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

Journal of Statistical Mechanics Theory and Experiment

Dynamical correlations and a quantum glass phase in a random hopping Bose–Hubbard model

Anna M. Piekarska, T. K. Kopeć

Published Feb 1, 2020• 4 citations
Publisher

Abstract

Abstract We investigate a system of interacting bosons with random intersite tunnelling amplitudes. We describe these by introducing Gaussian-distributed hopping integrals into the standard Bose–Hubbard model. This system has been recently shown to exhibit a quantum phase transition to a glassy state. The latter is characterized by a quenched disorder of boson wave-function phases. In this aspect, the system resembles quantum spin-glass systems that attracted much attention. By exploiting this analogy, we employ the well-established methodology originated by Sherrington and Kirkpatrick, which bases on the replica trick and the Trotter–Suzuki expansion. This treatment transforms the original quantum problem into an effective classical one with an additional time-like dimension. Here, we focus on autocorrelation functions of canonical variables of the effective system in the time-like domain. Deep in the disordered phase, we find a highly dynamical nature of correlations in agreement with the expected short memory of the system. This behaviour weakens while approaching and passing the phase boundary, where in the glassy phase asymptotically non-vanishing correlations are encountered. Thus, the state features infinite memory, which is consistent with the quenched nature of glassy disorder with random but frozen boson phases.

DOI
10.1088/1742-5468/ab633b

Related papers

Emergence of a superglass phase in the random-hopping Bose-Hubbard model

Anna M. Piekarska, T. K. Kopeć

We study an experimentally feasible system of strongly correlated bosons with random hoppings described by the infinite-range Bose-Hubbard model on a lattice with hopping integrals given by independent random variables of Gaussian distribution with nonzero mean. We solve this quantum model in the thermodynamic limit, employing the replica method and the Trotter-Suzuki formula. We find and describe a superglass phase that emerges at the interface between glass and superfluid phases. Both glassy and long-range orderings are present in the superglass and compete with each other, as revealed by the anticorrelation of their order parameters. We present phase diagrams in various cross sections of the multidimensional space of system parameters. In selected parameter subspaces, we compare the results to those of nondisordered, diagonally disordered, and once celebrated spin-glass systems.

arXiv:2202.05570•Physical review. B./Physical review. B•May 10, 2022•5 citations

Quantum Glass of Interacting Bosons with Off-Diagonal Disorder

Anna M. Piekarska, T. K. Kopeć

We study disordered interacting bosons described by the Bose-Hubbard model with Gaussian-distributed random tunneling amplitudes. It is shown that the off-diagonal disorder induces a spin-glass-like ground state, characterized by randomly frozen quantum-mechanical U(1) phases of bosons. To access criticality, we employ the "n-replica trick," as in the spin-glass theory, and the Trotter-Suzuki method for decomposition of the statistical density operator, along with numerical calculations. The interplay between disorder, quantum, and thermal fluctuations leads to phase diagrams exhibiting a glassy state of bosons, which are studied as a function of model parameters. The considered system may be relevant for quantum simulators of optical-lattice bosons, where the randomness can be introduced in a controlled way. The latter is supported by a proposition of experimental realization of the system in question.

arXiv:1803.08156•Physical Review Letters•Apr 16, 2018•7 citations

Transition from disordered solid to Bose glass in a Bose-Hubbard model with disorder and long-range interactions

Kohenjit Pebam, Laxmi Angom, Bhumika Thoudam +3 more

The introduction of disorder in the extended Bose-Hubbard model gives rise to new glassy quantum phases, namely the Bose-glass and disordered solid phases. In this work, we present a rich phase diagram of interacting bosons in a disordered two-dimensional optical lattice, modeled by the disordered Bose-Hubbard model. We systematically probe the effect of long-range interaction truncated to the nearest neighbors and next-nearest neighbors on the phase diagram. We investigate the zero-temperature ground-state quantum phases using the single-site Gutzwiller mean-field theory. We also employ strong-coupling perturbative expansion to identify the nature of ground-state solid phases analytically. At sufficiently high disorder strength, we observe a quantum phase transition between the disordered solid and Bose-glass phases. We have investigated this transition in greater detail using cluster Gutzwiller mean-field theory to study the effect of intersite correlations which is absent in the single-site Gutzwiller mean-field theory. We have also studied this phase transition from the perspective of percolation theory.

