Pith. sign in

REVIEW 3 major objections 5 minor 39 references

Bose-Hubbard Model on a Honeycomb Superlattice: Quantum Phase Transitions and Lattice Effects

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

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

Pith's one-line read At unit filling, bosons on a honeycomb superlattice show three ground-state phases—superfluid, uniform Mott, and sublattice-imbalanced Mott—with continuous superfluid-insulator transitions in the 3D XY universality class.

desk verdict The ground-state QMC phase diagram for the honeycomb superlattice is solid and worth publishing; the finite-temperature BKT section has a factor-2 error in the universal-jump line that overstates T_c and needs fixing. read the letter →

arxiv 2506.06984 v1 pith:3D3JETFC submitted 2025-06-08 cond-mat.quant-gas quant-ph

Wei-Wei Wang , Jin Yang , Jian-Ping Lv , Chao Zhang This is my paper
classification cond-mat.quant-gasquant-ph
keywords Bose-HubbardmodelhoneycombsuperlatticequantumphasetransitionMottinsulatorsuperfluidMonteCarloBKTcold-atomexperiments
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 uses quantum Monte Carlo simulations with the worm algorithm to map the phase diagram of the Bose-Hubbard model on a honeycomb superlattice at unit filling. Its central claim is that competition between the onsite interaction U/t and a staggered potential Δ/t produces three ground-state phases: a superfluid, a uniform Mott insulator with one boson per site, and a sublattice-imbalanced Mott insulator with double occupancy on one sublattice and vacancy on the other. All superfluid-to-Mott transitions are reported as continuous, with a correlation-length exponent ν≈0.67 matching the 3D XY universality class. The paper also computes the finite-temperature Berezinskii-Kosterlitz-Thouless melting of the superfluid, giving critical temperatures Tc/t as a function of Δ/t. A sympathetic reader would care because these are concrete, quantitative predictions for cold-atom experiments with honeycomb optical superlattices, including a density-imbalanced Mott phase that has no direct analogue in square-lattice superlattices.

What carries the argument

The central object is the Hamiltonian of Eq. (1): a Bose-Hubbard model on a honeycomb lattice with a staggered onsite potential −Δ on sublattice A, which breaks sublattice symmetry and produces a periodic double-well structure within each unit cell. The argument is carried by the worm-algorithm path-integral quantum Monte Carlo method, which yields the superfluid density ρ_s from winding-number fluctuations, compressibility, the structure factor, and a sublattice density imbalance Δn=|⟨n_A⟩−⟨n_B⟩| that distinguishes MI-I from MI-II. Critical boundaries are extracted from the finite-size scaling form ρ_s $L^{{d+z-2}}$=(1+$aL^{{-ω}}$) f($L^{{1/ν}}$(U/t−(U/t)_c), $βL^{{-z}}$) with z=1 and a fixed correction exponent ω=0.789. The finite-temperature boundary uses the BKT universal jump criterion ρ_s(T_c)=T_c/π with finite-size extrapolation in 1/$ln^{2}$ L.

What would settle it

A decisive check would be to rerun the ground-state analysis near one critical point, say (U/t≈2.80, Δ/t=20), using β much larger than L (for example β=4L) and a free correction exponent rather than fixed ω=0.789. If the extracted critical point shifts by more than the quoted uncertainty, or if the scaling collapse fails with z=1, then the reported boundaries do not represent genuine ground-state transitions and the second-order claim is not established.

Watch

Extended reading notes

Core claim

The paper's central discovery is that at unit filling the Bose-Hubbard model on a honeycomb superlattice hosts three distinct ground states. The uniform Mott insulator (MI-I) has ⟨n_A⟩≈⟨n_B⟩≈1 and is stabilized by interactions; the sublattice-imbalanced Mott insulator (MI-II) has ⟨n_A⟩≈2 and ⟨n_B⟩≈0, stabilized by a large staggered potential. Between them lies a robust superfluid region. Finite-size scaling of the superfluid density indicates that both SF–MI-I and SF–MI-II transitions are continuous second-order transitions with critical exponent ν≈0.67, consistent with the 3D XY universality class, and for Δ/t=20 the critical points are located as (U/t)_c=2.7970±0.0005, 14.0381±0.0005, and 25.1357±0.0005. At finite temperature and fixed U/t=25, the superfluid melts via a BKT transition over the window 21≲Δ/t≲29, with Tc extracted from the universal superfluid-density jump.

