Pith. sign in

REVIEW 2 major objections 5 minor 1 cited by

Quantum phases and transitions of bosons on a comb lattice

T0 review · 2 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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

Pith's one-line read At commensurate fillings with $p>2$ and $p_\perp>2$, the comb-lattice Bose-Hubbard model generically hosts four zero-temperature phases, with Kosterlitz-Thouless and extraordinary boundary transitions between them.

desk verdict The four-phase picture is appealing, but the paper's own Eq. (13) makes the advertised multicritical structure impossible in the p⊥ > 2 regime; this needs major revision before it can stand. read the letter →

arxiv 2412.06915 v2 pith:3P5NBKPX submitted 2024-12-09 cond-mat.quant-gas

Leo Radzihovsky , Emil Pellett This is my paper · ORCID
classification cond-mat.quant-gas
keywords Bose-Hubbardmodelcomblatticefish-boneLuttingerliquidincoherentsuperfluidKosterlitz-Thoulesstransitionextraordinaryboundarycriticalityquantumphasetransitions
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

The paper argues that the comb-lattice Bose-Hubbard model—a one-dimensional backbone of bosons coupled at every site to an otherwise independent one-dimensional 'tooth' chain—has a zero-temperature phase diagram with four distinct phases at commensurate fillings whose denominators exceed two: a gapped Mott insulator, a backbone Luttinger liquid (gapless quasi-one-dimensional superfluid with power-law correlations along the backbone), a transverse Luttinger liquid (power-law correlations along the teeth), and the previously studied incoherent superfluid (long-range order along the one-dimensional backbone). The insulator-to-Luttinger-liquid transitions are Kosterlitz-Thouless, the transverse-Luttinger-liquid-to-incoherent-superfluid transition is also Kosterlitz-Thouless, and the backbone-Luttinger-liquid-to-incoherent-superfluid transition is an extraordinary boundary transition that splits into two regimes at a multicritical point. If correct, this places the incoherent superfluid inside a broader family of quantum phases rather than as an isolated phenomenon, and predicts where in hopping space each phase appears. The result is testable in cold-atom optical lattices and quantum simulators, and it shows how a correlated one-dimensional bath can qualitatively change the order of a one-dimensional system.

What carries the argument

The machinery is a low-energy field-theoretic description in terms of two coupled order-parameter fields: $\psi$ for the backbone and $\Psi$ for the transverse teeth, obtained by Hubbard-Stratonovich decoupling of the Bose-Hubbard model. The teeth are independent 1D chains, so at low energy each is a Luttinger liquid with parameter $g_\perp$, and the backbone is a sine-Gordon model with Luttinger parameter $g$. The lattice commensurability produces cosine potentials $u\cos(2p\theta_0)$ and $u_\perp\cos(2p_\perp\theta_x)$; their relevance, controlled by $2/p^2$ and $2/p_\perp^2$, decides whether a phase is gapped or a Luttinger liquid. The hybridization $c$ between $\psi$ and $\Psi$, with renormalization-group eigenvalue $\lambda=1-1/(4g)-1/(4g_\perp)$, decides whether the backbone and teeth order independently or lock together, producing the extraordinary-LL and extraordinary-log regimes. The transverse interchain hopping along the backbone has eigenvalue $\lambda_J=1-1/(2g_\perp)$, which explains why a distinct $\mathrm{LL}_\perp$ phase requires $p_\perp>2$.

What would settle it

Quantum Monte Carlo on the comb-lattice Bose-Hubbard model at $p=1$, $p_\perp=3$, measuring the superfluid stiffness along the backbone and along the teeth, would settle the phase diagram: a distinct $\mathrm{LL}_\perp$ phase must appear between the Mott insulator and the incoherent superfluid, and the $\mathrm{LL}_b$–iSF transition must show extraordinary boundary scaling rather than Kosterlitz-Thouless behavior. The asserted eigenvalue $\lambda$ can be checked independently by extracting the scaling dimension of the hybridization $c$ in a transfer-matrix or Wilsonian renormalization-group calculation.

