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:1009.3555 · Physical Review A

Quantum Monte Carlo method for pairing phenomena: Supercounterfluid of two-species Bose gases in optical lattices

Takahiro Ohgoe, Naoki Kawashima

Published Feb 28, 2011• 15 citations
arXivHTMLPDF

Abstract

We study the supercounterfluid (SCF) states in the two-component hard-core Bose-Hubbard model on a square lattice, using the quantum Monte Carlo method based on the worm (directed-loop) algorithm. Since the SCF state is a state of a pair condensation characterized by $\ensuremath{\langle}{a}^{\ifmmode\dagger\else\textdagger\fi{}}b\ensuremath{\rangle}\ensuremath{\ne}0,\ensuremath{\langle}a\ensuremath{\rangle}=0$, and $\ensuremath{\langle}b\ensuremath{\rangle}=0$, where $a$ and $b$ are the order parameters of the two components, it is important to study behaviors of the pair-correlation function $\ensuremath{\langle}{a}_{i}{b}_{i}^{\ifmmode\dagger\else\textdagger\fi{}}{a}_{j}^{\ifmmode\dagger\else\textdagger\fi{}}{b}_{j}\ensuremath{\rangle}$. For this purpose, we propose a choice of the worm head for calculating the pair-correlation function. From this pair correlation, we confirm the Kosterlitz-Thouless character of the SCF phase. The simulation efficiency is also improved in the SCF phase.

DOI
10.1103/physreva.83.023622

Related papers

Quantum Monte Carlo Study of Two Component Bosons and Entanglement

鍾佳民

This thesis is divided into two parts. In the first part we study quantum phases in bosonic systems in an optical lattice by using numerical unbiased Quantum Monte Carlo (QMC) method. Ultracold atoms experiments in optical lattices provide a possibility to simulate the materials of condensed matter in a clean and well-controled way. We focus on two components bosonic systems where exotic phases such as pair-superfluid and pair-supersolid appear. In the second part we provide numerical methods based on QMC simulations to study the entanglement properties of strong correlated systems. By employing the replica trick, we reconstruct the entanglement spectrum from the Renyi entropies. Furthermore, we study the trace of the power of the partial transposed reduced density matrix, which is related to the entanglement measurement negativity for mixed states. In the following we briefly summarize each chapter. In Chapter 1 we very briefly introduce the cold atom systems and the connection with QMC simulations. In Chapter 2 we review the QMC method based on the path integral (world line) representation. We focus on the directed worm algorithm which is an efficient algorithm with global updtae for bosonic and spin systems. All the following methods in this thesis – the method of two component bosonic systems, the reconstruction of entanglement spectrum and the measuring of partial transposed quantities, are based on directed worm algorithm introduced in this chapter. In Chapter 3 we discuss two component bosons in a square lattice. We show that the interspecies attraction and nearest-neighbor intraspecies repulsion result in the pair-supersolid phase, where a diagonal solid order coexists with an off-diagonal pair-superfluid order. The quantum and thermal transitions out of the pair-supersolid phase are characterized. It is found that there is a direct first-order transition from the pair-supersolid phase to the double-superfluid phase without an intermediate region. Furthermore, the melting of the pair-supersolid occurs in two steps. Upon heating, first the pair-superfluid is destroyed via a Kosterlitz-Thouless transition, then the solid order melts via an Ising transition. In Chapter 4 we represent a new method to reconstruct a subset of the entanglement spectrum of quantum many body systems by QMC, where the method can in principle be applied to two or higher dimension. The approach builds on the replica trick to evaluate particle number resolved traces of the first n of powers of a reduced density matrix. From this information we reconstruct first n entanglement spectrum levels using a polynomial root solver. We illustrate the power and limitations of the method by an application to the extended Bose-Hubbard model in one dimension where we are able to resolve the quasidegeneracy of the entanglement spectrum in the Haldane-insulator phase. In general, the method is able to reconstruct the largest few eigenvalues in each symmetry sector. In Chapter 5 we devise a Quantum Monte Carlo (QMC) method to calculate the moments of the partially transposed reduced density matrix at finite temperature. These are used to construct scale invariant combinations that are related to the negativity, a true measure of entanglement for two intervals embedded in a chain. In particular, we study several scale invariant combinations of the moments for the 1D hard-core boson model. For two adjacent intervals unusual finite size corrections are present, showing parity effects that oscillate with a filling dependent period. For large chains we find perfect agreement with conformal field theory (CFT) calculations. Oppositely, for disjoint intervals corrections are more severe and CFT is recovered only asymptotically. Furthermore, we provide evidence that their exponent is the same as that governing the corrections of the mutual information. Additionally we study the 1D Bose-Hubbard model in the superfluid phase. The finite-size effects are smaller and QMC data are already in impressive agreement with CFT at moderate large sizes.