Load-bearing premise

The entire phase diagram depends on the assumption that setting inverse temperature β=L with dynamical exponent z=1 already captures ground-state behavior, and that every SF–MI transition is described by the same scaling form with a single correlation-length exponent and a fixed correction exponent ω=0.789; if either assumption fails, the quoted critical points and the conclusion that all transitions are continuous would need revision.

Editorial extensions

If this is right

  • The (U/t, Δ/t) ground-state phase diagram at unit filling is a direct quantitative prediction: at Δ/t=0 the superfluid survives up to U/t≈11.5, and the SF–MI boundaries for other Δ can be compared with future cold-atom measurements.
  • The MI-II phase should appear in experiments as a staggered density pattern with double occupancy on the deep sublattice and vacancy on the shallow one, detectable as a sublattice density contrast via Bragg scattering or quantum gas microscopy.
  • Every SF–MI transition is predicted to be continuous and to belong to the 3D XY universality class, so the critical exponent ν≈0.67 and the crossing behavior of ρ_sL should be observable as system size is varied.
  • At fixed U/t=25, the superfluid exists only in the window 21≲Δ/t≲29; its BKT critical temperature Tc/t as a function of Δ/t, extracted from the universal superfluid-density jump, is a concrete finite-temperature prediction.
  • The phase diagram provides guidance for which experimental parameters realize each phase, including a robust superfluid between two distinct Mott insulators.

Reading between the lines

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

  • The MI-II phase is effectively a density-wave Mott insulator at unit total filling; by analogy with other superlattice models, one might expect it to coexist with or give way to additional phases (e.g., supersolid or pair-superfluid) at higher fillings, which the paper does not explore.
  • The appearance of a superfluid region sandwiched between two Mott phases at large Δ suggests a kind of interaction-induced delocalization effect: strong interactions may favor distributing particles over the two sublattices rather than letting the potential pile them up; a direct analysis of doublon-vacancy correlations would test this picture.
  • A natural extension would be to compute the same phase diagram for non-unit fillings or for a rectangular rather than staggered potential, which the worm-algorithm method can handle directly; the resulting phase boundaries would tell whether the MI-II phase persists away from exact unit filling.
  • The paper fixes ω=0.789 in the scaling fits; letting ω float as a free parameter (or using a different functional form for corrections) would provide a sharper test of the universality claim and is within reach of the same simulations.
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.

Referee Report

3 major / 5 minor

Summary. The paper presents path-integral quantum Monte Carlo (worm algorithm) simulations of the Bose-Hubbard model on a honeycomb superlattice with a staggered potential Δ. At unit filling, it reports three ground-state phases: a superfluid (SF), a uniform Mott insulator (MI-I), and a sublattice-imbalanced Mott insulator (MI-II) with double occupancy on the deep sublattice and vacancy on the shallow one. The SF-MI transitions are claimed to be continuous, with correlation-length exponents ν consistent with the 3D XY universality class, based on finite-size scaling of the superfluid density at Δ/t=20. The paper also constructs a finite-temperature phase diagram for U/t=25 and extracts BKT critical temperatures via the universal jump condition.

Significance. The paper extends the well-studied superlattice Bose-Hubbard problem to a honeycomb geometry and provides concrete quantitative predictions (ground-state phase diagram, BKT line) for cold-atom experiments. The QMC approach is unbiased, and the reported data collapse at Δ/t=20, with ν≈0.67 in agreement with the accepted 3D XY value, is a genuine strength and supports the continuity claim at that cut. The reentrant SF region between the two Mott phases is an interesting qualitative outcome. However, the full boundary and the finite-temperature line are not yet backed by the same level of evidence.

