Pith. sign in

REVIEW 3 major objections 5 minor 1 cited by

Probing universal phase diagram of dimensional crossover with an atomic quantum simulator

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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

Pith's one-line read An interacting atomic gas produces the full finite-temperature dimensional-crossover phase diagram and the paper identifies five quantum-to-thermal routes in it

desk verdict Solid experimental map of dimensional crossover, but the fifth 'TFDC' transition type needs an independent superfluid-stiffness check before it becomes a reference. read the letter →

arxiv 2506.18464 v1 pith:K3ITLYBV submitted 2025-06-23 cond-mat.quant-gas

Jinyuan Tian , Zhongcheng Yu , Jing Liu , Chi-Kin Lai , Lorenzo Pizzino , Chengyang Wu , Hongmian Shui , Thierry Giamarchi
show 2 more authors
Hepeng Yao Xiaoji Zhou
This is my paper · ORCID
classification cond-mat.quant-gas
keywords dimensionalcrossoverquantumsimulatorBose-Einsteincondensateopticallatticezero-momentumfractionfinite-temperaturephasediagramuniversalityclassBose-Hubbardmodel
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

An interacting cold atomic gas in a lattice whose depths and temperature can be set independently is used to probe how effective dimensionality changes with temperature. The paper claims that, at low temperature, the gas realizes distinct quantum regimes of effective dimension 3, 2, 1, and 0, and that heating always produces a thermal phase sitting between the zero-dimensional and positive-dimensional regimes. It further claims that the quantum-to-thermal transition occurs through four known universality classes depending on dimension, and, in some anisotropy ranges, through a fifth class in which the 3D gas first becomes a 1D or 2D quantum gas before turning thermal. A sympathetic reader would care because this would provide a single controlled map of dimensional crossover, which could serve as a reference for anisotropic quantum materials.

What carries the argument

The load-bearing object is the zero-momentum fraction $f^i_c$ (Eq. 1): the fraction of atoms whose momentum lies within $\pm 2\pi/L_i$ of zero along direction $i$, extracted from time-of-flight images. It acts as a one-number coherence probe, and the bend in $f^i_c$ versus lattice depth, located by a piecewise fit, defines the critical depth $V_c$ separating coherent from incoherent coupling along that direction; at large depths the measured curve joins the harmonic-oscillator prediction for a single site, marking fully decoupled 0D systems. The same observable, together with the measured correlation length, separates the thermal regime from the 0D regime. For the fifth transition, the crossover temperatures are compared with the field-theory scale $T_{3\mathrm{-}1\mathrm{D}}=A_B t_\perp^{-\nu}$, $\nu=2K/(4K-1)$, where $K$ is the Luttinger parameter; this scale is what lets thermal fluctuations erase coherence along one direction while the other direction stays quantum. In the companion Monte Carlo calculation, the superfluid fraction computed from winding numbers plays the same role.

What would settle it

Perform an independent measurement of superfluid stiffness at the same $V_{2D}$, $V_{1D}$, and $T$ as the points labeled III–VI and I–II, for example by monitoring the momentum response to a small lattice boost: if the temperature at which stiffness vanishes does not match the $f_c$ breakpoint, or if the two drops in $f_y$ and $f_z$ at the TFDC points do not coincide with direction-dependent changes in the one-body correlation length, the claimed phase boundaries are an artifact of the fitting rule.