Physical Review A•Oct 13, 2025•0 citations

Bose-glass phase of a one-dimensional disordered Bose fluid: Metastable states, quantum tunneling, and droplets

N. Dupuis, Romain Daviet

We study a one-dimensional disordered Bose fluid using bosonization, the replica method, and a nonperturbative functional renormalization-group approach. We find that the Bose-glass phase is described by a fully attractive strong-disorder fixed point characterized by a singular disorder correlator whose functional dependence assumes a cuspy form that is related to the existence of metastable states. At nonzero momentum scale k, quantum tunneling between the ground state and low-lying metastable states leads to a rounding of the cusp singularity into a quantum boundary layer (QBL). The width of the QBL depends on an effective Luttinger parameter K_{k}∼k^{θ} that vanishes with an exponent θ=z-1 related to the dynamical critical exponent z. The QBL encodes the existence of rare "superfluid" regions, controls the low-energy dynamics, and yields a (dissipative) conductivity vanishing as ω^{2} in the low-frequency limit. These results reveal the glassy properties (pinning, "shocks," or static avalanches) of the Bose-glass phase and can be understood within the "droplet" picture put forward for the description of glassy (classical) systems.

arXiv:1912.08236•Physical review. E•Apr 30, 2020•19 citations

Green’s function approach to the Bose–Hubbard model with disorder

R S Souza, Axel Pelster, F. E. A. dos Santos

Abstract We analyse the distinction between the three different ground states presented by a system of spinless bosons with short-range interactions submitted to a random potential using the disordered Bose–Hubbard model. The criteria for identifying the superfluid, the Mott-insulator, and the Bose-glass phases at finite temperatures are discussed for small values of the kinetic energy associated with the tunnelling of particles between potential wells. Field theoretical considerations are applied in order to construct a diagrammatic hopping expansion to the finite-temperature Green’s function. By performing a summation of subsets of diagrams we are able to find the condition to the long-range correlations which leads to the phase boundary between superfluid and insulating phases. The perturbative expression to the local correlations allows us to calculate an approximation to the single-particle density of states of low-energy excitations in the presence of small hopping, which characterizes unambiguously the distinction between the Mott-insulator and the Bose-glass phases. We obtain the phase diagram for bounded on-site disorder. It is demonstrated that our analysis is capable of going beyond the mean-field theory results for the classification of these different ground states.

arXiv:2108.13187•New Journal of Physics•Jul 19, 2021•8 citations

Glassy properties of the Bose-glass phase of a one-dimensional disordered Bose fluid

N. Dupuis

We study a one-dimensional disordered Bose fluid using bosonization, the replica method, and a nonperturbative functional renormalization-group approach. The Bose-glass phase is described by a fully attractive strong-disorder fixed point characterized by a singular disorder correlator whose functional dependence assumes a cuspy form that is related to the existence of metastable states. At nonzero momentum scale, quantum tunneling between these metastable states leads to a rounding of the nonanalyticity in a quantum boundary layer that encodes the existence of rare superfluid regions responsible for the ω^{2} behavior of the (dissipative) conductivity in the low-frequency limit. These results can be understood within the "droplet" picture put forward for the description of glassy (classical) systems.