major comments (3)
  1. [Sec. V, Fig. 5(a)] The text states the universal BKT jump as ρ_s(T_c)=2m k_B T_c/(πħ^2), which, with the superfluid-density definition ρ_s=⟨W^2⟩/(d L^{d−2} β) in Sec. III and m=ħ=1, is ρ_s=2T/π. The dashed line in Fig. 5(a) is instead ρ_s=T/π. This factor-of-two difference is not a matter of convention: if an effective mass m*=1/(2t) is intended, the paper must state it and reconcile it with the ρ_s estimator; otherwise the finite-size intersections T_c(L) are systematically overestimated, and the 1/ln^2 L extrapolation in Fig. 5(b) propagates this bias into the T_c(Δ/t) curve of Fig. 4. The authors should correct the criterion or the figure and re-evaluate the BKT line.
  2. [Sec. IV, Fig. 3 and Table I] The finite-size scaling analysis that underlies the SF-MI boundary is presented for a single superlattice depth, Δ/t=20. Table I lists three critical points all at this cut, and the main data collapse is shown only for these data. Yet Fig. 2 draws the SF-MI boundary over a wide range of Δ/t and the abstract claims continuous SF-MI transitions in general. To make the phase diagram quantitative, please report scaling analyses for at least a few other Δ/t cuts (including one near the apparent meeting of MI-I, MI-II, and SF) or explicitly state how the other boundary points in Fig. 2 were obtained and what their uncertainties are.
  3. [Secs. III-IV, Fig. 2] The sublattice imbalance Δn is used to distinguish MI-I from MI-II, with MI-I defined by Δn=0. For any Δ>0 the Hamiltonian explicitly breaks sublattice symmetry, so Δn is strictly positive in the ground state, although it may be very small in the strongly interacting MI-I regime. The paper does not quantify this residual imbalance, nor does it demonstrate that the MI-I/MI-II boundary is a true phase transition (e.g., a discontinuity in Δn or a change in the character of the compressibility) rather than a crossover. Please specify the operational criterion used to draw that boundary in Fig. 2 and clarify the nature of the transition.
minor comments (5)
  1. [Sec. IV, Eq. (4)] 'prefered fits' should be 'preferred fits'; also, the prose description of the fitted polynomial orders for the three transitions (a3 and a4 terms) would be easier to follow if placed in the caption of Table I.
  2. [Sec. IV, simulation geometry paragraph] 'simulate the system on a regular grid consisting of N×N sites' is ambiguous for a honeycomb lattice, which has two sites per unit cell; please state the total number of sites and the boundary conditions explicitly.
  3. [Sec. V, first sentence] 'we investigated' should be 'we investigate' for consistency; also, the dotted vs dashed line description in Fig. 5(a) caption should be harmonized with the text.
  4. [References] Several entries contain formatting errors (e.g., 'K. S Novoselov' in Ref. [2], 'S. P Kou' in Ref. [20], 'J. A. Koziol...' in Ref. [25]); these should be corrected.
  5. [Sec. IV, Eq. (3) and Table I] The correction exponent ω=0.789 is adopted as an input; please state its source and briefly discuss the stability of the fitted critical points and ν values against changing ω or including higher-order corrections.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the QMC data collapse, fitted exponents, and phase boundaries are independent numerical results; the BKT jump-line discrepancy is a consistency issue, not a circular derivation.

full rationale

The central phase diagram and critical exponents come from worm-algorithm QMC simulations, which measure superfluid density, compressibility, structure factor, and sublattice density imbalance directly. The phase boundaries in Fig. 2 are located from finite-size scaling of the raw winding-number data via Eqs. (2)-(4); the critical exponent nu is a free parameter of the least-squares fit and is quoted as 0.674(2), 0.669(2), and 0.679(2), then compared with the external 3D XY value rather than fixed to it. The SF-MI transitions being continuous is therefore a data-driven conclusion, not a restatement of the inputs. The fixed correction exponent omega = 0.789 is adopted from Ref. [30], a previous study by one of the authors, but this is a technical finite-size-scaling assumption and is not equivalent to the claimed phase diagram or exponents; at most it affects precision or robustness. The finite-temperature BKT analysis contains an internal inconsistency: the text states the universal jump as rho_s(T_c) = 2 m k_B T_c/(pi hbar^2), while Fig. 5(a) uses the line rho_s = T/pi; with m = hbar = 1 these differ by a factor of two. This is a correctness or implementation issue that may bias the reported T_c values, but it does not make the derivation circular because the incorrect criterion is not the claim being derived. Self-citations in Refs. [30], [31], [34], and [35] are used for standard scaling forms and BKT criteria, not as uniqueness theorems or as the sole support for the central conclusions. The paper also benchmarks against previous honeycomb-lattice results at Delta/t = 0 and against the known 3D XY exponent, providing independent points of contact. No load-bearing step reduces by construction to its own inputs, so the circularity score is 0.