Watch

Extended reading notes

Core claim

The paper reports that a trapped rubidium-87 Bose–Einstein condensate loaded into a 2D triangular lattice plus a 1D lattice, with lattice depths and temperature independently varied, displays the full low-temperature hierarchy of quantum dimensional regimes: 3D when both tunnel couplings are coherent, 2D or 1D when one direction is incoherent, and 0D when all sites are decoupled. At finite temperature a thermal (classical) phase appears between the 0D regime and the positive-dimensional regimes, because the 0D regime is a gapped Mott insulator whose gap melts at the lowest temperature while coherence in higher dimensions survives thermal fluctuations longer. For fixed anisotropy, the heating path is claimed to belong to four known universality classes — BEC transition in 3D, Berezinskii–Kosterlitz–Thouless transition in 2D, Tomonaga–Luttinger-liquid transition in 1D, and Mott-gap melting in 0D — and, for a region of intermediate anisotropy, to a fifth 'TFDC' class in which the 3D quantum gas first loses coherence along one direction, becoming a 1D or 2D quantum gas, and only then enters the thermal phase; two distinct temperatures $T_1$ and $T_2$ separate the three stages. This assignment is anchored by agreement with quantum Monte Carlo superfluid-fraction phase diagrams and by the temperature formulas for the four standard transitions.

Load-bearing premise

The phase map rests entirely on the zero-momentum fraction $f_c$ being a faithful measure of coherence and on the piecewise-fit bend being the true transition boundary, with no independent order parameter such as measured superfluid stiffness to confirm it.

Editorial extensions

If this is right

  • For any anisotropic bosonic simulator whose inter-site tunneling is controlled by exponentially sensitive lattice depths, the same phase map should reappear, with the thermal phase always separating the 0D quantum regime from the positive-dimensional quantum regimes.
  • Heating a fixed-anisotropy system prepared near the 3D-to-low-D crossover should first erase coherence along the weaker direction and only later destroy the remaining low-dimensional quantum coherence, so temperature can be used as a directional coherence filter.
  • The standard transitions have calculable anchors: $T_{\mathrm{BEC}}$ for 3D, $T_{\mathrm{BKT}}$ for 2D, a correlation-length condition for 1D, and $T_{\mathrm{melt}}\sim 0.4\Delta/k_B$ for 0D, so other simulators can be benchmarked against these numbers.
  • Square or honeycomb lattice geometries should exhibit the same physics at correspondingly deeper potentials, since the crossover condition is the product $zt$ of tunneling and coordination number, not the lattice depth itself.

Reading between the lines

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

  • Beyond the paper: the same zero-momentum-fraction ruler could be applied to other momentum-resolved quantum simulator platforms, turning the phase-classification scheme into a generic finite-temperature diagnostic rather than a property of this particular lattice.
  • Beyond the paper: if the TFDC sequence is generic, layered or quasi-one-dimensional conductors should show two separated thermal scales — one where transverse coherence is lost and a higher one where the remaining low-dimensional order becomes thermal — which could be sought in anisotropic transport data.
  • Beyond the paper: comparing $f_c$ with a directly measured superfluid stiffness at the same lattice depths and temperatures would test whether the fifth transition is a genuinely new universality class or an artifact of classifying phases through a single observable.
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

3 major / 5 minor

Summary. The manuscript reports an ultracold-gas experiment in which a 87Rb Bose-Einstein condensate is loaded into a two-dimensional triangular lattice plus a one-dimensional lattice, with independent control of lattice depths along the xy-plane and z direction. By measuring the zero-momentum fraction fc along two directions and the first-order correlation function, the authors construct finite-temperature phase diagrams in the (V2D, V1D) plane and identify quantum 3D, 2D, 1D, and 0D regimes together with an intervening thermal regime. They further classify the quantum-to-thermal transition into four known universality classes (BEC, BKT, TLL, and Mott melting) and report a fifth, "TFDC" type in which a 3D quantum system first crosses into a low-dimensional quantum regime and only then becomes thermal. Quantum Monte Carlo simulations for homogeneous systems reproduce the overall topology of the experimental phase diagrams.

