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arXiv:1205.6484 · Physical Review A

Superfluid to normal phase transition in strongly correlated bosons in two and three dimensions

Juan Carrasquilla, Marcos Rigol

Published Oct 26, 2012• 37 citations
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Abstract

Using quantum Monte Carlo simulations, we investigate the finite-temperature phase diagram of hard-core bosons ($XY$ model) in two- and three-dimensional lattices. To determine the phase boundaries, we perform a finite-size-scaling analysis of the condensate fraction and/or the superfluid stiffness. We then discuss how these phase diagrams can be measured in experiments with trapped ultracold gases, where the systems are inhomogeneous. For that, we introduce a method based on the measurement of the zero-momentum occupation, which is adequate for experiments dealing with both homogeneous and trapped systems, and compare it with previously proposed approaches.

DOI
10.1103/physreva.86.043629

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Using quantum Monte Carlo simulations, we investigate the finite-temperature phase diagram of hard-core bosons (XYXYXY model) in two- and three-dimensional lattices. To determine the phase boundaries, we perform a finite-size-scaling analysis of the condensate fraction and/or the superfluid stiffness. We then discuss how these phase diagrams can be measured in experiments with trapped ultracold gases, where the systems are inhomogeneous. For that, we introduce a method based on the measurement of the zero-momentum occupation, which is adequate for experiments dealing with both homogeneous and trapped systems, and compare it with previously proposed approaches.
Using quantum Monte Carlo simulations, we investigate the finite-temperature phase diagram of hard-core bosons ( XY model) in two-dimensional lattices. To determine the phase boundaries, we perform a finite-size-scaling analysis of the superfluid stiffness in two different ways and find that both approaches provide results of comparable accuracy. Furthermore, we discuss how such a phase diagram can be determined by measuring the occupancy of the zero momentum mode in homogeneous and trapped systems. The latter approach can be used in current experiments with ultracold gases.
We propose a general method for obtaining the finite temperature phase diagram of strongly correlated quantum models emulated by optical lattice experiments using only the density profile of atoms in the trap. We illustrate the procedure explicitly for the Bose-Hubbard model by using "exact" quantum Monte Carlo simulations in a trap with up to 10(6) bosons. We show that kinks in the local compressibility, arising from critical fluctuations, demarcate the boundaries between superfluid and normal phases in the trap. The temperature of the bosons in the optical lattice is determined from the density profile at the edge. Our method can be applied to other phase transitions even when reliable numerical results are not available.
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 investigate the temperature-dependent behavior emerging in the vicinity of the superfluid (SF) to Mott insulator (MI) transition of interacting bosons in a two-dimensional optical lattice, described by the Bose-Hubbard model. The equilibrium phase diagram at finite temperatures is computed by means of the cluster mean-field theory (CMF) where the effect of non-local correlations is analyzed systematically by finite-size scaling of the cluster size. The phase diagram exhibits a rich structure including a transition and a crossover of the SF and MI phases respectively to a normal fluid (NF) state at finite temperature. In order to characterize these phases, and the NF transition and crossover scales, we calculate, in addition to the condensate amplitude, the superfluid fraction, sound velocity and compressibility. The phase boundaries obtained by CMF with finite-size scaling agree quantitatively with quantum Monte Carlo (QMC) results as well as with experiments. The von Neumann entanglement entropy of a cluster exhibits critical enhancement near the SF-MI quantum critical point (QCP). We also discuss the behavior of the transition lines near this QCP at the particle-hole symmetric point located at the tip of a Mott lobe as well as away from particle-hole symmetry.
We determine the finite-temperature phase diagram of the square lattice hard-core boson Hubbard model with nearest neighbor repulsion using quantum Monte Carlo simulations. This model is equivalent to an anisotropic spin-1/2 XXZ model in a magnetic field. We present the rich phase diagram with a first order transition between a solid and superfluid phase, instead of a previously conjectured supersolid and a tricritical end point to phase separation. Unusual reentrant behavior with ordering upon increasing the temperature is found, similar to the Pomeranchuk effect in 3He.
We use quantum Monte Carlo (QMC) simulations to study the combined effects of harmonic confinement and temperature for bosons in a two-dimensional(2D) optical lattice. The scale-invariant, finite temperature state diagram is presented for the Bose-Hubbard model in terms of experimental parameters -- the particle number, confining potential and interaction strength. To distinguish the nature of the spatially separated superfluid, Mott insulator, and normal Bose liquid phases, we examine the local density, compressibility, superfluid density, and Green's function. In the annular superfluid rings, as the width of the ring decreases, the long-range superfluid correlations start to deviate from an equivalent homogeneous 2D system. At zero temperature, the correlation decay is intermediate between one-dimension and two-dimensions, while at a finite temperature, the decay is similar to that in one-dimension at a much lower temperature. The calculations reveal shortcomings of the local density approximation in describing superfluid properties of trapped bosons. We also present the finite-temperature phase diagram for the homogeneous two dimensional Bose-Hubbard model. We compare our state diagram with the results of a recent experiment at NIST on a harmonically trapped 2D lattice [Phys. Rev. Lett. 105, 110401 (2010)], and identify a finite-temperature effect in the experiment.