys. Rev. Lett. 133, 010402 (2024)

2024
[56]

Banerjee, S

T. Banerjee, S. Das, and K. Sengupta, arXiv:2412.03654 (unpublised)

arXiv
[57]

Simon, W

J. Simon, W. S. Bakr, R. Ma, M. E. Tai, P. M. Preiss, and M. Greiner, Nature (London) 472, 307 (2011); W. Bakr, A. Peng, E. Tai, R. Ma, J. Simon, J. Gillen, S. Foelling, L. Pollet, and M. Greiner, Science 329, 547 (2010)

2011
[58]

Bernien, S

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Om- ran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletic, and M. D. Lukin, Nature 551, 579 (2017)

2017
[59]

Bluvstein, A

D. Bluvstein, A. Omran, H. Levine, A. Keesling, G. Se- meghini, S. Ebadi, T. T. Wang, A. A. Michailidis, N. Maskara, W. W. Ho, S. Choi, M. Serbyn, M. Greiner, V. Vuletic, and M. D. Lukin, Science 371, 1355 (2021)

2021
[60]

Ebadi, T

S. Ebadi, T. T. Wang, H. Levine, A. Keesling, G. Se- meghini, A. Omran, D. Bluvstein, R. Samajdar, H. Pich- ler, W. W. Ho, S. Choi, S. Sachdev, M. Greiner, V. Vuletic, and M. D. Lukin, Nature 595, 227 (2021)

2021
[61]

Sachdev, K

S. Sachdev, K. Sengupta, and S. M. Girvin, Phys. Rev. B 66, 075128 (2002)

2002
[62]

Fendley, K

P. Fendley, K. Sengupta, and S. Sachdev, Physical Re- view B 69, 075106 (2004)

2004
[63]

Kolodrubetz, D

M. Kolodrubetz, D. Pekker, B. K. Clark, and K. Sen- gupta, Phys. Rev. B 85, 100505(R) (2012); R. Ghosh, A. Sen, and K. Sengupta, Phys. Rev. B 97, 014309 (2018)

2012

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.

[1] [1]

and spin liquids [2]. For fractional quantum Hall sys- tems, a strong magnetic field in the kinetic term of the Hamiltonian of non-interacting electrons leads to an ex- tensive degeneracy; the mechanism of the lifting of this degeneracy by Coulomb interactions between the elec- trons is central to the realization of fractional quantum Hall states hosting ...

work page Pith review arXiv 2025

[2] [2]

, (A.18) which is precisely cnm according to Eq. (A.15). Hence cmn = cnm. (A.19) We can prove another identity. From Eq. (A.15), we find that cmn + cnm = Z T 0 dt1 Z T 0 dt2 fm(t1) fn(t2), (A.20) where there is now no ordering of t1, t2 on the right hand side; so we just have two separate integrals. Doing the integrals explicitly and using Eq. (A.19), we ...

work page

[3] [3]

We find that for large drive amplitudes, where H (1) F controls the dy- namics, ∆C remains pinned to zero as expected from the presence of the emergent symmetry. In contrast, for lower drive amplitudes, where higher order terms in HF which do not respect this symmetry become important, 7 0 20×103 40×103 0 0.4 0 500 1000 -0.5 0 0.5 1 m ΔC 0 20×103 40×103 0...

work page 2020

[4] [4]

In contrast to the ramp studied earlier where the system passes through the degenerate point only once, these features depend sensitively on τ

We find that the second passage through the degener- ate points leads to an enhancement of F and a reduction of Q. In contrast to the ramp studied earlier where the system passes through the degenerate point only once, these features depend sensitively on τ . For smaller val- ues of τ , both F (τ ) and Q(τ ) are found to attain values much closer to zero ...

work page

[5] [5]

See, for example, H. L. Stormer, D. C. Tsui, and A. C. Gossard, Rev. Mod. Phys. 71, S298 (1999)

work page 1999

[6] [6]

Kivelson and S

See, for example, S. Kivelson and S. L. Sondhi, Nature Rev. Phys. 5, 368 (2023)

work page 2023

[7] [7]

R. B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983)

1983

[8] [8]

J. K. Jain, Phys. Rev. Lett. 63, 199 (1989)

1989