Significance. If established, this would be the first experimental realization of the full finite-temperature dimensional-crossover phase diagram for an interacting atomic simulator, including the proposed thermal-fluctuation-driven dimensional crossover (TFDC) transition. The paper has clear strengths: two complementary observables (fc and G^(1)) are used to locate boundaries; the QMC simulations provide an independent theoretical cross-check of the phase-diagram topology; the comparisons for the 3D and 2D transition temperatures use parameter-free textbook expressions and agree to 2.6% and 15.5%, respectively; and the data are deposited on Zenodo. The central novelty, however, rests on a single measured observable at two special points, and the universality-class assignment rests on one-point temperature matching rather than on a scaling or critical-exponent analysis. The claim is therefore defensible but not yet fully supported.

major comments (3)
  1. [Fig. 3, points I and II] The fifth TFDC transition type is inferred entirely from two breakpoints in fc^y and fc^z as functions of temperature. The G^(1) data shown in Fig. 3(a3) and (b3) are obtained by Fourier transforming the same measured momentum distributions used to compute fc, so they do not constitute an independent confirmation of an intermediate quantum regime. The intermediate plateau could in principle arise from a smooth, direction-dependent decoherence process in a finite trapped system rather than from a distinct low-dimensional quantum phase. I ask the authors to provide an independent order parameter for the intermediate regime, for example direction-resolved superfluid stiffness from QMC for the specific parameters of points I and II, or at minimum a quantitative model showing that the two-breakpoint structure cannot be reproduced by a smooth crossover.
  2. [Sec. "Common quantum-to-thermal transition", Eqs. (3)-(6)] The assignment of the four universality classes is based on comparing a single measured transition temperature with a textbook formula for each dimensionality. This is not sufficient to establish a universality class. In particular, Eq. (5) uses the hand-picked criterion ξ(T=T1D)=L/10 and agrees with experiment only within 31.8%, and Eq. (6) uses an ad hoc prefactor T_melt=0.4Δ/k_B. These comparisons do not discriminate, for example, a BKT transition from a crossover. The authors should either provide a scaling collapse, critical behavior of the order parameter, or finite-size QMC data showing diverging or universal quantities (e.g., superfluid-stiffness jump) for the relevant transitions.
  3. [Supplemental Sec. S3 and Methods III] The text states in S3 that fc is "as effective as the superfluid fraction" for determining crossover points, citing Refs. [23, 29], but this equivalence is not demonstrated for the present finite-temperature lattice system. The QMC phase diagrams in Fig. 2 use a superfluid-fraction threshold fs<0.1%, yet no QMC superfluid-fraction results are reported for the TFDC points I and II in Fig. 3. Since the TFDC claim rests on the existence of a regime in which coherence along z survives while coherence in the xy-plane is lost, the authors should compute and show fs^y and fs^z as functions of temperature for those two parameter sets. Without such data, the central novel claim is not yet supported by an independent probe.
minor comments (5)
  1. [Fig. 2 caption] The caption labels panels (a1)-(a4) but the text refers to (b1), (c1), and (d1); please make the panel labeling consistent.
  2. [Eq. (1)] The definition of fc contains n(k) with implicit normalization and integration over kx and kz; clarifying that n(k) is the momentum distribution normalized to the total atom number would improve readability.
  3. [Fig. 3] The caption says "The white region is the estimated transition temperature," but the plotted transition regions appear as shaded bands in the figures; please check the color description.
  4. [Sec. "Experimental sequence"] The sentence "With the images from the two probes along the x and z directions" is slightly confusing because fc^y is described as a probe of the y direction; please clarify which images correspond to which axis.
  5. [General] The paper would benefit from a short discussion of how the finite system size and harmonic trapping affect the extraction of the critical lattice depths Vc, especially since the QMC comparison is made with homogeneous systems and the quantitative agreement is only qualitative.