•Jan 1, 2014•0 citations

Quantum Monte Carlo study of ultracold bosons in optical lattices

Barbara Capogrosso-Sansone

In this dissertation I present results for lattice boson systems based on quantum Monte Carlo simulations by the Worm algorithm. Lattice bosons can be realized by ultracold gases in optical lattices and, under certain conditions, they are described by the Bose-Hubbard model. I will discuss the ground state, i.e. the phase diagram and properties of elementary excitations, as well as finite temperature thermodynamic properties of the two- and three-dimensional systems. These results provide bench-marks and guidance for experimentalists. I will also discuss the phase diagram of the one-dimensional hard-core Bose-Hubbard model with three-body interactions. The model is realized by cold polar molecules in optical lattices. The ground state presents a novel solid phase at unconventional filling, characterized by coexisting charge density wave and bond orders. Such phase has not been predicted by the preexisting mean field theory.

•Jan 1, 2008•1 citation

Emergent supercounterfluid and quantum phase diagram of two-component interacting bosons in a one-dimensional optical lattice

Saisai He, Yang Liu, Bin Xi +3 more

Motivated by a recent experiment that realizes nearest-neighbor dipolar couplings in an optical lattice [C. Lagoin et al., Nature (London) 609, 485 (2022)], we study a one-dimensional version of the two-component extended Bose-Hubbard model via the density-matrix renormalization group method. By using the nearest-neighbor and on-site interaction parameters from the experiment, we start by mapping the quantum phase diagram in the hopping parameter ${t}_{A}\text{\ensuremath{-}}{t}_{B}$ plane with boson densities ${\ensuremath{\rho}}_{A}={\ensuremath{\rho}}_{B}=1/2$. In addition to the density-wave phase reported in the experiment, we find several regimes of superfluidity when one or both hopping parameters are large enough, and interestingly there is a supercounterfluid phase at moderate and comparable hopping parameters. The universality classes of these phase transitions are analyzed from the correlation functions, excitation gaps, and entanglement entropy. In particular, a Berezinskii-Kosterlitz-Thouless type is recognized for several gapped-to-gapless transitions. In addition, we also study the quantum phase transitions by varying ${\ensuremath{\rho}}_{B}$ from 0 to 1 while keeping ${\ensuremath{\rho}}_{A}=1/2$. We identify a supersolid phase in a wide range of $1/2<{\ensuremath{\rho}}_{B}<1$. Our work paves the way for realizing exotic many-body phases in cold-atom experiments upon proper tuning of experimental parameters.

arXiv:2503.18154•Physical review. B./Physical review. B•Jun 3, 2025•0 citations

Superfluid and Mott-insulator phases of one-dimensional Bose-Fermi mixtures

Aleksander Zujev, A. Baldwin, Richard T. Scalettar +3 more

We study the ground state phases of Bose-Fermi mixtures in one-dimensional optical lattices with quantum Monte Carlo simulations using the canonical worm algorithm. Depending on the filling of bosons and fermions, and the on-site intra- and interspecies interaction, different kinds of incompressible and superfluid phases appear. On the compressible side, correlations between bosons and fermions can lead to a distinctive behavior of the bosonic superfluid density and the fermionic stiffness, as well as of the equal-time Green functions, which allow one to identify regions where the two species exhibit anticorrelated flow. We present here complete phase diagrams for these systems at different fillings and as a function of the interaction parameters.