Watch

Extended reading notes

Core claim

The central claim is that the zero-temperature phase diagram of the Bose-Hubbard model on a comb lattice—a one-dimensional backbone coupled at every site to an independent one-dimensional tooth—contains four generic phases at commensurate fillings with denominators $p>2$ and $p_\perp>2$: a gapped Mott insulator, a backbone Luttinger liquid with quasi-long-range order along the backbone, a transverse Luttinger liquid with quasi-long-range order along the teeth, and the incoherent superfluid with long-range order along the one-dimensional backbone. The incoherent superfluid, previously studied in isolation, is thereby embedded in a larger phase diagram. The paper also claims that the transitions between these phases are not all of the same type: the Mott transitions out to the two Luttinger liquids are Kosterlitz-Thouless, the $\mathrm{LL}_\perp$–iSF transition is Kosterlitz-Thouless, and the $\mathrm{LL}_b$–iSF transition is an extraordinary boundary transition, with a multicritical point separating an 'extraordinary-LL' regime from an 'extraordinary-log' regime. For $p_\perp\le 2$ the distinct $\mathrm{LL}_\perp$ phase disappears and the phase diagram reduces to the previously studied one.

Load-bearing premise

The calculation assumes the backbone–teeth hybridization scales as $\lambda=1-\frac{1}{4g}-\frac{1}{4g_\perp}$ under coarse-graining, a formula stated without derivation; this exponent fixes the multicritical point $g_c=2/(8-p_\perp^2)$ and splits the $\mathrm{LL}_b$–iSF transition into extraordinary-LL and extraordinary-log regimes, so any correction to it moves the predicted boundary.

Editorial extensions

If this is right

  • At filling denominators $p>2$ and $p_\perp>2$, the zero-temperature phase diagram of the comb-lattice Bose-Hubbard model contains four phases: gapped Mott insulator, backbone and transverse Luttinger liquids, and the incoherent superfluid.
  • The Mott-insulator-to-Luttinger-liquid transitions are Kosterlitz-Thouless, governed by the Luttinger parameters crossing $g_{c1}=2/p^2$ and $g_{\perp c1}=2/p_\perp^2$.
  • The backbone-Luttinger-liquid-to-incoherent-superfluid transition belongs to an extraordinary boundary universality class and splits into extraordinary-LL and extraordinary-log regimes meeting at $g_c=2/(8-p_\perp^2)$.
  • The transverse-Luttinger-liquid-to-incoherent-superfluid transition is Kosterlitz-Thouless, with backbone hopping becoming relevant once $g_\perp>1/2$.
  • For $p_\perp\le 2$ there is no distinct $\mathrm{LL}_\perp$ phase; it merges with the incoherent superfluid, so the $\mathrm{LL}_\perp$–iSF transition is absent.

Reading between the lines

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

  • If the phase diagram holds, the incoherent superfluid should be tunably suppressed or enlarged by changing the teeth filling denominator $p_\perp$, because the multicritical point $g_c$ depends on $p_\perp$; this gives a control knob absent in earlier studies of the incoherent superfluid alone.
  • The same backbone–teeth boundary structure should appear in any quasi-1D system coupled to an array of 1D Luttinger baths, so the prediction is transferable to coupled-wire and cold-atom geometries beyond the specific comb lattice.
  • A direct check of the asserted scaling eigenvalue $\lambda=1-1/(4g)-1/(4g_\perp)$ would not only fix $g_c$ but also determine whether the extraordinary-log regime is wide enough to observe in finite-size simulations; measuring the correlation-length exponent across the $\mathrm{LL}_b$–iSF boundary would do this.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The manuscript studies the zero-temperature Bose-Hubbard model on a comb lattice—a one-dimensional backbone coupled at each site to semi-infinite one-dimensional teeth—using mean-field, perturbative, and sine-Gordon/RG arguments. It proposes a phase diagram containing a gapped Mott insulator (MI), a backbone Luttinger liquid (LLb), a transverse Luttinger liquid (LL⊥), and the previously identified incoherent superfluid (iSF). The principal new claims are that for low commensurability p>2, p⊥>2 these four phases coexist; that the LLb–iSF transition is an 'extraordinary' boundary transition split by a multicritical point into extraordinary-LL and extraordinary-log regimes; that the LL⊥–iSF transition is of Kosterlitz-Thouless type; and that at irrational fillings only the iSF phase is stable. The paper also discusses experimental and quantum-Monte-Carlo tests of these predictions.

