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 the Physical Society of Japan

Quantum Monte Carlo Simulation of a Boson System for Superfluid - Insulator Transition on Two-Dimensional Random Surfaces

Masahito Hashimoto, Masako Takasu

Published Aug 15, 1999• 1 citation
Publisher

Abstract

We study the superfluid-insulator transition of the 2-D boson system on random surfaces. Using quantum Monte Carlo simulation and grand-canonical ensemble, we investigate the random Hubbard model and study the phase transition between the superfluid phase and the Bose glass insulator phase. Changing the chemical potential µ, we observe the transition from the superfluid phase to the insulator phase. We show the dimensional dependence of the transition by comparing the results of 2-D and 1-D boson systems. To study the localization of the boson paths, we perform the simulation on the anisotropic surfaces, and discuss the crossover from 2-D system to 1-D system.

DOI
10.1143/jpsj.68.2684

Related papers

Reentrant Superfluid-Insulator Transitions of Random Boson Hubbard Models

Naomichi Hatano

Superfluid-insulator transitions are studied for the ground state of the Boson Hubbard model with random potentials. The topology of the phase diagram is discussed. Reentrant transitions between the superfluid phase and the Bose-glass insulator phase are found in an arbitrary number of dimensions. The present results are based on a perturbational scaling argument and a quantum Monte Carlo calculation. The Monte Carlo algorithm is also reported in detail.

Journal of the Physical Society of Japan•May 15, 1995•8 citations

Superfluid-insulator transition in the disordered two-dimensional Bose-Hubbard model

Fei Lin, Erik Schwartz Sørensen, David M. Ceperley

We investigate the superfluid-insulator transition in the disordered two-dimensional Bose-Hubbard model through quantum Monte Carlo simulations. The Bose-Hubbard model is studied in the presence of site disorder, and the quantum critical point between the Bose glass and superfluid is determined in the grand canonical ensemble at $\ensuremath{\mu}/U=0$ (close to $\ensuremath{\rho}=0.5$), $\ensuremath{\mu}/U=0.375$ (close to $\ensuremath{\rho}=1$), and $\ensuremath{\mu}/U=1$ as well as in the canonical ensemble at $\ensuremath{\rho}=0.5$ and 1. Particular attention is paid to disorder averaging, and it is shown that a large number of disorder realizations are needed in order to obtain reliable results. Typically, more than $100\phantom{\rule{0.16em}{0ex}}000$ disorder realizations were used. In the grand canonical ensemble, we find $Z{t}_{c}/U=0.112(1)$ with $\ensuremath{\mu}/U=0.375$, significantly different from previous studies. When compared to the critical point in the absence of disorder ($Z{t}_{c}/U=0.2385$), this result confirms previous findings showing that disorder enlarges the superfluid region. At the critical point, we then study the dynamic conductivity.

arXiv:1107.3107•Physical Review B•Sep 13, 2011•39 citations

Superfluid-insulator transition in disordered boson systems

Werner Krauth, Nandini Trivedi, David M. Ceperley

We present results of path-integral Monte Carlo simulations of bosons on a two-dimensional square lattice in a random potential of average strength V and with on-site repulsion U. We find that the superfluid density ${\mathrm{\ensuremath{\rho}}}_{\mathit{s}}$ is enhanced by increasing V and U in certain regions of parameter space. By combining the results of ${\mathrm{\ensuremath{\rho}}}_{\mathit{s}}$, with the behavior of the density-density correlation function on lattices of size up to 10\ifmmode\times\else\texttimes\fi{}10, we study the superfluid--to--Mott-insulator transition and the transition from a superfluid to a disorder-localized (``Bose glass'') phase.

Physical Review Letters•Oct 1, 1991•298 citations

Superfluid Transition in a Bose Gas with Correlated Disorder

Sebastiano Pilati, S. Giorgini, Nikolay V. Prokof'ev

The superfluid transition of a three-dimensional gas of hard-sphere bosons in a disordered medium is studied using quantum Monte Carlo methods. Simulations are performed in continuous space both in the canonical and in the grand-canonical ensemble. At fixed density we calculate the shift of the transition temperature as a function of the disorder strength, while at fixed temperature we determine both the critical chemical potential and the critical density separating normal and superfluid phases. In the regime of strong disorder the normal phase extends up to large values of the degeneracy parameter, and the critical chemical potential exhibits a linear dependence in the intensity of the random potential. The role of interactions and disorder correlations is also discussed.

arXiv:0902.0696•Physical Review Letters•Apr 16, 2009•42 citations

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

Lode Pollet

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.