arXiv:1903.12374•Physical review. E•Sep 30, 2019•19 citations
Abstract We investigate a system of interacting bosons with random intersite tunnelling amplitudes. We describe these by introducing Gaussian-distributed hopping integrals into the standard Bose–Hubbard model. This system has been recently shown to exhibit a quantum phase transition to a glassy state. The latter is characterized by a quenched disorder of boson wave-function phases. In this aspect, the system resembles quantum spin-glass systems that attracted much attention. By exploiting this analogy, we employ the well-established methodology originated by Sherrington and Kirkpatrick, which bases on the replica trick and the Trotter–Suzuki expansion. This treatment transforms the original quantum problem into an effective classical one with an additional time-like dimension. Here, we focus on autocorrelation functions of canonical variables of the effective system in the time-like domain. Deep in the disordered phase, we find a highly dynamical nature of correlations in agreement with the expected short memory of the system. This behaviour weakens while approaching and passing the phase boundary, where in the glassy phase asymptotically non-vanishing correlations are encountered. Thus, the state features infinite memory, which is consistent with the quenched nature of glassy disorder with random but frozen boson phases.
We study an experimentally feasible system of strongly correlated bosons with random hoppings described by the infinite-range Bose-Hubbard model on a lattice with hopping integrals given by independent random variables of Gaussian distribution with nonzero mean. We solve this quantum model in the thermodynamic limit, employing the replica method and the Trotter-Suzuki formula. We find and describe a superglass phase that emerges at the interface between glass and superfluid phases. Both glassy and long-range orderings are present in the superglass and compete with each other, as revealed by the anticorrelation of their order parameters. We present phase diagrams in various cross sections of the multidimensional space of system parameters. In selected parameter subspaces, we compare the results to those of nondisordered, diagonally disordered, and once celebrated spin-glass systems.
We study disordered interacting bosons described by the Bose-Hubbard model with Gaussian-distributed random tunneling amplitudes. It is shown that the off-diagonal disorder induces a spin-glass-like ground state, characterized by randomly frozen quantum-mechanical U(1) phases of bosons. To access criticality, we employ the "n-replica trick," as in the spin-glass theory, and the Trotter-Suzuki method for decomposition of the statistical density operator, along with numerical calculations. The interplay between disorder, quantum, and thermal fluctuations leads to phase diagrams exhibiting a glassy state of bosons, which are studied as a function of model parameters. The considered system may be relevant for quantum simulators of optical-lattice bosons, where the randomness can be introduced in a controlled way. The latter is supported by a proposition of experimental realization of the system in question.
The introduction of disorder in the extended Bose-Hubbard model gives rise to new glassy quantum phases, namely the Bose-glass and disordered solid phases. In this work, we present a rich phase diagram of interacting bosons in a disordered two-dimensional optical lattice, modeled by the disordered Bose-Hubbard model. We systematically probe the effect of long-range interaction truncated to the nearest neighbors and next-nearest neighbors on the phase diagram. We investigate the zero-temperature ground-state quantum phases using the single-site Gutzwiller mean-field theory. We also employ strong-coupling perturbative expansion to identify the nature of ground-state solid phases analytically. At sufficiently high disorder strength, we observe a quantum phase transition between the disordered solid and Bose-glass phases. We have investigated this transition in greater detail using cluster Gutzwiller mean-field theory to study the effect of intersite correlations which is absent in the single-site Gutzwiller mean-field theory. We have also studied this phase transition from the perspective of percolation theory.
We study a one-dimensional disordered Bose fluid using bosonization, the replica method, and a nonperturbative functional renormalization-group approach. We find that the Bose-glass phase is described by a fully attractive strong-disorder fixed point characterized by a singular disorder correlator whose functional dependence assumes a cuspy form that is related to the existence of metastable states. At nonzero momentum scale k, quantum tunneling between the ground state and low-lying metastable states leads to a rounding of the cusp singularity into a quantum boundary layer (QBL). The width of the QBL depends on an effective Luttinger parameter K_{k}∼k^{θ} that vanishes with an exponent θ=z-1 related to the dynamical critical exponent z. The QBL encodes the existence of rare "superfluid" regions, controls the low-energy dynamics, and yields a (dissipative) conductivity vanishing as ω^{2} in the low-frequency limit. These results reveal the glassy properties (pinning, "shocks," or static avalanches) of the Bose-glass phase and can be understood within the "droplet" picture put forward for the description of glassy (classical) systems.
Abstract We analyse the distinction between the three different ground states presented by a system of spinless bosons with short-range interactions submitted to a random potential using the disordered Bose–Hubbard model. The criteria for identifying the superfluid, the Mott-insulator, and the Bose-glass phases at finite temperatures are discussed for small values of the kinetic energy associated with the tunnelling of particles between potential wells. Field theoretical considerations are applied in order to construct a diagrammatic hopping expansion to the finite-temperature Green’s function. By performing a summation of subsets of diagrams we are able to find the condition to the long-range correlations which leads to the phase boundary between superfluid and insulating phases. The perturbative expression to the local correlations allows us to calculate an approximation to the single-particle density of states of low-energy excitations in the presence of small hopping, which characterizes unambiguously the distinction between the Mott-insulator and the Bose-glass phases. We obtain the phase diagram for bounded on-site disorder. It is demonstrated that our analysis is capable of going beyond the mean-field theory results for the classification of these different ground states.
We study a one-dimensional disordered Bose fluid using bosonization, the replica method, and a nonperturbative functional renormalization-group approach. The Bose-glass phase is described by a fully attractive strong-disorder fixed point characterized by a singular disorder correlator whose functional dependence assumes a cuspy form that is related to the existence of metastable states. At nonzero momentum scale, quantum tunneling between these metastable states leads to a rounding of the nonanalyticity in a quantum boundary layer that encodes the existence of rare superfluid regions responsible for the ω^{2} behavior of the (dissipative) conductivity in the low-frequency limit. These results can be understood within the "droplet" picture put forward for the description of glassy (classical) systems.