Significance. The paper addresses a topical problem—a one-dimensional quantum system entangled with a correlated quantum bath—and provides a concrete microscopic model with falsifiable predictions. If the proposed phase diagram is correct, it would place the previously established iSF phase in a larger context and connect it to boundary-criticality universality classes. The authors are commendably cautious about the tetracritical scenario and explicitly call for numerical verification. However, the central new quantitative prediction, the multicritical point on the LLb–iSF boundary, rests on an asserted RG eigenvalue whose stated formula gives negative Luttinger parameters for the advertised p⊥>2 regime. Until this internal inconsistency is resolved by a derivation or by a corrected phase diagram, the headline result is not established.

major comments (2)
  1. [Two-dimensional Luttinger model, Eq. (13)] The RG eigenvalue λ = 1 − 1/(4g) − 1/(4g⊥) is introduced immediately before Eq. (13) with the phrase 'simple analysis shows,' but no derivation is provided. This is load-bearing because λ=0, together with g⊥,c2=2/p⊥^2, fixes the multicritical point gc=2/(8−p⊥^2) and the extraordinary-LL/extraordinary-log split on the LLb–iSF boundary. As written, the formula is internally inconsistent with the p⊥>2 regime advertised in Fig. 2: for every integer p⊥≥3 the denominator 8−p⊥^2 is negative, so gc<0, whereas g is a positive Luttinger parameter. For instance, p⊥=3 gives gc=−2. The stated consistency condition 2/p^2<gc then fails for the authors' example p=1, which also violates the assumed p>2. Thus, for the parameter regime claimed in the paper, the multicritical point and the two-regime structure do not follow from the presented formula. The authors need to either derive λ and the relevant g⊥ value from the actual boundary action, or restrict the claim to p⊥<√8 (only p⊥=2 among integers, which is outside the main p⊥>2 diagram) and revise the phase diagram and example accordingly.
  2. [Results section, last sentence] The statement 'For irrational fillings, only the iSF phase is stable' is a strong assertion that is not derived in the paper. The sine-Gordon analyses of Eqs. (12) and (14) apply to commensurate fillings where lattice-pinning terms are present; for incommensurate fillings those terms are absent, and one would generically expect Luttinger-liquid behavior. Whether hybridization between the backbone and teeth destabilizes the LLb and LL⊥ phases for irrational fillings requires an explicit RG calculation or a supporting argument. Please either derive this claim, state it as a conjecture, or clarify the precise sense in which it is meant.
minor comments (5)
  1. [Model and Eqs. (4)–(7)] The symbol c is used both for the hybridization coupling in Eq. (7) and for the local correlator C(τ−τ′) in Eqs. (4)–(6); this notational clash should be removed.
  2. [Two-dimensional Luttinger model, paragraphs (iii) and (iv)] The notation g⊥,c2 is used with two different meanings: in paragraph (iii) it denotes the value 2/p⊥^2 at the LLb–iSF boundary, while in paragraph (iv) it denotes the LL⊥–iSF boundary value 1/2. Please rename one of these critical Luttinger parameters.
  3. [Results section] The text says the analysis allows 'beyond on-site interaction' but Eq. (1) contains only the on-site repulsion U; footnote [45] should be incorporated into the model definition so the main text is self-consistent.
  4. [Throughout] The phase labels are used inconsistently: 'SFb' appears in paragraph (iii) where the surrounding text uses 'LLb', and the abstract uses 'LLp' while the body uses 'LL⊥'. Please standardize the phase names.
  5. [Introduction, Ref. [27]] Reference [27] is cited as 'unpublished' in a list of polaron-like problems; if it is not essential to a specific claim, replace it with a citable source or remove it.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the new phase-transition predictions are derived from standard RG and sine-Gordon inputs, and the self-cited iSF phase is used as an externally supported input rather than as the target of derivation.