Circularity Check

0 steps flagged · score 2.0 of 10

No construction-level circularity: the phase diagram is cross-checked by QMC superfluid stiffness and transition temperatures against external formulas; only minor self-cited heuristics appear.

full rationale

The paper's central experimental observable is the zero-momentum fraction fc (Eq. 1), and the regime boundaries are obtained by piecewise fits. This is operational rather than circular: the same fc data are not used as the theoretical prediction. The QMC phase diagrams (Fig. 2(a2)-(d2)) are computed from superfluid stiffness, an independent observable, and reproduce the experimental phase diagrams; the transition temperatures are compared with parameter-free expressions for BEC (Eq. 3), BKT (Eq. 4) and with stated criteria for 1D (Eq. 5 with L/10) and 0D (Eq. 6 with 0.4 prefactor). The L/10 and 0.4 choices are explicit conventions, not hidden fits to the same data, and they affect only the quantitative comparison, not the existence of the two-breakpoint TFDC signature. Some methodological support is imported from self-cited prior work (Refs. [23,28,29], e.g. the claim in S3 that fc is as effective as superfluid fraction), and the TFDC intermediate regime is inferred from fc plateaus without a QMC superfluid-stiffness check at those specific points; these are robustness concerns, but no equation or fitted parameter reduces by construction to the claimed result. Therefore no significant circularity.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on three free-parameter-like conventions (0.4 prefactor, L/10 correlation-length criterion, and the QMC f_s threshold) plus four domain assumptions about the observable, the temperature labeling, the homogeneous QMC mapping, and the applicability of known transition formulas. No new physical entities are introduced; TFDC is a name for a crossover sequence, not a new particle or force.

free parameters (3)
  • 0D melting prefactor = 0.4
    In the Fig. 4(d) text, the paper states 'In practice, we take T_melt = 0.4 Delta/k_B = 28 nK' and then finds agreement with the observed 35 +/- 8 nK. The prefactor is not derived; using Delta/k_B = 57 nK would give a poorer match, so 0.4 is effectively chosen to fit the 0D boundary.
  • 1D TLL correlation-length criterion = xi(T = T_1D) = L/10
    The 1D transition temperature is predicted by setting the TLL correlation length to L/10, stated as 'In practice, we take xi(T=T_1D)=L/10'. This convention is arbitrary and directly sets T_1D; a different fraction would change the predicted temperature and the claimed agreement, which is within 31.8% in Fig. 4(c).
  • QMC superfluid-fraction threshold = f_s < 0.1%
    The QMC phase boundaries are defined by the criterion f_s < 0.1%, cited from reference [28]. This threshold, rather than a physics-derived condition, sets the numerical phase diagram in Fig. 2(a2)-(d2).
assumptions (4)
  • domain assumption The zero-momentum fraction f_c is a faithful, quantitative order parameter for coherence or superfluid order along a given direction.
    All experimental phase boundaries use f_c (Eq. 1) with a piecewise fit; no independent order parameter is measured. The assumption is supported by references [23,28,29,33] but is not verified in this experiment.
  • domain assumption Adiabatic lattice loading keeps the system isentropic, so the initial BEC temperature labels the final lattice system's temperature.
    The paper states 'we always load the lattice adiabatically and thus each diagram is isentropic' and reports diagrams at initial BEC temperatures. Any heating or entropy change during the 80 ms ramp and 20 ms hold would shift the effective temperatures.
  • domain assumption A homogeneous Bose-Hubbard model simulated by QMC captures the universal phase diagram of the trapped, inhomogeneous experiment.
    Fig. 2 compares experimental diagrams with QMC for 'equivalent homogeneous systems'; only qualitative agreement is claimed, so the mapping of trap parameters into homogeneous lattice parameters is an approximation.
  • domain assumption Known finite-temperature transition formulas for BEC, BKT, TLL, and Mott melting are applicable to the trapped finite-size system and can identify universality classes by a transition-temperature comparison.
    The classification in Fig. 4 compares single transition temperatures with Eqs. (3)-(6); this assumes no size or geometry corrections that would change the class assignment.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Probing universal phase diagram of dimensional crossover with an atomic quantum simulator." pith.science (2026). https://pith.science/paper/K3ITLYBV

