Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0807.4142 · Physical Review A

Gutzwiller approach to the Bose-Hubbard model with random local impurities

Pierfrancesco Buonsante, Francesco Massel, Vittorio Penna, A. Vezzani

Published Jan 26, 2009• 33 citations
arXivHTMLPDF

Abstract

Recently it has been suggested that fermions whose hopping amplitude is quenched to extremely low values provide a convenient source of local disorder for lattice bosonic systems realized in current experiment on ultracold atoms. Here we investigate the phase diagram of such systems, which provide the experimental realization of a Bose-Hubbard model whose local potentials are randomly extracted from a binary distribution. Adopting a site-dependent Gutzwiller description of the state of the system, we address one- and two-dimensional lattices and obtain results agreeing with previous findings, as far as the compressibility of the system is concerned. We discuss the expected peaks in the experimental excitation spectrum of the system, related to the incompressible phases, and the superfluid character of the partially compressible regions characterizing the phase diagram of systems with binary disorder. In our investigation we make use of several analytical results whose derivation is described in appendixes, and whose validity is not limited to the system under concern.

DOI
10.1103/physreva.79.013623

Related papers

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

Julia Stasińska, Mateusz Łącki, Omjyoti Dutta +2 more

We investigate the phase diagrams of theoretical models describing bosonic atoms in a lattice in the presence of randomly localized impurities. By including multiband and nonlinear hopping effects we enrich the standard model containing only the chemical-potential disorder with the site-dependent hopping term. We compare the extension of the MI and the BG phase in both models using a combination of the local mean-field method and a Hartree-Fock-like procedure, as well as the Gutzwiller-ansatz approach. We show analytical argument for the presence of triple points in the phase diagram of the model with chemical-potential disorder. These triple points, however, cease to exist after the addition of the hopping disorder.

arXiv:1410.1034•Physical Review A•Dec 24, 2014•4 citations

Ultracold bosons in lattices with binary disorder

Konstantin V. Krutitsky, Michael Thorwart, Reinhold Egger +1 more

Quantum phases of ultracold bosons with repulsive interactions in lattices in the presence of quenched disorder are investigated. The disorder is assumed to be caused by the interaction of the bosons with impurity atoms having a large effective mass. The system is described by the Bose-Hubbard Hamiltonian with random on-site energies which have a discrete binary probability distribution. The phase diagram at zero temperature is calculated using several methods like a strong-coupling expansion, an exact numerical diagonalization, and a Bose-Fermi mapping valid in the hard-core limit. It is shown that the Mott-insulator phase exists for any strength of disorder in contrast to the case of continuous probability distribution. We find that the compressibility of the Bose glass phase varies in a wide range and can be extremely low. Furthermore, we evaluate experimentally accessible quantities like the momentum distribution, the static and dynamic structure factors, and the density of excited states. The influence of finite temperature is discussed as well.

arXiv:0801.2343•Physical Review A•May 16, 2008•29 citations

Bosons in a two-dimensional bichromatic quasiperiodic potential: Analysis of the disorder in the Bose-Hubbard parameters and phase diagrams

Astrid Elisa Niederle, Heiko Rieger

Experimental realizations of disorder in optical lattices generate a distribution of the Bose-Hubbard (BH) parameters, like on-site potentials, hopping strengths, and interaction energies. We analyze this distribution for bosons in a two-dimensional bichromatic quasiperiodic potential by determining the generalized Wannier functions and calculating the corresponding BH parameters. Using a local mean-field cluster analysis, we study the effect of the corresponding disorder on the phase diagrams. We find a substantial amount of disorder in the hopping strengths, which produces strong deviations from the phase diagram of the disordered BH model with purely random on-site potentials.

arXiv:1501.03143•Physical Review A•Apr 28, 2015•12 citations

One-dimensional Bose-Fermi-Hubbard model in the heavy-fermion limit

Alexander Mering, Michael Fleischhauer

We study the phase diagram of the zero-temperature, one-dimensional Bose-Fermi-Hubbard model for fixed fermion density in the limit of small fermionic hopping. This model can be regarded as an instance of a disordered Bose-Hubbard model with dichotomic values of the stochastic variables. Phase boundaries between compressible, incompressible (Mott-insulating), and partially compressible phases are derived analytically within a generalized strong-coupling expansion and numerically using density matrix renormalization group (DMRG) methods. We show that first-order correlations in the partially compressible phases decay exponentially, indicating a glass-type behavior. Fluctuations within the respective incompressible phases are determined using perturbation theory and are compared to DMRG results.

arXiv:0709.2386•Physical Review A•Feb 1, 2008•52 citations

Mean-field phase diagram for Bose-Hubbard Hamiltonians with random hopping

Pierfrancesco Buonsante, Francesco Massel, Vittorio Penna +1 more

The zero temperature phase diagram for ultracold bosons in a random 1D potential is obtained through a site decoupling mean-field scheme performed over a Bose-Hubbard (BH) Hamiltonian, whose hopping term is considered as a random variable. As for the model with random on-site potential, the presence of disorder leads to the appearance of a Bose glass phase. The different phases—i.e., Mott insulator, superfluid, and Bose glass—are characterized in terms of condensate fraction and superfluid fraction. Furthermore, the boundary of the Mott lobes is related to an off-diagonal Anderson model featuring the same disorder distribution as the original BH Hamiltonian.