full rationale

The paper's derivation chain is not circular. The central new content is the phase diagram and transition structure (MI-LLb, MI-LL⊥, LL⊥-iSF, LLb-iSF), obtained from standard Luttinger-liquid and sine-Gordon RG analysis: KT transitions at gc1 = 2/p^2 and g⊥,c1 = 2/p⊥^2, the interchain-hopping relevance condition λ_J = 1 - 1/(2g⊥) giving g⊥,c2 = 1/2, and the hybridization eigenvalue λ = 1 - 1/(4g) - 1/(4g⊥) locating the multicritical point. These are stated as RG results rather than fitted to the target phase boundaries, so the predictions are not equivalent to inputs by construction. The self-citations to Refs. [10,11] (Radzihovsky and collaborators) are used to establish the previously known iSF phase as an input; the paper explicitly notes that this phase 'has also been demonstrated in QMC simulations' (Ref. [37]) and is supported by other independent QMC work (Refs. [23,39]). Moreover, the paper does not invoke its own prior work to forbid alternative scenarios; it explicitly lists alternative first-order or tetracritical possibilities that it cannot exclude. The assertion of the c-eigenvalue without derivation, and the apparent inconsistency that gc = 2/(8 - p⊥^2) is negative for integer p⊥ ≥ 3, are correctness or rigor concerns, not circularity, because the claims do not reduce to their inputs by definition or by fitting. Accordingly, the appropriate circularity finding is no significant circularity.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

No parameters are fitted to data in this paper; J, J⊥, μ and U are model inputs, and the Luttinger parameters g, g⊥ are left as unspecified functions. No new particles, forces, or conserved quantities are introduced; the comb geometry is a physical lattice, not a postulated entity.

assumptions (5)
  • domain assumption Bose-Hubbard model on the comb lattice (Eq. 1) with uniform on-site repulsion U.
    The model is the starting point; the paper argues results are generic to weak perturbations but does not derive the model from a more fundamental theory.
  • standard math Coherent-state path integral and Hubbard-Stratonovich decoupling (Eqs. 2-7) leading to the low-energy action.
    Standard technique in boson systems; no proof given in the paper.
  • domain assumption Luttinger liquid / sine-Gordon description of 1D bosons at commensurate filling (Eqs. 12, 14).
    Invoked from Ref. 42; the paper does not rederive bosonization.
  • ad hoc to paper The hybridization RG eigenvalue λ = 1 - 1/(4g) - 1/(4g⊥).
    Stated without derivation and used to locate the multicritical point; this is a load-bearing asserted result.
  • domain assumption Extraordinary boundary criticality framework from Refs. 12 and 13.
    Adopted to classify the LLb-iSF transition; the paper relies on these external results.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Quantum phases and transitions of bosons on a comb lattice." pith.science (2026). https://pith.science/paper/3P5NBKPX

@misc{pith2026241206915,
  author       = {Pith},
  title        = {Pith review of: Quantum phases and transitions of bosons on a comb lattice},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3P5NBKPX}},
  note         = {Machine review of arXiv:2412.06915}
}
read the original abstract

Motivated to elucidate the nature of quantum phases and their criticality when entangled with a correlated quantum bath, we study interacting bosons on a "comb lattice" -- a one-dimensional backbone (system) coupled at its sites to otherwise independent one-dimensional "teeth" chains (bath). We map out the corresponding phase diagram, detailing the nature of the phases and phase transitions. Controlled by the backbone and teeth hopping amplitudes, on-site interaction and chemical potential, phases include a Mott-insulator (MI), backbone (LLb) and teeth (LLp) Luttinger liquids, and the long-range ordered incoherent superfluid (iSF). We explore their properties and potential realizations in condensed matter and cold-atom experiments and simulations.

Figures

Figures reproduced from arXiv: 2412.06915 by the authors.

Figure 1
Figure 1. FIG. 1. (Inset) A “fish-bone” (equivalently “comb”) lat [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Schematic phase diagram for hopping amplitudes [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Long-Range Order in a Strictly Short-Range Quasi-2D XY Model: When Critical Fluctuations Matter

    cond-mat.stat-mech 2025-06 conditional novelty 8.0 of 10

    In a strictly short-range XY model made of a plane intersected by parallel planes, true long-range order appears along the intersection lines when the parallel planes enter a Berezinskii-Kosterlitz-Thouless critical phase.