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

The central claim rests on a standard QMC simulation, so no new theoretical entities are introduced. The main burdens are the single-band Bose-Hubbard modeling assumption, the β=L ground-state convention, the finite-size scaling form with a fixed correction exponent, and the BKT jump criterion used to convert ρs curves into critical temperatures. The reported critical points and exponents are fitted outputs of the data collapse rather than chosen inputs.

free parameters (5)
  • Critical point (U/t)_c for SF-MI-II at Δ/t=20 = 2.7970 ± 0.0005
    Fitted from finite-size scaling of ρs; this is the reported phase boundary, not an input assumption.
  • Critical point (U/t)_c for MI-II-SF at Δ/t=20 = 14.0381 ± 0.0005
    Fitted from finite-size scaling of ρs for the reentrant superfluid boundary.
  • Critical point (U/t)_c for SF-MI-I at Δ/t=20 = 25.1357 ± 0.0005
    Fitted from finite-size scaling of ρs at large U.
  • Correction-to-scaling exponent ω = 0.789
    Adopted and fixed before the fits; the paper does not justify this value or test sensitivity to it.
  • Correlation-length exponent ν = 0.674(2), 0.669(2), 0.679(2)
    Extracted from the same data collapse; compared with the 3D XY value 0.672.
assumptions (5)
  • standard math The path-integral worm-algorithm QMC gives unbiased estimates of superfluid density, compressibility, and density in the thermodynamic limit.
    Invoked in Section III; standard numerical method [12].
  • domain assumption The honeycomb superlattice is modeled by a single-band Bose-Hubbard Hamiltonian with nearest-neighbor hopping, onsite U, and staggered potential Δ; no higher bands, longer-range couplings, or trap effects.
    Hamiltonian Eq. (1) and experimental realization in Section VI.
  • domain assumption Setting β = L captures ground-state behavior (dynamical exponent z = 1).
    Section III: 'We set the inverse temperature as β = 1/T = L... consistent with a dynamical critical exponent of z = 1.'
  • ad hoc to paper The finite-size scaling form Eq. (3) with a single correlation-length exponent ν and a fixed correction exponent ω = 0.789 applies to all three SF-MI transitions.
    Section IV, Eq. (3) and Table I; ω is adopted without independent justification.
  • ad hoc to paper The universal BKT jump condition for the QMC superfluid density is ρs = T/π (i.e., the prefactor 2m/ħ² is set to 1).
    Section V and Fig. 5(a); the text first states ρs = 2mk_BT/(πħ²), then plots ρs = T/π without defining m and ħ lattice units.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Bose-Hubbard Model on a Honeycomb Superlattice: Quantum Phase Transitions and Lattice Effects." pith.science (2026). https://pith.science/paper/3D3JETFC

@misc{pith2026250606984,
  author       = {Pith},
  title        = {Pith review of: Bose-Hubbard Model on a Honeycomb Superlattice: Quantum Phase Transitions and Lattice Effects},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3D3JETFC}},
  note         = {Machine review of arXiv:2506.06984}
}
abstract

We investigate the ground-state and finite-temperature phase diagrams of the Bose-Hubbard model on a honeycomb superlattice. The interplay between the superlattice potential depth $\Delta/t$ and the onsite interaction $U/t$ gives rise to three distinct quantum phases at zero temperature: a superfluid phase, a Mott insulator I phase with unit filling on each site, and a Mott insulator II phase characterized by density imbalance-double occupancy on one sublattice and vacancy on the other at unit filling. The SF-MI transitions are found to be continuous, consistent with second-order quantum phase transitions. We further extend our analysis to finite temperatures within the superfluid regime. Our work highlights how a honeycomb superlattice geometry enables access to interaction- and lattice-modulation-driven quantum phases, including a density-imbalanced Mott insulator and a robust superfluid regime, offering concrete theoretical predictions for cold-atom experiments.

Figures

Figures reproduced from arXiv: 2506.06984 by the authors.

