Anomalous Quantum Glass of Bosons in a Random Potential in Two Dimensions

Abstract

We present a quantum Monte Carlo study of the "quantum glass" phase of the 2D Bose-Hubbard model with random potentials at filling ρ = 1. In the narrow region between the Mott and superfluid phases the compressibility has the form κ ∼ exp(−b/T α ) + c with α < 1 and c vanishing or very small. Thus, at T = 0 the system is either incompressible (a Mott glass) or nearly incompressible (a Mott-glass-like anomalous Bose glass). At stronger disorder, where a glass reappears from the superfluid, we find a conventional highly compressible Bose glass. On a path connecting these states, away from the superfluid at larger Hubbard repulsion, a change of the disorder strength by only 10% changes the low-temperature compressibility by more than four orders of magnitude, lending support to two types of glass states separated by a phase transition or a sharp cross-over. PACS numbers: 64.70.Tg, 67.85.Hj, 67.10.Fj There are two types of ground states of interacting lattice bosons in the absence of disorder; the superfluid (SF) and the Mott-insulator (MI). In the Bose-Hubbard model (BHM) with repulsive on-site interactions [1,2] an MI state has an integer number of particles per site and there is a gap to states with added or removed particles. The gapless SF can have any filling fraction. These phases and the quantum phase transitions between them are well understood [1][2][3][4][5][6] and have been realized experimentally with ultracold atoms in optical lattices [7,8].If disorder in the form of random site potentials is introduced in the BHM (which can also be accomplished in optical lattices [9,10]) a third state appears-an insulating but gapless quantum glass. This state has been the subject of numerous studies [1][2][3][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] but many of its properties are still not well understood. Two types of glass states are known; the compressible Bose glass (BG) and the incompressible Mott glass (MG), with the latter commonly believed to appear only at commensurate filling fractions in systems with particle-hole symmetry [18][19][20][26][27][28][29]. The currently prevailing notion is that the glass state in the 2D BHM with random potentials is always of the compressible BG type [20][21][22]25].We here present quantum Monte Carlo (QMC) results for the two-dimensional (2D) site-disordered BHM, showing that there is actually an extended parameter region in which the BG is either replaced by an MG or has an anomalously small (in practice undetectable) compressibility. The system is described by the Hamiltonianwhere ij are nearest neighbors on the square lattice, bsite occupation numbers, and ǫ i random potentials uniformly distributed in the range [−Λ − µ, Λ − µ] about the average chemical potential µ. We study the model using the stochastic series expansion (SSE) QMC method with directed loop updates [30]. We adjust the chemical potential so that the mean filling-fraction ρ = n i = 1 (to within < 10 −5 ) when averaged over sites i, disorder realizations, quantum and thermal ...

Bose and Mott glass phases in dimerized quantum antiferromagnets

“…Such phases have also been seen in other materials [26][27][28][29] and in quantum Monte Carlo simulations [30][31][32][33][34].…”

“…Any such BoseHubbard-like model may be treated using the methods outlined here, with the microscopic differences appearing only in the UV-scale starting values of the flow parameters. This prediction lends weight to previous numerical quantum Monte-Carlo work [31,34]. It may also explain the controversy over the existence of a direct MI/SF transition at the tips of the Mott lobes in the disordered Bose-Hubbard model: previous works which used compressibility as the criterion for the onset of a glassy phase will necessarily have missed the transition between the Mott insulator and the Mott glass.…”

“…The key question we are trying to answer in the present work is whether the glassy phase formed in disordered Bose-Hubbard models is always a compressible Bose glass [46], or if the more elusive incompressible Mott glass may exist at the high-symmetry tips of the Mott lobes [30,31,33,34]. First seen in 1d fermion systems [47,48], the Mott glass has also been predicted to exist in the O(2) quantum rotor model [49][50][51][52], which maps to the Bose-Hubbard model at commensurate fillings, and has been experimentally observed in the disordered quantum antiferromagnet DTN [25].…”

Measuring the Edwards-Anderson order parameter of the Bose glass: A quantum gas microscope approach

“…Numerically, q appears to be bounded from above by the value of the variance κ = ij [ n i n j − n i n j ]. Previous studies have shown that the variance is suppressed near the tip of the Mott lobes [38,39], with some suggesting that it vanishes entirely [66,67]. The suppression of κ results in the corresponding suppression of q in the vicinity of the tips of the Mott lobes, where we would in any case expect local mean-field theory to break down.…”

Directed-Loop Quantum Monte Carlo Method for Retarded Interactions

“…For the vertices defined by Eqs. (8) and (9) of the main text, we have to distinguish two cases: the directed loop either hits a unit operator, or any other operator. For the former case, the path goes straight through the subvertex with probability 1 and changes its vertex type.…”