Reference graph

Works this paper leans on

49 extracted references · 45 canonical work pages · cited by 1 Pith paper

  1. [1]

    A. O. Caldeira and A. J. Leggett, Influence of Dissipation on Quantum Tunneling in Macroscopic Systems , Phys. Rev. Lett. 46, 211 (1981)

    work page 1981

  2. [2]

    A. O. Caldeira and A. J. Leggett, Quantum tunnelling in a dissipative system , Ann. Phys. (NY) 149, 374 (1983)

    work page 1983

  3. [3]

    A. O. Caldeira and A. J. Leggett, Path integral ap- proach to quantum Brownian motion , Physica A 121, 587 (1983)

    work page 1983

  4. [4]

    Decoherence and the Appearance of a Clas- sical World in Quantum Theory

    E. Joos, Decoherence Through Interaction with the Envi- ronment, in “Decoherence and the Appearance of a Clas- sical World in Quantum Theory”, Springer, Berlin, Hei- delberg. https://doi.org/10.1007/978-3-662-05328-7 3

    doi:10.1007/978-3-662-05328-7

  5. [5]

    Brandt, Qubit devices and the issue of quan- tum decoherence, Progress in Quantum Electronics 22, 257 ( 1999)

    Howard E. Brandt, Qubit devices and the issue of quan- tum decoherence, Progress in Quantum Electronics 22, 257 ( 1999)

    work page 1999

  6. [6]

    W. G. Unruh, Maintaining coherence in quantum com- puters, Phys. Rev. A, 51, 992 (1995)

    work page 1995

  7. [7]

    DiVincenzo, Quantum computation , Science 270, 255 (1995)

    D.P. DiVincenzo, Quantum computation , Science 270, 255 (1995)

    work page 1995

  8. [8]

    Burovski, E

    E. Burovski, E. Kozik, A. Kuklov, N. Prokof’ev, and B. Svistunov, Superfluid Interfaces in Quantum Solids , Phys. Rev. Lett. 94, 165301 (2005)

    work page 2005

Show all 49 references
  1. [9]

    Radzihovsky, A

    L. Radzihovsky, A. Kuklov, N. Prokof’ev, and B. Svis- tunov, Superfluid Edge Dislocation: Transverse Quantum Fluid, Phys. Rev. Lett. 131, 196001 (2023). 6

    2023

  2. [10]

    Anatoly Kuklov, Nikolay Prokof’ev, Leo Radzihovsky, Boris Svistunov, Transverse Quantum Fluids, Phys. Rev. B 109, L100502 (2024)

    2024

  3. [11]

    Anatoly Kuklov, Lode Pollet, Nikolay Prokof’ev, Leo Radzihovsky, Boris Svistunov, Universal Correlations as Fingerprints of Transverse Quantum Fluids , Phys. Rev. A 109, L011302 (2024)

    2024

  4. [12]

    Metlitski Bound- ary Criticality of the 3D O(N) Model: From Normal to Extraordinary, Phys

    Francesco Parisen Toldin and Max A. Metlitski Bound- ary Criticality of the 3D O(N) Model: From Normal to Extraordinary, Phys. Rev. Lett. 128, 215701 (2022)

    2022

  5. [13]

    Metlitski, Boundary criticality of the O(N ) model in d = 3 critically revisited, arXiv:2009.05119

    Max A. Metlitski, Boundary criticality of the O(N ) model in d = 3 critically revisited, arXiv:2009.05119

    2009 arXiv

  6. [14]

    Grover and A

    T. Grover and A. Vishwanath, Quantum Criticality in Topological Insulators and Superconductors: Emer- gence of Strongly Coupled Majoranas and Supersymme- try, arXiv:1206.1332

    arXiv

  7. [15]

    R. P. Feynman, Statistical Mechanics: A Set Of Lectures, Publisher W. A. Benjamin (1972)

    1972

  8. [16]