@misc{pith2026250618464,
  author       = {Pith},
  title        = {Pith review of: Probing universal phase diagram of dimensional crossover with an atomic quantum simulator},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/K3ITLYBV}},
  note         = {Machine review of arXiv:2506.18464}
}
read the original abstract

Dimensionality is a fundamental concept in physics, which plays a hidden but crucial role in various domains, including condensed matter physics, relativity and string theory, statistical physics, etc. In quantum physics, reducing dimensionality usually enhances fluctuations and leads to novel properties. Owing to these effects, quantum simulators in which dimensionality can be controlled have emerged as a new area of interest. However, such a platform has only been studied in specific regimes and a universal phase diagram is lacking. Here, we produce an interacting atomic quantum simulator with continuous tunability of anisotropy and temperature, and probe the universal phase diagram of dimensional crossover. At low temperatures, we identify the regimes from quantum three to zero dimensions. By increasing temperature, we observe the non-trivial emergence of a thermal regime situated between the quantum zero and integer dimensions. We show that the quantum-to thermal transition falls into four different universality classes depending on the dimensionality. Surprisingly, we also detect a fifth type where the high-dimensional quantum system can reach the thermal phase by crossing a low-dimensional quantum regime. Our results provide a crucial foundation for understanding the projective condensed matter structures in unconventional dimensions.

Figures

Figures reproduced from arXiv: 2506.18464 by the authors.

Figure 1
Figure 1. Illustration of the experiment. (a1) Sketch of the BEC system loading into a laser potential consisting of crossover optical dipole trap (OT, red cylinders), 1D optical lattice (1D OL, green arrows, z direction) and 2D triangular optical lattices (OL, blue arrows, x-y plane). The gravity is along the y-direction, while 1D lattice is aligned along the z-direction. The yellow arrows show the two probes. (a2) The momen… view at source ↗
Figure 2
Figure 2. The universal phase diagram of dimensional crossover at different temperatures. (a1)-(a4) are the experimentally measured phase diagrams at initial BEC temperatures T = 23(5), 36(3), 199(25) and 223(29) nK, as a function of the lattice amplitudes V2D and V1D. Here, we observe quantum regimes at 3D (purple), 2D (blue), 1D (green), 0D (yellow) as well as the thermal regime (TH, red). The transition points are judged b… view at source ↗
Figure 3
Figure 3. Special category of finite temperature transition We show the zero-momentum fraction along two directions f y c (blue circles) and f z c (green circles) as a function of temperature T, for two different cases: (a1) V2D = 3.0 Er, V1D = 20.0 Er and (b1) V2D = 7.0 Er, V1D = 5.0 Er. Error bars represent the standard de￾viation of five measurements. The colored areas represent the judged regimes. The white region is the … view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: The common quantum-to-thermal transition for differ￾ent integer dimensionalites The behavior of zero-momentum frac￾tion fc along the y (blue) and z (green) directions as a function of temperature T. At the lowest temperature, the system is a quantum gas in the 3D (a, V…

Review history (2 revisions) →

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. Magnetic Field Induced Band Deformation in a Lieb Lattice:Aharonov-Bohm Caging and Zeeman Splitting

    cond-mat.quant-gas 2025-08 reject novelty 2.0 of 10

    Spin-resolved flat bands in a magnetized Lieb lattice are simply the zero-field bands shifted by ±Bz, because the Hamiltonian is block diagonal in spin.

Reference graph

Works this paper leans on

48 extracted references · 44 canonical work pages · cited by 1 Pith paper

  1. [1]

    R. M. Wald,General relativity(University of Chicago press, 2010)

    2010

  2. [2]

    Akkermans,Statistical mechanics and quantum fields on fractals, Contemp

    E. Akkermans,Statistical mechanics and quantum fields on fractals, Contemp. Math.601, 1 (2013)

    work page 2013

  3. [3]

    Jagannathan,The fibonacci quasicrystal: Case study of hidden dimensions and multifractality, Rev

