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:cond-mat/9312034 · Physical Review Letters

Coexistence of diagonal and off-diagonal long-range order: A Monte Carlo study

Anne van Otterlo, Karl-Heinz Wagenblast

Published May 30, 1994• 78 citations
arXivHTMLPDF

Abstract

The zero temperature properties of interacting two dimensional lattice bosons are investigated. We present Monte Carlo data for soft-core bosons that demonstrate the existence of a phase in which crystalline long-range order and off-diagonal long-range order (superfluidity) coexist. We comment on the difference between hard- and soft-core bosons and compare our date to mean-field results that predict a larger coexistence region. Furthermore, we determine the critical exponents for the various phase transitions.

DOI
10.1103/physrevlett.72.3598

Related papers

Quantum phase transitions of interacting bosons and the supersolid phase

Anne van Otterlo, Karl-Heinz Wagenblast, R. Baltin +3 more

We investigate the properties of strongly interacting bosons in two dimensions at zero temperature using mean-field theory, a variational ansatz for the ground-state wave function, and Monte Carlo methods. With on-site and short-range interactions a rich phase diagram is obtained. Apart from the homogeneous superfluid and Mott-insulating phases, inhomogeneous charge-density wave phases appear, that are stabilized by the finite-range interaction. Furthermore, our analysis demonstrates the existence of a supersolid phase, in which both long-range order (related to the charge-density wave) and off-diagonal long-range order coexist. We also obtain the critical exponents for the various phase transitions.

arXiv:cond-mat/9508065•Physical review. B, Condensed matter•Dec 1, 1995•124 citations

Phase diagram of interacting bosons on the honeycomb lattice

Stefan Weßel

We study the ground-state properties of repulsively interacting bosons on the honeycomb lattice using large-scale quantum Monte Carlo simulations. In the hard-core limit, the half-filled system develops long-ranged diagonal order for sufficiently strong nearest-neighbor repulsion. This staggered solid melts at a first-order quantum phase transition into the superfluid phase, without the presence of any intermediate supersolid phase. Within the superfluid phase, both the superfluid density and the compressibility exhibit local minima near the particle (hole) density of one quarter, while the density and the condensate fraction show inflection points in this region. Relaxing the hard-core constraint, supersolid phases emerge for soft-core bosons. The suppression of the superfluid density is found to persist for sufficiently large, finite on-site repulsion.

arXiv:cond-mat/0701337•Physical Review B•May 2, 2007•53 citations

Superfluid-Insulator Transition of Interacting Multi-Component Bosons

Yukitoshi Motome, Masatoshi Imada

Various types of superfluid-insulator transitions are investigated for two-component lattice boson systems in two dimensions with on-site hard-core repulsion and the component-dependent intersite interaction. The mean-field phase diagram is obtained by the Gutzwiller-type variational technique in the plane of filling and interaction parameters. Various ground-state properties are also studied by the quantum Monte Carlo method. Our model exhibits two types of diagonal long-range orders; the density order around the density $n=1/2$ and the Ising-type component order near $n=1$. The quantum Monte Carlo results for the transitions from the superfluid state to these two ordered states show marked contrast with the Gutzwiller results. Namely, although they are both accompanied by phase separation into commensurate ($n=1/2$ or $n=1$) and incommensurate density phases, these transitions are both continuous. The continuous growth of the component correlation severely suppresses the superfluidity as well as the inverse of the effective mass in the critical region of the component order transition in contrast to the persistence of the superfluidity in the density-ordered state. We propose a mechanism of the mass enhancement observed even far from the Mott insulating filling $n=1$, when the Ising-type component order persists into $n \neq 1$. Possible relevance of this type of mass enhancement in other systems is also discussed.

arXiv:cond-mat/9603028•Mar 5, 1996•0 citations

Superfluid-Insulator Transition of Interacting Multi-Component Bosons – Gutzwiller Variational and Quantum Monte Carlo Study –