    G. T. Zimanyi, K. Vladar, and A. Zawadowski, Path- integral method for a heavy particle moving in a periodic potential and screened by a light degenerate Fermi gas, Phys. Rev. B. 36, 3186 (1987)

    1987

  9. [17]

    A. H. Castro Neto and Matthew P. A. Fisher, Dynamics of a heavy particle in a Luttinger liquid , Phys. Rev. B 53, 9713 (1996)

    1996

  10. [18]

    T¨ urker and K

    O. T¨ urker and K. Yang, String-like theory of quantum Hall interfaces , Phys. Rev. B 106, 245138 (2022)

    2022

  11. [19]

    A. H. Castro Neto, C. de C. Chamon, and C. Nayak, Open Luttinger Liquids, Phys. Rev. Lett.79, 4629 (1997)

    1997

  12. [20]

    Pankov, S

    S. Pankov, S. Florens, A. Georges, G. Kotliar, and S. Sachdev, Non-Fermi-liquid behavior from two-dimensional antiferromagnetic fluctuations: A renormalization-group and large-N analysis , Phys. Rev. B 69, 054426 (2004)

    2004

  13. [21]

    Werner, M

    P. Werner, M. Troyer, and S. Sachdev, Quantum spin chains with site dissipation , J. Phys. Soc. Jpn. 74, 67 (2005)

    2005

  14. [22]

    Z. Cai, U. Schollw¨ ock, and L. Pollet,Identifying a Bath- Induced Bose Liquid in Interacting Spin-Boson Models , Phys. Rev. Lett. 113, 260403 (2014)

    2014

  15. [23]

    Z. Yan, L. Pollet, J. Lou, X. Wang, Y. Chen, and Z. Cai, Interacting lattice systems with quantum dissipation: A quantum Monte Carlo study , Phys. Rev. B 97, 035148 (2018)

    2018

  16. [24]

    Weber, D

    M. Weber, D. J. Luitz, and F. F. Assaad, Dissipation- Induced Order: The S = 1/2 Quantum Spin Chain Cou- pled to an Ohmic Bath , Phys. Rev. Lett. 129, 056402 (2022)

    2022

  17. [25]

    B. Danu, M. Vojta, T. Grover, and F. F. Assaad, Spin chain on a metallic surface: Dissipation-induced order versus Kondo entanglement , Phys. Rev. B 106, L161103 (2022)

    2022

  18. [26]

    Martin and T

    S. Martin and T. Grover, A stable, critical phase in- duced by Berry phase and dissipation in a spin-chain , arXiv:2307.13889

    arXiv

  19. [27]

    Radzihovsky, unpublished

    L. Radzihovsky, unpublished

  20. [28]

    Chakravarty and A

    S. Chakravarty and A. J. Leggett, Dynamics of the Two- State System with Ohmic Dissipation , Phys. Rev. Lett. 52, 5 (1984)

    1984

  21. [29]

    Schmid, Diffusion and Localization in a Dissipative Quantum System , Phys

    A. Schmid, Diffusion and Localization in a Dissipative Quantum System , Phys. Rev. Lett. 51, 1506 (1983)

    1983

  22. [30]

    Guinea, V

    F. Guinea, V. Hakim, and A. Muramatsu, Diffusion and Localization of a Particle in a Periodic Potential Coupled to a Dissipative Environment , Phys. Rev. Lett. 54, 263 (1985)

    1985

  23. [31]

    Weiss and H

    U. Weiss and H. Grabert, Quantum diffusion of a particle in a periodic potential with ohmic dissipation, Phys. Lett. A 108, 63 (1985)

    1985

  24. [32]

    Matthew P. A. Fisher and W. Zwerger, Quantum Brow- nian motion in a periodic potential , Phys. Rev. B. 32, 6190 (1985)

    1985

  25. [33]

    A. J. Leggett, S. Chakravarty, A. T. Dorsey, Matthew P. A. Fisher, Anupam Garg, and W. Zwerger, Dynamics of the dissipative two-state system , Rev. Mod. Phys. 59 (1987)

    1987

  26. [34]