arXiv:1307.5430•Comptes Rendus Physique•Sep 10, 2013•28 citations

Anomalous Quantum Glass of Bosons in a Random Potential in Two Dimensions

Yan-Cheng Wang, Wenan Guo, Anders W. Sandvik

We present a quantum Monte Carlo study of the "quantum glass" phase of the two-dimensional Bose-Hubbard model with random potentials at filling ρ=1. In the narrow region between the Mott and superfluid phases, the compressibility has the form κ∼exp(-b/T^{α})+c with α<1 and c vanishing or very small. Thus, at T=0 the system is either incompressible (a Mott glass) or nearly incompressible (a Mott-glass-like anomalous Bose glass). At stronger disorder, where a glass reappears from the superfluid, we find a conventional highly compressible Bose glass. On a path connecting these states, away from the superfluid at larger Hubbard repulsion, a change of the disorder strength by only 10% changes the low-temperature compressibility by more than 4 orders of magnitude, lending support to two types of glass states separated by a phase transition or a sharp crossover.

arXiv:1110.3213•Physical Review Letters•Mar 11, 2015•15 citations
We study the superfluid-insulator transition of the 2-D boson system on random surfaces. Using quantum Monte Carlo simulation and grand-canonical ensemble, we investigate the random Hubbard model and study the phase transition between the superfluid phase and the Bose glass insulator phase. Changing the chemical potential µ, we observe the transition from the superfluid phase to the insulator phase. We show the dimensional dependence of the transition by comparing the results of 2-D and 1-D boson systems. To study the localization of the boson paths, we perform the simulation on the anisotropic surfaces, and discuss the crossover from 2-D system to 1-D system.
We investigate the superfluid-insulator transition in the disordered two-dimensional Bose-Hubbard model through quantum Monte Carlo simulations. The Bose-Hubbard model is studied in the presence of site disorder, and the quantum critical point between the Bose glass and superfluid is determined in the grand canonical ensemble at $\ensuremath{\mu}/U=0$ (close to $\ensuremath{\rho}=0.5$), $\ensuremath{\mu}/U=0.375$ (close to $\ensuremath{\rho}=1$), and $\ensuremath{\mu}/U=1$ as well as in the canonical ensemble at $\ensuremath{\rho}=0.5$ and 1. Particular attention is paid to disorder averaging, and it is shown that a large number of disorder realizations are needed in order to obtain reliable results. Typically, more than 100000100\phantom{\rule{0.16em}{0ex}}000100000 disorder realizations were used. In the grand canonical ensemble, we find Ztc/U=0.112(1)Z{t}_{c}/U=0.112(1)Ztc​/U=0.112(1) with $\ensuremath{\mu}/U=0.375$, significantly different from previous studies. When compared to the critical point in the absence of disorder (Ztc/U=0.2385Z{t}_{c}/U=0.2385Ztc​/U=0.2385), this result confirms previous findings showing that disorder enlarges the superfluid region. At the critical point, we then study the dynamic conductivity.
We present results of path-integral Monte Carlo simulations of bosons on a two-dimensional square lattice in a random potential of average strength V and with on-site repulsion U. We find that the superfluid density ${\mathrm{\ensuremath{\rho}}}_{\mathit{s}}$ is enhanced by increasing V and U in certain regions of parameter space. By combining the results of ${\mathrm{\ensuremath{\rho}}}_{\mathit{s}}$, with the behavior of the density-density correlation function on lattices of size up to 10\ifmmode\times\else\texttimes\fi{}10, we study the superfluid--to--Mott-insulator transition and the transition from a superfluid to a disorder-localized (``Bose glass'') phase.
The superfluid transition of a three-dimensional gas of hard-sphere bosons in a disordered medium is studied using quantum Monte Carlo methods. Simulations are performed in continuous space both in the canonical and in the grand-canonical ensemble. At fixed density we calculate the shift of the transition temperature as a function of the disorder strength, while at fixed temperature we determine both the critical chemical potential and the critical density separating normal and superfluid phases. In the regime of strong disorder the normal phase extends up to large values of the degeneracy parameter, and the critical chemical potential exhibits a linear dependence in the intensity of the random potential. The role of interactions and disorder correlations is also discussed.
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.
We present a quantum Monte Carlo study of the "quantum glass" phase of the two-dimensional Bose-Hubbard model with random potentials at filling ρ=1. In the narrow region between the Mott and superfluid phases, the compressibility has the form κ∼exp(-b/T^{α})+c with α<1 and c vanishing or very small. Thus, at T=0 the system is either incompressible (a Mott glass) or nearly incompressible (a Mott-glass-like anomalous Bose glass). At stronger disorder, where a glass reappears from the superfluid, we find a conventional highly compressible Bose glass. On a path connecting these states, away from the superfluid at larger Hubbard repulsion, a change of the disorder strength by only 10% changes the low-temperature compressibility by more than 4 orders of magnitude, lending support to two types of glass states separated by a phase transition or a sharp crossover.