    A. Jagannathan,The fibonacci quasicrystal: Case study of hidden dimensions and multifractality, Rev. Mod. Phys.93, 045001 (2021)

    work page 2021

  4. [4]

    Pathria and P

    R. Pathria and P. D. Beale, inStatistical Mechanics (Fourth Edi- tion)(Academic Press, 2022)

    work page 2022

  5. [5]

    Orenstein and A

    J. Orenstein and A. J. Millis,Advances in the physics of high- temperature superconductivity, Science288, 468 (2000)

    work page 2000

  6. [6]

    Giamarchi,Theoretical framework for quasi-one dimen- sional systems, Chem

    T. Giamarchi,Theoretical framework for quasi-one dimen- sional systems, Chem. Rev.104, 5037 (2004)

    work page 2004

  7. [7]

    Jerome and C

    D. Jerome and C. Bourbonnais,Quasi one-dimensional organic conductors: from Fröhlich conductivity and Peierls insulating state to magnetically-mediated superconductivity, a retrospec- tive, Comptes Rendus. Physique25, 17 (2024)

    work page 2024

  8. [8]

    M. I. Eremets,High Pressure Experimental Methods(Oxford University Press, 1996)

    work page 1996

Show all 48 references
  1. [9]

    Dressel, K

    M. Dressel, K. Petukhov, B. Salameh, P. Zornoza, and T. Gi- amarchi,Scaling behavior of the longitudinal and transverse transport in quasi-one-dimensional organic conductors, Phys. Rev. B71, 075104 (2005)

    2005

  2. [10]

    Bloch, J

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

    2008

  3. [11]

    Hadzibabic and J

    Z. Hadzibabic and J. Dalibard,Two-dimensional Bose flu- ids: An atomic physics perspective, Riv. Nuovo Cim.34, 389 (2011)

    2011

  4. [12]

    M. A. Cazalilla, R. Citro, T. Giamarchi, E. Orignac, and M. Rigol,One dimensional bosons: From condensed matter systems to ultracold gases, Rev. Mod. Phys.83, 1405 (2011)

    2011

  5. [13]

    Paredes, A

    B. Paredes, A. Widera, V . Murg, O. Mandel, S. Folling, I. Cirac, GV. Shlyapnikov, TW. Hansch, and I. Bloch,Tonks-Girardeau gas of ultracold atoms in an optical lattice, Nature429, 277 (2004)

    2004

  6. [14]

    Kinoshita, T

    T. Kinoshita, T. Wenger, and D. S. Weiss,Observation of a one- dimensional Tonks-Girardeau gas, Science305, 1125 (2004)

    2004

  7. [15]

    Giamarchi,Quantum physics in one dimension, vol

    T. Giamarchi,Quantum physics in one dimension, vol. 121 of International Series of Monographs on Physics(Oxford Uni- versity Press, Oxford, 2004)

    2004

  8. [16]

    Goldman, J

    N. Goldman, J. Dalibard, A. Dauphin, F. Gerbier, M. Lewen- stein, P. Zoller, and I. B. Spielman,Direct imaging of topolog- ical edge states in cold-atom systems, Proc. Natl. Acad. Sci. U.S.A.110, 6736 (2013)

    2013

  9. [17]

    Tarnowski, F

    M. Tarnowski, F. N. Ünal, N. Fläschner, B. S. Rem, A. Eckardt, K. Sengstock, and C. Weitenberg,Measuring topology from dy- namics by obtaining the Chern number from a linking number, Nat. Commun.10, 1728 (2019)

    2019

  10. [18]

    Struck, C

    J. Struck, C. Ölschläger, R. L. Targat, P. Soltan-Panahi, A. Eckardt, M. Lewenstein, P. Windpassinger, and K. Seng- stock,Quantum simulation of frustrated classical magnetism in triangular optical lattices, Science333, 996 (2011)

    2011

  11. [19]