Figure 1
Figure 1. (a) Schematic illustration of the honeycomb super [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Phase diagram of the system described by Eq. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Scaling behavior of the superfluid density [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (2 more)
Figure 5
Figure 5. Figure 5: (a). To systematically extract Tc, we adopt the finite-size intersection approach illustrated in [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 4
Figure 4. Figure 4: Finite-temperature phase diagram at fixed interac [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

39 extracted references · 38 canonical work pages

  1. [1]

    Helical microtubules of graphitic carbon,

    S. Iijima, “Helical microtubules of graphitic carbon,” na- ture 354, 56–58 (1991)

    work page 1991

  2. [2]

    The rise of graphene,

    A. K. Geim and K. S Novoselov, “The rise of graphene,” Nature materials 6, 183–191 (2007)

    work page 2007

  3. [3]

    Bosonic fractional quantum hall conductance in shaken honeycomb optical lattices without flat bands,

    S. Miao, Z. Zhang, Y. Zhao, Zihan Zhao, H. Wang, and J. Hu, “Bosonic fractional quantum hall conductance in shaken honeycomb optical lattices without flat bands,” Phys. Rev. B106, 054310 (2022)

    work page 2022

  4. [4]

    Interacting chiral electrons at the 2d dirac points: a re- view,

    M. Hirata, A. Kobayashi, C. Berthier, and K. Kanoda, “Interacting chiral electrons at the 2d dirac points: a re- view,” Reports on Progress in Physics84, 036502 (2021)

    work page 2021

  5. [5]

    Cold bosonic atoms in optical lattices,

    D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, “Cold bosonic atoms in optical lattices,” Phys. Rev. Lett. 81, 3108–3111 (1998)

    work page 1998

  6. [6]

    Quantumtransportof bosonic cold atoms in double-well optical lattices,

    Y.Qian, M.Gong, andC.Zhang,“Quantumtransportof bosonic cold atoms in double-well optical lattices,” Phys. Rev. A 84, 013608 (2011)

    work page 2011

  7. [7]

    Many-body physics with ultracold gases,

    I. Bloch, J. Dalibard, and W. Zwerger, “Many-body physics with ultracold gases,” Rev. Mod. Phys.80, 885– 964 (2008)

    2008

  8. [8]

    The cold atom hubbard tool- box,

    D. Jaksch and P. Zoller, “The cold atom hubbard tool- box,” Annals of Physics315, 52–79 (2005), special Issue

    work page 2005

Show all 39 references
  1. [9]

    Multi-component quantum gases in spin-dependent hexagonal lattices,

    P. Soltan-Panahi, J. Struck, P. Hauke, A. Bick, W. Plenkers, G. Meineke, C. Becker, P. Windpassinger, M. Lewenstein, and K. Sengstock, “Multi-component quantum gases in spin-dependent hexagonal lattices,” Nature Physics 7, 434–440 (2011)

    2011

  2. [10]

    Quantum phase transition to unconventional multi-orbital superfluidity in optical lattices,

    P. Soltan-Panahi, D.-S. Lühmann, J. Struck, P. Wind- passinger, and K. Sengstock, “Quantum phase transition to unconventional multi-orbital superfluidity in optical lattices,” Nature Physics8, 71–75 (2012)

    2012

  3. [11]

    Creating, moving and merging dirac points with a fermi gas in a tunable honeycomb lattice,

    L. Tarruell, D. Greif, T. Uehlinger, G. Jotzu, and T. Esslinger, “Creating, moving and merging dirac points with a fermi gas in a tunable honeycomb lattice,” Nature 483, 302–305 (2012)

    2012

  4. [12]

    Exact, complete, and universal continuous-time world- line monte carlo approach to the statistics of discrete quantum systems,

    N. V. Prokof’ev, B. V. Svistunov, and I. S. Tupitsyn, “Exact, complete, and universal continuous-time world- line monte carlo approach to the statistics of discrete quantum systems,” Journal of Experimental and Theo- retical Physics 87, 310–321 (1998)

    1998

  5. [13]

    Superfluid to mott insulator tran- sition of hardcore bosons in a superlattice,

    I. Hen and M. Rigol, “Superfluid to mott insulator tran- sition of hardcore bosons in a superlattice,” Phys. Rev. B 80, 134508 (2009)