arXiv:cond-mat/0611059•Laser Physics•Apr 1, 2007•14 citations

Mean-field phase diagram of cold lattice bosons in disordered potentials

Pierfrancesco Buonsante, Vittorio Penna, A. Vezzani +1 more

We address the phase diagram of the disordered Bose-Hubbard model that has been realized in several recent experiments in terms of optically trapped ultracold bosons. We show that a systematic description of all of the expected quantum phases can be obtained at both zero and finite temperature via a site-dependent decoupling mean-field approach. Also, we relate the boundaries of the Mott-insulating phase to an off-diagonal noninteracting Anderson model whose spectral features provide an avenue for determining the debated nature of the phase surrounding the Mott lobes. Our approach is simple yet effective, and scalable to systems with experimentally relevant sizes and features.

arXiv:cond-mat/0610476•Physical Review A•Jul 3, 2007•48 citations
Recently it has been suggested that fermions whose hopping amplitude is quenched to extremely low values provide a convenient source of local disorder for lattice bosonic systems realized in current experiment on ultracold atoms. Here we investigate the phase diagram of such systems, which provide the experimental realization of a Bose-Hubbard model whose local potentials are randomly extracted from a binary distribution. Adopting a site-dependent Gutzwiller description of the state of the system, we address one- and two-dimensional lattices and obtain results agreeing with previous findings, as far as the compressibility of the system is concerned. We discuss the expected peaks in the experimental excitation spectrum of the system, related to the incompressible phases, and the superfluid character of the partially compressible regions characterizing the phase diagram of systems with binary disorder. In our investigation we make use of several analytical results whose derivation is described in appendixes, and whose validity is not limited to the system under concern.
We investigate the phase diagrams of theoretical models describing bosonic atoms in a lattice in the presence of randomly localized impurities. By including multiband and nonlinear hopping effects we enrich the standard model containing only the chemical-potential disorder with the site-dependent hopping term. We compare the extension of the MI and the BG phase in both models using a combination of the local mean-field method and a Hartree-Fock-like procedure, as well as the Gutzwiller-ansatz approach. We show analytical argument for the presence of triple points in the phase diagram of the model with chemical-potential disorder. These triple points, however, cease to exist after the addition of the hopping disorder.
Quantum phases of ultracold bosons with repulsive interactions in lattices in the presence of quenched disorder are investigated. The disorder is assumed to be caused by the interaction of the bosons with impurity atoms having a large effective mass. The system is described by the Bose-Hubbard Hamiltonian with random on-site energies which have a discrete binary probability distribution. The phase diagram at zero temperature is calculated using several methods like a strong-coupling expansion, an exact numerical diagonalization, and a Bose-Fermi mapping valid in the hard-core limit. It is shown that the Mott-insulator phase exists for any strength of disorder in contrast to the case of continuous probability distribution. We find that the compressibility of the Bose glass phase varies in a wide range and can be extremely low. Furthermore, we evaluate experimentally accessible quantities like the momentum distribution, the static and dynamic structure factors, and the density of excited states. The influence of finite temperature is discussed as well.
Experimental realizations of disorder in optical lattices generate a distribution of the Bose-Hubbard (BH) parameters, like on-site potentials, hopping strengths, and interaction energies. We analyze this distribution for bosons in a two-dimensional bichromatic quasiperiodic potential by determining the generalized Wannier functions and calculating the corresponding BH parameters. Using a local mean-field cluster analysis, we study the effect of the corresponding disorder on the phase diagrams. We find a substantial amount of disorder in the hopping strengths, which produces strong deviations from the phase diagram of the disordered BH model with purely random on-site potentials.
We study the phase diagram of the zero-temperature, one-dimensional Bose-Fermi-Hubbard model for fixed fermion density in the limit of small fermionic hopping. This model can be regarded as an instance of a disordered Bose-Hubbard model with dichotomic values of the stochastic variables. Phase boundaries between compressible, incompressible (Mott-insulating), and partially compressible phases are derived analytically within a generalized strong-coupling expansion and numerically using density matrix renormalization group (DMRG) methods. We show that first-order correlations in the partially compressible phases decay exponentially, indicating a glass-type behavior. Fluctuations within the respective incompressible phases are determined using perturbation theory and are compared to DMRG results.
The zero temperature phase diagram for ultracold bosons in a random 1D potential is obtained through a site decoupling mean-field scheme performed over a Bose-Hubbard (BH) Hamiltonian, whose hopping term is considered as a random variable. As for the model with random on-site potential, the presence of disorder leads to the appearance of a Bose glass phase. The different phases—i.e., Mott insulator, superfluid, and Bose glass—are characterized in terms of condensate fraction and superfluid fraction. Furthermore, the boundary of the Mott lobes is related to an off-diagonal Anderson model featuring the same disorder distribution as the original BH Hamiltonian.
We address the phase diagram of the disordered Bose-Hubbard model that has been realized in several recent experiments in terms of optically trapped ultracold bosons. We show that a systematic description of all of the expected quantum phases can be obtained at both zero and finite temperature via a site-dependent decoupling mean-field approach. Also, we relate the boundaries of the Mott-insulating phase to an off-diagonal noninteracting Anderson model whose spectral features provide an avenue for determining the debated nature of the phase surrounding the Mott lobes. Our approach is simple yet effective, and scalable to systems with experimentally relevant sizes and features.