    Hadzibabic, P

    Z. Hadzibabic, P. Krüger, M. Cheneau, B. Battelier, and J. Dal- ibard,Berezinskii–kosterlitz–thouless crossover in a trapped atomic gas, Nature441, 1118 (2006)

    2006

  12. [20]

    Ha, C.-L

    L.-C. Ha, C.-L. Hung, X. Zhang, U. Eismann, S.-K. Tung, and C. Chin,Strongly interacting two-dimensional bose gases, Phys. Rev. Lett.110, 145302 (2013)

    2013

  13. [21]

    Chauveau, C

    G. Chauveau, C. Maury, F. Rabec, C. Heintze, G. Brochier, S. Nascimbene, J. Dalibard, J. Beugnon, S. M. Roccuzzo, and S. Stringari,Superfluid fraction in an interacting spatially mod- ulated Bose-Einstein condensate, Phys. Rev. Lett.130, 226003 (2023)

    2023

  14. [22]

    J. Tao, M. Zhao, and I. B. Spielman,Observation of anisotropic superfluid density in an artificial crystal, Phys. Rev. Lett.131, 163401 (2023)

    2023

  15. [23]

    Y . Guo, H. Yao, S. Ramanjanappa, S. Dhar, M. Horvath, L. Pizzino, T. Giamarchi, M. Landini, and H.-C. Nägerl,Obser- vation of the 2D–1D crossover in strongly interacting ultracold bosons, Nat. Phys.20, 934 (2024)

    2024

  16. [24]

    Karkihalli Umesh, J

    K. Karkihalli Umesh, J. Schulz, J. Schmitt, M. Weitz, G. von Freymann, and F. Vewinger,Dimensional crossover in a quan- tum gas of light, Nat. Phys.20, 1810 (2024)

    2024

  17. [25]

    A. Ho, M. Cazalilla, and T. Giamarchi,Deconfinement in a 2D optical lattice of coupled 1D boson systems, Phys. Rev. Lett. 92, 130405 (2004)

    2004

  18. [26]

    M. A. Cazalilla, A. F. Ho, and T. Giamarchi,Interacting bose gases in quasi-one-dimensional optical lattices, New J. Phys. 8, 158 (2006)

    2006

  19. [27]

    Bollmark, N

    G. Bollmark, N. Laflorencie, and A. Kantian,Dimensional crossover and phase transitions in coupled chains: Density ma- trix renormalization group results, Phys. Rev. B102, 195145 (2020)

    2020

  20. [28]

    H. Yao, L. Pizzino, and T. Giamarchi,Strongly-interacting bosons at 2D-1D dimensional crossover, SciPost Phys.15, 050 (2023)

    2023

  21. [29]

    Pizzino, H

    L. Pizzino, H. Yao, and T. Giamarchi,Finite size analysis for interacting bosons at the one-two dimensional crossover, Phys. Rev. Res.7, 013021 (2025)

    2025

  22. [30]

    S. Jin, X. Guo, P. Peng, X. Chen, X. Li, and X. Zhou,Finite temperature phase transition in a cross-dimensional triangular lattice, New J. Phys.21, 073015 (2019)

    2019

  23. [31]

    S. Jin, W. Zhang, X. Guo, X. Chen, X. Zhou, and X. Li,Evi- dence of potts-nematic superfluidity in a hexagonalsp 2 optical lattice, Phys. Rev. Lett.126, 035301 (2021)

    2021

  24. [32]

    Greiner, O

    M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch,Quantum phase transition from a superfluid to a mott insulator in a gas of ultracold atoms, Nature415, 39 (2002)

    2002

  25. [33]

    Plisson, B

    T. Plisson, B. Allard, M. Holzmann, G. Salomon, A. Aspect, P. Bouyer, and T. Bourdel,Coherence properties of a two- dimensional trapped bose gas around the superfluid transition, Phys. Rev. A84, 061606 (2011)

    2011

  26. [34]

