Density matrix renormalization group for disordered bosons in one dimension

Abstract

We calculate the zero-temperature phase diagram of the disordered Bose-Hubbard model in one dimension using the density matrix renormalization group. For integer filling the Mott insulator is always separated from the superfluid by a Bose glass phase. There is a reentrance of the Bose glass both as a function of the repulsive interaction and of disorder. At half-filling where no Mott insulator exists, the superfluid density has a maximum where the kinetic and repulsive energies are about the same. Superfluidity is suppressed both for small and very strong repulsion but is always monotonic in disorder.

Phase Transition of Interacting Disordered Bosons in One Dimension

“…One interesting possibility, which was argued in [2], was the possibility of the existence of two localized phases, the BG corresponding to a strong interaction, strong disorder fixed point while another would correspond to a weak interaction, strong disorder fixed point. These predictions on the phase diagram and the flow were found to be in good agreement with numerical studies of this problem [4,5].…”

“…It can be obtained from the Euclidean action S as FðxÞ ¼ 0 he i½ðx;0ÞÀð0;0Þ i S . Performing the perturbation theory with respect to (5) and taking into account the flow of parameters, one obtains for jxj ) a …”

Bose-Hubbard model with random impurities: Multiband and nonlinear hopping effects

“…The phase diagram of the disordered Bose-Hubbard model has been studied by a number of methods including the quantum Monte Carlo [59][60][61][62][63], renormalization group [64,65], density-matrix renormalization group techniques [66][67][68], tensor networks-based algorithms, or various mean-field approaches [6,52,53,69]. In this work we propose an extension of the local mean-field method, thus let us first briefly review the mean-field approaches used earlier.…”

Using entanglement to discern phases in the disordered one-dimensional Bose-Hubbard model

“…An ideal method for analysing one-dimensional systems is the density-matrix RG (DMRG) [24]. It has been applied with great success to a number of physical systems from quantum chemistry [25] to quantum information [26], including the disordered Bose-Hubbard model [27,28]. The phase diagrams obtained using these methods for the one-dimensional case [19,28], whilst qualitatively agreeing, are quantitatively quite different.…”