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arXiv:1610.03603 · Physical Review A

Quantitative studies of the critical regime near the superfluid-to-Mott-insulator transition

Hao Lee, Shiang Fang, Daw-Wei Wang

Published May 22, 2017• 2 citations
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Abstract

We investigate the critical behaviors of correlation length and critical exponents for strongly interacting bosons in a two-dimensional optical lattice via quantum Monte Carlo simulations. By comparing the full numerical results to those given by the effective theory, we quantitatively determine the critical regime where the universal scaling behaviors apply at a finite temperature, for both classical Berezinskii-Kosterlitz-Thouless transition and quantum phase transition from superfluid to Mott insulator. Our results represent the critical regime that should be observed in present experimental conditions.

DOI
10.1103/physreva.95.053622

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We investigate the critical behaviors of correlation length and critical exponents for strongly interacting bosons in a two-dimensional optical lattice via quantum Monte Carlo simulations. By comparing the full numerical results to those given by the effective theory, we quantitatively determine the critical regime where the universal scaling behaviors apply at a finite temperature, for both classical Berezinskii-Kosterlitz-Thouless transition and quantum phase transition from superfluid to Mott insulator. Our results represent the critical regime that should be observed in present experimental conditions.
We present numerical simulations on a lattice model of bosons in two dimensions using a path integral quantum Monte Carlo algorithm. At finite temperature we observe the Kosterlitz-Thouless transition and by a finite-size analysis determine the transition temperature. In the limit of zero temperature we find two distinct phases: at a special commensurate density (number of bosons integer multiple of the number of sites), the system is superfluid for small values of the interaction, but the superfluidity vanishes at a critical value of the interaction and the system becomes a Mott insulator. For an incommensurate density, the system remains superfluid at all values of the repulsive interaction between bosons. The superfluid density, however, vanishes as a commensurate density is approached for sufficiently large interaction. We estimate the critical exponents for these transitions.
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 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 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.
We perform large-scale quantum Monte Carlo (QMC) simulations for strongly interacting bosons in a two-dimensional optical lattice trap and confirm an excellent agreement with the benchmarking in situ density measurements by the Chicago group [N. Gemelke et al., Nature (London) 460, 995 (2009)]. We further present a general finite-temperature phase diagram for both the uniform and the trapped systems, demonstrating how the universal scaling properties near the superfluid-to-Mott insulator transition can be observed from the in situ density profile. The characteristic temperature to find such quantum criticality is estimated to be of the order of the single-particle bandwidth, which should be achievable in the present experiments. Finally, we examine the validity regime of the local fluctuation-dissipation theorem, which can be a used as a thermometry in the strongly interacting regime.
We present numerical evidence from Monte Carlo simulations that the superfluid-insulator quantum phase transition of interacting bosons subject to strong disorder in one dimension is controlled by the strong-randomness critical point. At this critical point the distribution of superfluid stiffness over disorder realizations develops a power-law tail reflecting a universal distribution of weak links. The Luttinger parameter on the other hand does not take on a universal value at this critical point, in marked contrast to the known Berezinskii-Kosterlitz-Thouless-like superfluid-insulator transition in weakly disordered systems. We develop a finite-size scaling procedure which allows us to directly compare the numerical results from systems of linear size up to 1024 sites with theoretical predictions obtained by Altman et al. [Phys. Rev. Lett. 93, 150402 (2004)] using a strong disorder renormalization group approach. The data shows good agreement with the scaling expected at the strong-randomness critical point.