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arXiv:2204.02240 · SciPost Physics

Strongly-interacting bosons at 2D-1D dimensional crossover

Hepeng Yao, Lorenzo Pizzino, Thierry Giamarchi

Published Aug 7, 2023• 16 citations
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Abstract

We study a two dimensional (2D) system of interacting quantum bosons, subjected to a continuous periodic potential in one direction. The correlation of such system exhibits a dimensional crossover between a canonical 2D behavior with Berezinski-Kosterlitz-Thouless (BKT) properties and a one-dimensional (1D) behavior when the potential is large and splits the system in essentially independent tubes. The latter is in the universality class of Tomonaga-Luttinger liquids (TLL). Using a continuous quantum Monte Carlo method, we investigate this dimensional crossover by computing longitudinal and transverse superfluid fraction as well as the superfluid correlation as a function of temperature, interactions and potential. Especially, we find the correlation function evolves from BKT to TLL type, with special intermediate behaviors appearing at the dimensional crossover. We discuss how the consequences of the dimensional crossover can be investigated in cold atomic gases experiments.

DOI
10.21468/scipostphys.15.2.050

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We study a two dimensional (2D) system of interacting quantum bosons, subjected to a continuous periodic potential in one direction. The correlation of such system exhibits a dimensional crossover between a canonical 2D behavior with Berezinski-Kosterlitz-Thouless (BKT) properties and a one-dimensional (1D) behavior when the potential is large and splits the system in essentially independent tubes. The latter is in the universality class of Tomonaga-Luttinger liquids (TLL). Using a continuous quantum Monte Carlo method, we investigate this dimensional crossover by computing longitudinal and transverse superfluid fraction as well as the superfluid correlation as a function of temperature, interactions and potential. Especially, we find the correlation function evolves from BKT to TLL type, with special intermediate behaviors appearing at the dimensional crossover. We discuss how the consequences of the dimensional crossover can be investigated in cold atomic gases experiments.
We study the universal critical behavior of two-dimensional (2D) lattice bosonic gases at the Berezinskii-Kosterlitz-Thouless (BKT) transition, which separates the low-temperature superfluid phase from the high-temperature normal phase. For this purpose, we perform quantum Monte Carlo simulations of the hard-core Bose-Hubbard (BH) model at zero chemical potential. We determine the critical temperature by using a matching method that relates finite-size data for the BH model with corresponding data computed in the classical XYXYXY model. In this approach, the neglected scaling corrections decay as inverse powers of the lattice size LLL, and not as powers of 1/lnL1/\mathrm{ln}L1/lnL, as in more standard approaches, making the estimate of the critical temperature much more reliable. Then, we consider the BH model in the presence of a trapping harmonic potential, and we verify the universality of the trap-size dependence at the BKT critical point. This issue is relevant for experiments with quasi-2D trapped cold atoms.
We study the thermodynamic properties of a 2D array of coupled one-dimensional Bose gases. The system is realized with ultracold bosonic atoms loaded in the potential tubes of a two-dimensional optical lattice. For negligible coupling strength, each tube is an independent weakly interacting 1D Bose gas featuring Tomonaga Luttinger liquid behavior. By decreasing the lattice depth, we increase the coupling strength between the 1D gases and allow for the phase transition into a 3D condensate. We extract the phase diagram for such a system and compare our results with theoretical predictions. Because of the high effective mass across the periodic potential and the increased 1D interaction strength, the phase transition is shifted to large positive values of the chemical potential. Our results are prototypical to a variety of low-dimensional systems, where the coupling between the subsystems is realized in a higher spatial dimension such as coupled spin chains in magnetic insulators.
We experimentally investigate the quantum criticality and Tomonaga-Luttinger liquid (TLL) behavior within one-dimensional (1D) ultracold atomic gases. Based on the measured density profiles at different temperatures, the universal scaling laws of thermodynamic quantities are observed. The quantum critical regime and the relevant crossover temperatures are determined through the double-peak structure of the specific heat. In the TLL regime, we obtain the Luttinger parameter by probing sound propagation. Furthermore, a characteristic power-law behavior emerges in the measured momentum distributions of the 1D ultracold gas, confirming the existence of the TLL.
We study a two-dimensional (2D) array of coupled 1D tubes of interacting bosons. Such systems can be produced by loading ultracold atoms in anisotropic optical lattices. We investigate the effects of coupling the tubes via hopping of the bosons (i.e. Josephson coupling). In the absence of a periodic potential along the tubes, or when such potential is incommensurate with the boson density, the system undergoes a transition from an array of incoherent Tomonaga–Luttinger liquids at high temperature to an anisotropic Bose–Einstein condensate (BEC), at low temperature. We determine the transition temperature and long wavelength excitations of the BEC. In addition to the usual gapless (Goldstone) mode found in standard superfluids, we also find a gapped mode associated with fluctuations of the amplitude of the order parameter. When a commensurate periodic potential is applied along the tubes, they can become 1D Mott insulators. Intertube hopping leads to a deconfinement quantum phase transition between the 1D Mott insulators and the anisotropic BEC. We also take into account the finite size of the gas tubes as realized in actual experiments. We map out the phase diagram of the quasi-1D lattice and compare our results with the existing experiments on such systems.
In this work, we extend the analysis of interacting bosons at 2D-1D dimensional crossover for finite size and temperature by using the field theory approach ( b o s o n i z a t i o n ) and quantum Monte Carlo simulations. Stemming from the fact that finite size low-dimensional systems are allowed only to have quasiordered phase, we consider the self-consistent harmonic approximation to compute the fraction of quasicondensate and its scaling with the system size. It allows us to understand the important role played by finite size and temperature across the dimensional crossover for deciding the condensate nature. Furthermore, we consider a mean-field approximation to compute the finite size effect on the crossover temperature for both weak and strong interactions. All the physical quantities we discuss here provide essential information for quantum gas at dimensional crossover and are directly detectable in cold atom experiments.
We study the phase diagram of two-dimensional, interacting bosons in the presence of a correlated disorder in continuous space, by using large-scale quantum Monte Carlo simulations at finite temperature. We show that the superfluid transition is strongly protected against disorder. It remains of the Berezinskii-Kosterlitz-Thouless type up to disorder strengths comparable to the chemical potential. Moreover, we study the transport properties in the strong disorder regime where a zero-temperature Bose-glass phase is expected. We show that the conductance exhibits a thermally activated behavior vanishing only at zero temperature. Our results point towards the existence of a Bose bad-metal phase as a precursor of the Bose-glass phase.