Phase Diagram and Spectral Function of the Two-Dimensional Disordered Bose-Hubbard Model: A Real-Space Dynamical Mean-Field Theory Analysis

Abstract

We numerically investigate the two-dimensional Bose-Hubbard model with local onsite disorder, where the competition between disorder and short-range interactions leads to the emergence of a Bose glass (BG) phase between the Mott insulator (MI) and superfluid (SF) phases. In order to analyze the inhomogeneous system we employ real-space bosonic dynamical mean-field theory (RBDMFT) and perform an ensemble average over disorder realizations. To distinguish the MI from the BG phase, we compare the Edwards-Anderson order parameter and the compressibility with the energy-gap condition. To identify the insulator to SF transition, we apply a percolation analysis to the condensate order parameter. In qualitative accordance with the theorem of inclusions we always find an intermediate BG phase between the SF and MI. However, the quantitative comparison indicates significant deviations between the MI to BG phase boundary expected in the thermodynamic limit and the one obtained for a finite system size. Additionally, RBMDFT is capable of reliably calculating spectral information throughout the phase diagram. Analyzing the spectral function reveals evidence for analytically predicted damped localized modes in the dispersion relation in the strong-coupling regime.

5 pages (main text), 8 pages (total), 6 figures, published in PRA on 22 May 2026

References in corpus (41)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Transition from a strongly interacting 1D superfluid to a Mott insulator
• The cold atom Hubbard toolbox
• Disordered quantum gases under control
• The `Higgs' Amplitude Mode at the Two-Dimensional Superfluid-Mott Insulator Transition
• Experimental study of the transport of coherent interacting matter-waves in a 1D random potential induced by laser speckle
• Momentum-Resolved Bragg Spectroscopy in Optical Lattices
• Mott insulator to superfluid transition in the Bose-Hubbard model: a strong-coupling approach
• Antiferromagnetic Order of Strongly Interacting Fermions in a Trap: Real-Space Dynamical Mean-Field Analysis
• Absence of a Direct Superfluid to Mott Insulator Transition in Disordered Bose Systems
• Exploring correlated 1D Bose gases from the superfluid to the Mott-insulator state by inelastic light scattering
• Cold atoms in the presence of disorder
• Detecting the Amplitude Mode of Strongly Interacting Lattice Bosons by Bragg Scattering
• Mott transition of fermionic atoms in a three-dimensional optical trap
• Phase diagram of the disordered Bose-Hubbard model
• Magnetic phases of two-component ultracold bosons in an optical lattice
• Dynamic properties of the one-dimensional Bose-Hubbard model
• Correlated bosons on a lattice: Dynamical mean-field theory for Bose-Einstein condensed and normal phases
• Probing the Bose-Glass--Superfluid Transition using Quantum Quenches of Disorder
• Zoo of quantum phases and excitations of cold bosonic atoms in optical lattices
• Phase Diagram of Commensurate Two-Dimensional Disordered Bose Hubbard Model
• Dynamical mean-field theory for bosons
• Dynamical Mean Field Theory for the Bose-Hubbard Model
• Mean-field phase diagram of cold lattice bosons in disordered potentials
• Superfluid clusters, percolation and phase transitions in the disordered, two dimensional Bose-Hubbard model
• Stochastic Mean-Field Theory: Method and Application to the Disordered Bose-Hubbard Model at Finite Temperature and Speckle Disorder
• Measurement of spectral functions of ultracold atoms in disordered potentials
• Stochastic Mean-Field Theory for the Disordered Bose-Hubbard Model
• Tunable anisotropic magnetism in trapped two-component Bose gases
• Observing the two-dimensional Bose glass in an optical quasicrystal
• Spectral properties of strongly correlated bosons in two-dimensional optical lattices
• Order via Nonlinearity in Randomly Confined Bose Gases
• Measuring the Edwards-Anderson order parameter of the Bose glass: a quantum gas microscope approach
• Hartree-Fock Mean-Field Theory for Trapped Dirty Bosons
• Analytical and numerical study of dirty bosons in a quasi-one-dimensional harmonic trap
• Numerical calculation of spectral functions of the Bose-Hubbard model using B-DMFT
• Excitation and dynamics in the extended bose-hubbard model
• Emergence of damped-localized excitations of the Mott state due to disorder
• The infinite occupation number basis of bosons - solving a numerical challenge
• Quantum-gas microscopy and Talbot interferometry of the Bose-glass phase
• Phase diagram of disordered Bose-Hubbard model based on mean-field and percolation analysis in two dimensions and at fixed $n=1$ filling