Yukitoshi Motome, Masatoshi Imada

Various types of superfluid-insulator transitions are investigated for two-component lattice boson systems in two dimensions with on-site hard-core repulsion and the component-dependent intersite interaction. The mean-field phase diagram is obtained by the Gutzwiller-type variational technique. Various ground-state properties are also studied by the quantum Monte Carlo method. Our model exhibits two types of diagonal long-range orders; the density order around the density n =1/2 and the Ising-type component order near n =1. In contrast to the Gutzwiller results, the Monte Carlo results show that the continuous growth of the component correlation severely suppresses the superfluidity as well as the inverse of the effective mass in the critical region of the component order transition. We propose a mechanism of this mass enhancement observed even far from the Mott insulating filling n =1, when the Ising-type component order persists into n ≠1. Possible relevance of this type of mass enhancement in other systems is also discussed.

Journal of the Physical Society of Japan•Jul 15, 1996•1 citation

Supersolid phase in two-dimensional soft-core bosons at finite temperature

Sebastiano Peotta, G. Spada, S. Giorgini +2 more

The supersolid phase of soft-core bosons in two dimensions is investigated using the self-consistent Hartree-Fock and quantum Monte Carlo methods. An approximate phase diagram at finite temperatures is initially constructed using the mean-field approach, which is subsequently validated through precise path-integral simulations, enabling a microscopic characterization of the various phases. Superfluid and melting/freezing transitions are analyzed through the superfluid density and the long-range behavior of correlation functions associated with positional and orientational order, in accordance with the general picture of Berezinskii-Kosterlitz-Thouless transitions. A broad region at low temperatures is identified where the supersolid phase exists, separating the uniform superfluid phase from the normal quasicrystal phase. Additionally, a potential intermediate hexatic phase with quasi-long-range orientational order is identified in a narrow region between the normal solid and fluid phases. These findings establish self-consistent Hartree-Fock theory beyond the local density approximation as an effective tool, complementary to computationally intensive quantum Monte Carlo simulations, for investigating the melting of the supersolid phase and the possible emergence of the hexatic superfluid phase in bosonic systems with various interaction potentials.

arXiv:2504.03482•Physical review. B./Physical review. B•Nov 7, 2025•2 citations

Simultaneous diagonal and off-diagonal order in the Bose-Hubbard Hamiltonian

Richard T. Scalettar, G. G. Batrouni, A. P. Kampf +1 more

The Bose-Hubbard model exhibits a rich phase diagram consisting both of insulating regimes where diagonal long-range (solid) order dominates as well as conducting regimes where off-diagonal long-range order (superfluidity) is present. In this paper we describe the results of quantum Monte Carlo calculations of the phase diagram, both for the hard- and soft-core cases, with a particular focus on the possibility of simultaneous superfluid and solid order. We also discuss the appearance of phase separation in the model. The simulations are compared with analytic calculations of the phase diagram and spin-wave dispersion.