    2009

  6. [14]

    Phase diagram for ultra- cold bosons in optical lattices and superlattices,

    P. Buonsante and A. Vezzani, “Phase diagram for ultra- cold bosons in optical lattices and superlattices,” Phys. Rev. A 70, 033608 (2004)

    2004

  7. [15]

    Quantum phases of ultracold bosonic atoms in a one-dimensional optical superlattice,

    A. Dhar, T. Mishra, R. V. Pai, and B. P. Das, “Quantum phases of ultracold bosonic atoms in a one-dimensional optical superlattice,” Phys. Rev. A83, 053621 (2011)

    2011

  8. [16]

    Quantum many-body dynam- ics of coupled double-well superlattices,

    P. Barmettler, A. M. Rey, E. Demler, M. D. Lukin, I. Bloch, and V. Gritsev, “Quantum many-body dynam- ics of coupled double-well superlattices,” Phys. Rev. A 78, 012330 (2008)

    2008

  9. [17]

    Exact study of the one- dimensional boson hubbard model with a superlattice po- tential,

    V. G. Rousseau, D. P. Arovas, M. Rigol, F. Hébert, G. G. Batrouni, and R. T. Scalettar, “Exact study of the one- dimensional boson hubbard model with a superlattice po- tential,” Phys. Rev. B73, 174516 (2006)

    2006

  10. [18]

    Topologi- cal edge states in the one-dimensional superlattice bose- hubbard model,

    F. Grusdt, M. Höning, and M. Fleischhauer, “Topologi- cal edge states in the one-dimensional superlattice bose- hubbard model,” Phys. Rev. Lett.110, 260405 (2013)

    2013

  11. [19]

    Probing local relaxation of cold atoms in 7 optical superlattices,

    A. Flesch, M. Cramer, I. P. McCulloch, U. Schollwöck, and J. Eisert, “Probing local relaxation of cold atoms in 7 optical superlattices,” Phys. Rev. A78, 033608 (2008)

    2008

  12. [20]

    Quan- tum phases of the bose-hubbard model in optical super- lattices,

    B.L. Chen, S.P. Kou, Y. Zhang, and S. Chen, “Quan- tum phases of the bose-hubbard model in optical super- lattices,” Phys. Rev. A81, 053608 (2010)

    2010

  13. [21]

    Fractional corner charges in a two-dimensional super- lattice bose-hubbard model,

    J. Bibo, I Lovas, Y. You, F. Grusdt, and F. Pollmann, “Fractional corner charges in a two-dimensional super- lattice bose-hubbard model,” Phys. Rev. B102, 041126 (2020)

    2020

  14. [22]

    Phase diagram of the hard-core bose-hubbard model on a checkerboard super- lattice,

    I. Hen, M. Iskin, and M. Rigol, “Phase diagram of the hard-core bose-hubbard model on a checkerboard super- lattice,” Phys. Rev. B81, 064503 (2010)

    2010

  15. [23]

    Optical superlattice for engineering hubbard couplings in quantum simula- tion,

    T. Chalopin, P. Bojović, D. Bourgund, S. Wang, T. Franz, I. Bloch, and T. Hilker, “Optical superlattice for engineering hubbard couplings in quantum simula- tion,” Phys. Rev. Lett.134, 053402 (2025)

    2025

  16. [24]

    Reentrant quantum phase transition in double-well op- tical lattices,

    I. Danshita, C. A. R. Sá de Melo, and C. W. Clark, “Reentrant quantum phase transition in double-well op- tical lattices,” Phys. Rev. A77, 063609 (2008)

    2008

  17. [25]

    Quantum phases of hardcore bosons with repulsive dipolar density- density interactions on two-dimensional lattices,

    J. A. Koziol, G. Morigi, and K. P. Schmidt, “Quantum phases of hardcore bosons with repulsive dipolar density- density interactions on two-dimensional lattices,” SciPost Phys. 17, 111 (2024)

    2024

  18. [26]

    Hubbard interaction at finite T on a Hexagonal lattice,

    L. Razmadze and T. Luu, “Hubbard interaction at finite T on a Hexagonal lattice,” PoS LA TTICE2024, 071 (2024)

    2024

  19. [27]