    Sudip Chakravarty, Gert-Ludwig Ingold, Steven Kivel- son, and Gergely Zimanyi, Quantum statistical mechan- ics of an array of resistively shunted Josephson junctions, Phys. Rev. B. 37, 3283 (1988)

    1988

  27. [35]

    Scalettar and Gergely T

    Ghassan George Batrouni, Richard T. Scalettar and Gergely T. Zimanyi, Quantum Critical Phenomena in One-Dimensional Bose Systems , Phys. Rev. Lett. 65, 1765 (1990)

    1990

  28. [36]

    Kampf, Gergely T

    Arno P. Kampf, Gergely T. Zimanyi, Superconductor- insulator phase transition in the boson Hubbard model , Phys. Rev. B. 47, 279 (1993)

    1993

  29. [37]

    Ribeiro, Paul McClarty, Pedro Ribeiro, Manuel Weber, Dissipation-induced long-range order in the one-dimensional Bose-Hubbard model , Phys

    Afonso L.S. Ribeiro, Paul McClarty, Pedro Ribeiro, Manuel Weber, Dissipation-induced long-range order in the one-dimensional Bose-Hubbard model , Phys. Rev. B 110, 115145 (2024)

    2024

  30. [38]

    Antiferromagnetic order enhanced by local dissipation

    Oscar Bouverot-Dupuis, Saptarshi Majumdar, Alberto Rosso, Laura Foini, “Antiferromagnetic order enhanced by local dissipation”, Phys. Rev. B 109, 205148 (2024)

    2024

  31. [39]

    Buonsante, R

    P. Buonsante, R. Burioni, D. Cassi, V. Penna, and A. Vezzani, Topology-induced confined superfluidity in inho- mogeneous arrays, Phys. Rev. B 70, 224510 (2004)

    2004

  32. [40]

    White, Critical properties of a comb lattice , SciPost Phys

    Natalia Chepiga, Steven R. White, Critical properties of a comb lattice , SciPost Phys. 9, 013 (2020)

    2020

  33. [41]

    C. L. Kane and M. P. A. Fisher, Transport in a one- channel Luttinger liquid , Phys. Rev. Lett. 68, 1220 (1992); Transmission through barriers and resonant tun- neling in an interacting one-dimensional electron gas , Phys. Rev. B 46 15233 (1992)

    1992

  34. [42]

    Giamarchi, Quantum physics in one dimension (Ox- ford Science Publications, Oxford, 2004)

    T. Giamarchi, Quantum physics in one dimension (Ox- ford Science Publications, Oxford, 2004)

    2004

  35. [43]

    However, a range of µ, can give distinct but commensurate fillings ν and ν⊥

    The backbone ν = q/p and transverse-chain ν⊥ = q⊥/p⊥ fillings (labelled by α = b, α) cannot be independently tuned with a single chemical potential µ. However, a range of µ, can give distinct but commensurate fillings ν and ν⊥. Furthermore, one can utilize single particle back...

  36. [44]

    Ongoing diagrammatic QMC by Chao Zhang, et al

  37. [45]

    In our field theoretic analysis of the generic phase dia- gram, we generalize BH model interaction beyond on-site to allow for Mott-insulating phases pinned at low com- mensurabilty fillings

  38. [46]

    Sachdev, Quantum Phase Transitions, Cambridge Uni- versity Press, 1999

    S. Sachdev, Quantum Phase Transitions, Cambridge Uni- versity Press, 1999

    1999

  39. [47]

    thanks Victor Gurarie for discussions on MI-SF transition

    L.R. thanks Victor Gurarie for discussions on MI-SF transition

  40. [48]

    S, Peter Schauss, Ron Belyansky, Jeremy T

    Elmer Guardado-Sanchez, Benjamin M. S, Peter Schauss, Ron Belyansky, Jeremy T. Young, Przemyslaw Bienias, Alexey V. Gorshkov, Thomas Iadecola, and Waseem S. Bakr, Quench dynamics of a Fermi gas with strong non- local interactions, Phys. Rev. X 11, 021036 (2021)

    2021

  41. [49]

    Pedram Roushan, private discussions

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.