arXiv:cond-mat/9411009•Physical review. B, Condensed matter•Apr 1, 1995•105 citations
The zero temperature properties of interacting two dimensional lattice bosons are investigated. We present Monte Carlo data for soft-core bosons that demonstrate the existence of a phase in which crystalline long-range order and off-diagonal long-range order (superfluidity) coexist. We comment on the difference between hard- and soft-core bosons and compare our date to mean-field results that predict a larger coexistence region. Furthermore, we determine the critical exponents for the various phase transitions.
We investigate the properties of strongly interacting bosons in two dimensions at zero temperature using mean-field theory, a variational ansatz for the ground-state wave function, and Monte Carlo methods. With on-site and short-range interactions a rich phase diagram is obtained. Apart from the homogeneous superfluid and Mott-insulating phases, inhomogeneous charge-density wave phases appear, that are stabilized by the finite-range interaction. Furthermore, our analysis demonstrates the existence of a supersolid phase, in which both long-range order (related to the charge-density wave) and off-diagonal long-range order coexist. We also obtain the critical exponents for the various phase transitions.
We study the ground-state properties of repulsively interacting bosons on the honeycomb lattice using large-scale quantum Monte Carlo simulations. In the hard-core limit, the half-filled system develops long-ranged diagonal order for sufficiently strong nearest-neighbor repulsion. This staggered solid melts at a first-order quantum phase transition into the superfluid phase, without the presence of any intermediate supersolid phase. Within the superfluid phase, both the superfluid density and the compressibility exhibit local minima near the particle (hole) density of one quarter, while the density and the condensate fraction show inflection points in this region. Relaxing the hard-core constraint, supersolid phases emerge for soft-core bosons. The suppression of the superfluid density is found to persist for sufficiently large, finite on-site repulsion.
Various types of superfluid-insulator transitions are investigated for two-component lattice boson systems in two dimensions with on-site hard-core repulsion and the component-dependent intersite interaction. The mean-field phase diagram is obtained by the Gutzwiller-type variational technique in the plane of filling and interaction parameters. Various ground-state properties are also studied by the quantum Monte Carlo method. Our model exhibits two types of diagonal long-range orders; the density order around the density n=1/2n=1/2n=1/2 and the Ising-type component order near n=1n=1n=1. The quantum Monte Carlo results for the transitions from the superfluid state to these two ordered states show marked contrast with the Gutzwiller results. Namely, although they are both accompanied by phase separation into commensurate (n=1/2n=1/2n=1/2 or n=1n=1n=1) and incommensurate density phases, these transitions are both continuous. The continuous growth of the component correlation severely suppresses the superfluidity as well as the inverse of the effective mass in the critical region of the component order transition in contrast to the persistence of the superfluidity in the density-ordered state. We propose a mechanism of the mass enhancement observed even far from the Mott insulating filling n=1n=1n=1, when the Ising-type component order persists into n≠1n \neq 1n=1. Possible relevance of this type of mass enhancement in other systems is also discussed.
Various types of superfluid-insulator transitions are investigated for two-component lattice boson systems in two dimensions with on-site hard-core repulsion and the component-dependent intersite interaction. The mean-field phase diagram is obtained by the Gutzwiller-type variational technique. Various ground-state properties are also studied by the quantum Monte Carlo method. Our model exhibits two types of diagonal long-range orders; the density order around the density n =1/2 and the Ising-type component order near n =1. In contrast to the Gutzwiller results, the Monte Carlo results show that the continuous growth of the component correlation severely suppresses the superfluidity as well as the inverse of the effective mass in the critical region of the component order transition. We propose a mechanism of this mass enhancement observed even far from the Mott insulating filling n =1, when the Ising-type component order persists into n ≠1. Possible relevance of this type of mass enhancement in other systems is also discussed.
The supersolid phase of soft-core bosons in two dimensions is investigated using the self-consistent Hartree-Fock and quantum Monte Carlo methods. An approximate phase diagram at finite temperatures is initially constructed using the mean-field approach, which is subsequently validated through precise path-integral simulations, enabling a microscopic characterization of the various phases. Superfluid and melting/freezing transitions are analyzed through the superfluid density and the long-range behavior of correlation functions associated with positional and orientational order, in accordance with the general picture of Berezinskii-Kosterlitz-Thouless transitions. A broad region at low temperatures is identified where the supersolid phase exists, separating the uniform superfluid phase from the normal quasicrystal phase. Additionally, a potential intermediate hexatic phase with quasi-long-range orientational order is identified in a narrow region between the normal solid and fluid phases. These findings establish self-consistent Hartree-Fock theory beyond the local density approximation as an effective tool, complementary to computationally intensive quantum Monte Carlo simulations, for investigating the melting of the supersolid phase and the possible emergence of the hexatic superfluid phase in bosonic systems with various interaction potentials.
The Bose-Hubbard model exhibits a rich phase diagram consisting both of insulating regimes where diagonal long-range (solid) order dominates as well as conducting regimes where off-diagonal long-range order (superfluidity) is present. In this paper we describe the results of quantum Monte Carlo calculations of the phase diagram, both for the hard- and soft-core cases, with a particular focus on the possibility of simultaneous superfluid and solid order. We also discuss the appearance of phase separation in the model. The simulations are compared with analytic calculations of the phase diagram and spin-wave dispersion.