arXiv:0711.4635•Physical Review A•Sep 26, 2008•30 citations

Quantum Monte Carlo Simulations of Drag Interaction in the Superfluid Phase of the 3-Component Bose-Hubbard Model

Eirik Erlandsen

We study Andreev-Bashkin drag interactions between the superflow of different components in the superfluid phase of a three-component Bose-Hubbard model without component-mixing interactions, relevant for cold atom systems subjected to an optical lattice. By means of directed worm algorithm path integral Monte Carlo simulations we produce the phase diagram of the superfluid drag density as a function of the nearest-neighbor hopping amplitude and the chemical potential in the case of component-symmetric parameters. In both one and two dimensions, we find an expected region of negative drag close to the tip of the first Mott lobe and a generalization of the two-component supercounterfluid phase in parts of this region. In addition, we also find a more trivial positive drag with strongest presence below the Mott lobe. Further, we investigate the dependence of the drag on the details of the intercomponent interactions strengths in the weakly-coupled regime. In accordance with mean-field results obtained by Stian Hartman, we find that, unlike in the two-component case, the drag is no longer independent of the sign of the intercomponent interaction strengths. In particular, the drag between component a and b can either be strengthened or weakened by increasing interaction strength between component a and c, depending on the sign of the interaction strength between b and c.

•Jan 1, 2018•0 citations

Vortex pairing in two-dimensional Bose gases

Christopher J. Foster, P. B. Blakie, Matthew J. Davis

Recent experiments on ultracold Bose gases in two dimensions have provided evidence for the existence of the Berezinskii-Kosterlitz-Thouless (BKT) phase via analysis of the interference between two independent systems. In this work we study the two-dimensional quantum degenerate Bose gas at finite temperature using the projected Gross-Pitaevskii equation classical field method. Although this describes the highly occupied modes of the gas below a momentum cutoff, we have developed a method to incorporate the higher momentum states in our model. We concentrate on finite-sized homogeneous systems in order to simplify the analysis of the vortex pairing. We determine the dependence of the condensate fraction on temperature and compare this to the calculated superfluid fraction. By measuring the first order correlation function we determine the boundary of the Bose-Einstein condensate and BKT phases, and find it is consistent with the superfluid fraction decreasing to zero. We reveal the characteristic unbinding of vortex pairs above the BKT transition via a coarse-graining procedure. Finally, we model the procedure used in experiments to infer system correlations [Hadzibabic et al., Nature 441, 1118 (2006)], and quantify its level of agreement with directly calculated in situ correlation functions.

