A review of Monte Carlo simulations for the Bose-Hubbard model with diagonal disorder

Abstract

We review the physics of the Bose-Hubbard model with disorder in the chemical potential focusing on recently published analytical arguments in combination with quantum Monte Carlo simulations. Apart from the superfluid and Mott insulator phases that can occur in this system without disorder, disorder allows for an additional phase, called the Bose glass phase. The topology of the phase diagram is subject to strong theorems proving that the Bose Glass phase must intervene between the superfluid and the Mott insulator and implying a Griffiths transition between the Mott insulator and the Bose glass. The full phase diagrams in 3d and 2d are discussed, and we zoom in on the insensitivity of the transition line between the superfluid and the Bose glass in the close vicinity of the tip of the Mott insulator lobe. We briefly comment on the established and remaining questions in the 1d case, and give a short overview of numerical work on related models.

30 pages, 8 figures

References in corpus (14)

• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Strongly interacting bosons in a disordered optical lattice
• Ultracold Bose Gases in 1D Disorder: From Lifshits Glass to Bose-Einstein Condensate
• Phase transition of one dimensional bosons with strong disorder
• The Stochastic Green Function (SGF) algorithm
• Directed update for the Stochastic Green Function algorithm
• Dirty-boson physics with magnetic insulators
• Phase transition of interacting disordered bosons in one dimension
• The insulating phases and superfluid-insulator transition of disordered boson chains
• Particle-hole symmetry and the dirty boson problem
• Superfluid clusters, percolation and phase transitions in the disordered, two dimensional Bose-Hubbard model
• Stochastic Mean-Field Theory for the Disordered Bose-Hubbard Model
• Quantum Phase Transitions of Hard-Core Bosons in Background Potentials
• Dirty Bosons: Twenty Years Later

Cited by in corpus (23)

• Quantum trajectories and open many-body quantum systems
• Probing the Bose-Glass--Superfluid Transition using Quantum Quenches of Disorder
• Superfluid density and quasi-long-range order in the one-dimensional disordered Bose-Hubbard model
• Reduced Density Matrix Functional Theory for Bosons
• Hubbard Models for Quasicrystalline Potentials
• Superfluid/Bose-glass transition in one dimension
• Dynamical vortex transitions in a gate-tunable Josephson junction array
• The Mean-Field Bose Glass in Quasicrystalline Systems
• Equilibrium phases of two-dimensional bosons in quasi-periodic lattices
• Numerical linked cluster expansions for inhomogeneous systems
• Liouvillian skin effects and fragmented condensates in an integrable dissipative Bose-Hubbard model
• Using entanglement to discern phases in the disordered one-dimensional Bose-Hubbard model
• Stochastic approximation of dynamical exponent at quantum critical point
• Finding the phase diagram of strongly-correlated disordered bosons using quantum quenches
• The effect of disorder on the phase diagrams of hard-core lattice bosons with cavity-mediated long-range and nearest-neighbor interactions
• Quench dynamics of a disordered array of dissipative coupled cavities
• Specialising Neural-network Quantum States for the Bose Hubbard Model
• Bose-Hubbard model with random impurities: Multiband and nonlinear hopping effects
• Quenched random mass disorder in the large N theory of vector bosons
• Self-energy functional theory with symmetry breaking for disordered lattice bosons
• The infinite occupation number basis of bosons - solving a numerical challenge
• Encoding strongly-correlated many-boson wavefunctions on a photonic quantum computer: application to the attractive Bose-Hubbard model
• Bosonic Haldane insulator in the presence of local disorder: A quantum Monte Carlo study