    Path-integral com- putation of superfluid densities,

    E. L. Pollock and D. M. Ceperley, “Path-integral com- putation of superfluid densities,” Phys. Rev. B36, 8343– 8352 (1987)

    1987

  20. [28]

    Refer- ence data for phase diagrams of triangular and hexagonal bosonic lattices,

    N. Teichmann, D. Hinrichs, and M. Holthaus, “Refer- ence data for phase diagrams of triangular and hexagonal bosonic lattices,” Europhysics Letters91, 10004 (2010)

    2010

  21. [29]

    Cluster gutzwiller method for bosonic lattice systems,

    D.-S. Lühmann, “Cluster gutzwiller method for bosonic lattice systems,” Phys. Rev. A87, 043619 (2013)

    2013

  22. [30]

    Equilibrium phases of two-dimensional bosons in quasiperiodic lattices,

    C. Zhang, A. Safavi-Naini, and B. Capogrosso- Sansone, “Equilibrium phases of two-dimensional bosons in quasiperiodic lattices,” Phys. Rev. A 91, 031604 (2015)

    2015

  23. [31]

    High- precision monte carlo study of several models in the three-dimensional u(1) universality class,

    W. Xu, Y. Sun, J.-P. Lv, and Y. Deng, “High- precision monte carlo study of several models in the three-dimensional u(1) universality class,” Phys. Rev. B 100, 064525 (2019)

    2019

  24. [32]

    Ordering, metasta- bility and phase transitions in two-dimensional systems,

    J. M. Kosterlitz and D. J. Thouless, “Ordering, metasta- bility and phase transitions in two-dimensional systems,” Journal of Physics C: Solid State Physics6, 1181 (1973)

    1973

  25. [33]

    Universal jump in the superfluid density of two-dimensional superfluids,

    D. R. Nelson and J. M. Kosterlitz, “Universal jump in the superfluid density of two-dimensional superfluids,” Phys. Rev. L 39, 1201 (1977)

    1977

  26. [34]

    Thermocrystallization of lattice dipolar bosons coupled to a high-finesse cavity,

    Y. Hebib, C. Zhang, M. Boninsegni, and B. Capogrosso- Sansone, “Thermocrystallization of lattice dipolar bosons coupled to a high-finesse cavity,” Phys. Rev. B 109, 174515 (2024)

    2024

  27. [35]

    Equilibrium phases of dipolar lattice bosons in the pres- ence of random diagonal disorder,

    C. Zhang, A. Safavi-Naini, and B. Capogrosso-Sansone, “Equilibrium phases of dipolar lattice bosons in the pres- ence of random diagonal disorder,” Phys. Rev. A 97, 013615 (2018)

    2018

  28. [36]

    Design of laser-coupled honeycomb opti- cal lattices supporting chern insulators,

    E. Anisimovas, F. Gerbier, T. Andrijauskas, and N. Goldman, “Design of laser-coupled honeycomb opti- cal lattices supporting chern insulators,” Phys. Rev. A 89, 013632 (2014)

    2014

  29. [37]

    Honeycomb optical lattices with harmonic confinement,

    J. Kusk Block and N. Nygaard, “Honeycomb optical lattices with harmonic confinement,” Phys. Rev. A81, 053421 (2010)

    2010

  30. [38]

    Observation of antiferromagnetic correla- tionsinthehubbardmodelwithultracoldatoms,

    Russell A Hart, Pedro M Duarte, Tsung-Lin Yang, Xinx- ing Liu, Thereza Paiva, Ehsan Khatami, Richard T Scalettar, Nandini Trivedi, David A Huse, and Ran- dall G Hulet, “Observation of antiferromagnetic correla- tionsinthehubbardmodelwithultracoldatoms,” Nature 519, 211–214 (2015)

    2015

  31. [39]

    Quantum gas magnifier for sub-lattice-resolved imaging of 3d quantum systems,

    Luca Asteria, Henrik P Zahn, Marcel N Kosch, Klaus Sengstock, and Christof Weitenberg, “Quantum gas magnifier for sub-lattice-resolved imaging of 3d quantum systems,” Nature 599, 571–575 (2021). 8 Table I. Fits of∆/t = 20 data to Eq. 4 with the correction exponentω = 0.789 is ...

    2021

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.