    Y . Kato, Q. Zhou, N. Kawashima, and N. Trivedi,Sharp peaks in the momentum distribution of bosons in optical lattices in the normal state, Nat. Phys.4, 617 (2008). 8

    2008

  27. [35]

    DeMarco, C

    B. DeMarco, C. Lannert, S. Vishveshwara, and T.-C. Wei, Structure and stability of mott-insulator shells of bosons trapped in an optical lattice, Phys. Rev. A71, 063601 (2005)

    2005

  28. [36]

    H. Yao, T. Giamarchi, and L. Sanchez-Palencia,Lieb-liniger bosons in a shallow quasiperiodic potential: Bose glass phase and fractal mott lobes, Phys. Rev. Lett.125, 060401 (2020)

    2020

  29. [37]

    Pitaevskii and S

    L. Pitaevskii and S. Stringari,Bose-Einstein Condensation (Clarendon Press, Oxford, 2003)

    2003

  30. [38]

    M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell,Observation of Bose-Einstein Condensation in a dilute atomic vapor, Science269, 198 (1995)

    1995

  31. [39]

    Prokof’ev, O

    N. Prokof’ev, O. Ruebenacker, and B. Svistunov,Critical point of a weakly interacting two-dimensional bose gas, Phys. Rev. Lett.87, 270402 (2001)

    2001

  32. [40]

    Pilati, S

    S. Pilati, S. Giorgini, and N. Prokof’ev,Critical temperature of interacting bose gases in two and three dimensions, Phys. Rev. Lett.100, 140405 (2008)

    2008

  33. [41]

    Del Maestro and I

    A. Del Maestro and I. Affleck,Interacting bosons in one dimen- sion and the applicability of luttinger-liquid theory as revealed by path-integral quantum monte carlo calculations, Phys. Rev. B82, 060515 (2010)

    2010

  34. [42]

    Gerbier,Boson mott insulators at finite temperatures, Phys

    F. Gerbier,Boson mott insulators at finite temperatures, Phys. Rev. Lett.99, 120405 (2007). [43]Data set is available from zenodo at doi: 10.5281/zen- odo.15308183

    2007 doi

  35. [44]

    Y . Guo, H. Yao, S. Dhar, L. Pizzino, M. Horvath, T. Giamarchi, M. Landini, and H.-C. Nägerl,Anomalous cooling of bosons by dimensional reduction, Sci. Adv.10, eadk6870 (2024)

    2024

  36. [45]

    Fabbri, M

    N. Fabbri, M. Panfil, D. Clément, L. Fallani, M. Inguscio, C. Fort, and J.-S. Caux,Dynamical structure factor of one- dimensional bose gases: Experimental signatures of beyond- luttinger-liquid physics, Phys. Rev. A91, 043617 (2015)

    2015

  37. [46]

    Meinert, M

    F. Meinert, M. Panfil, M. J. Mark, K. Lauber, J.-S. Caux, and H.-C. Nägerl,Probing the excitations of a lieb-liniger gas from weak to strong coupling, Phys. Rev. Lett.115, 085301 (2015)

    2015

  38. [47]

    K.-Y . Li, Y . Zhang, K. Yang, K.-Y . Lin, S. Gopalakrishnan, M. Rigol, and B. L. Lev,Rapidity and momentum distributions of one-dimensional dipolar quantum gases, Phys. Rev. A107, L061302 (2023)

    2023

  39. [48]

    Boninsegni, N

    M. Boninsegni, N. Prokof’ev, and B. Svistunov,Worm algo- rithm for continuous-space path integral monte carlo simula- tions, Phys. Rev. Lett.96, 070601 (2006)

    2006

  40. [49]

    Boninsegni, N

    M. Boninsegni, N. V . Prokof’ev, and B. V . Svistunov,Worm algorithm and diagrammatic monte carlo: A new approach to continuous-space path integral monte carlo simulations, Phys. Rev. E74, 036701 (2006). 9 Supplemental Material for Probing universal phase diagram of dimensiona...

    2006

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.