arXiv:0912.1675•Physical Review A•Feb 24, 2010•64 citations
We study the supercounterfluid (SCF) states in the two-component hard-core Bose-Hubbard model on a square lattice, using the quantum Monte Carlo method based on the worm (directed-loop) algorithm. Since the SCF state is a state of a pair condensation characterized by \ensuremath⟨a\ifmmode†\else\textdagger\fib\ensuremath⟩\ensuremath≠0,\ensuremath⟨a\ensuremath⟩=0\ensuremath{\langle}{a}^{\ifmmode\dagger\else\textdagger\fi{}}b\ensuremath{\rangle}\ensuremath{\ne}0,\ensuremath{\langle}a\ensuremath{\rangle}=0\ensuremath⟨a\ifmmode†\else\textdagger\fib\ensuremath⟩\ensuremath=0,\ensuremath⟨a\ensuremath⟩=0, and \ensuremath⟨b\ensuremath⟩=0\ensuremath{\langle}b\ensuremath{\rangle}=0\ensuremath⟨b\ensuremath⟩=0, where aaa and bbb are the order parameters of the two components, it is important to study behaviors of the pair-correlation function \ensuremath⟨aibi\ifmmode†\else\textdagger\fiaj\ifmmode†\else\textdagger\fibj\ensuremath⟩\ensuremath{\langle}{a}_{i}{b}_{i}^{\ifmmode\dagger\else\textdagger\fi{}}{a}_{j}^{\ifmmode\dagger\else\textdagger\fi{}}{b}_{j}\ensuremath{\rangle}\ensuremath⟨ai​bi\ifmmode†\else\textdagger\fi​aj\ifmmode†\else\textdagger\fi​bj​\ensuremath⟩. For this purpose, we propose a choice of the worm head for calculating the pair-correlation function. From this pair correlation, we confirm the Kosterlitz-Thouless character of the SCF phase. The simulation efficiency is also improved in the SCF phase.
This thesis is divided into two parts. In the first part we study quantum phases in bosonic systems in an optical lattice by using numerical unbiased Quantum Monte Carlo (QMC) method. Ultracold atoms experiments in optical lattices provide a possibility to simulate the materials of condensed matter in a clean and well-controled way. We focus on two components bosonic systems where exotic phases such as pair-superfluid and pair-supersolid appear. In the second part we provide numerical methods based on QMC simulations to study the entanglement properties of strong correlated systems. By employing the replica trick, we reconstruct the entanglement spectrum from the Renyi entropies. Furthermore, we study the trace of the power of the partial transposed reduced density matrix, which is related to the entanglement measurement negativity for mixed states. In the following we briefly summarize each chapter. In Chapter 1 we very briefly introduce the cold atom systems and the connection with QMC simulations. In Chapter 2 we review the QMC method based on the path integral (world line) representation. We focus on the directed worm algorithm which is an efficient algorithm with global updtae for bosonic and spin systems. All the following methods in this thesis – the method of two component bosonic systems, the reconstruction of entanglement spectrum and the measuring of partial transposed quantities, are based on directed worm algorithm introduced in this chapter. In Chapter 3 we discuss two component bosons in a square lattice. We show that the interspecies attraction and nearest-neighbor intraspecies repulsion result in the pair-supersolid phase, where a diagonal solid order coexists with an off-diagonal pair-superfluid order. The quantum and thermal transitions out of the pair-supersolid phase are characterized. It is found that there is a direct first-order transition from the pair-supersolid phase to the double-superfluid phase without an intermediate region. Furthermore, the melting of the pair-supersolid occurs in two steps. Upon heating, first the pair-superfluid is destroyed via a Kosterlitz-Thouless transition, then the solid order melts via an Ising transition. In Chapter 4 we represent a new method to reconstruct a subset of the entanglement spectrum of quantum many body systems by QMC, where the method can in principle be applied to two or higher dimension. The approach builds on the replica trick to evaluate particle number resolved traces of the first n of powers of a reduced density matrix. From this information we reconstruct first n entanglement spectrum levels using a polynomial root solver. We illustrate the power and limitations of the method by an application to the extended Bose-Hubbard model in one dimension where we are able to resolve the quasidegeneracy of the entanglement spectrum in the Haldane-insulator phase. In general, the method is able to reconstruct the largest few eigenvalues in each symmetry sector. In Chapter 5 we devise a Quantum Monte Carlo (QMC) method to calculate the moments of the partially transposed reduced density matrix at finite temperature. These are used to construct scale invariant combinations that are related to the negativity, a true measure of entanglement for two intervals embedded in a chain. In particular, we study several scale invariant combinations of the moments for the 1D hard-core boson model. For two adjacent intervals unusual finite size corrections are present, showing parity effects that oscillate with a filling dependent period. For large chains we find perfect agreement with conformal field theory (CFT) calculations. Oppositely, for disjoint intervals corrections are more severe and CFT is recovered only asymptotically. Furthermore, we provide evidence that their exponent is the same as that governing the corrections of the mutual information. Additionally we study the 1D Bose-Hubbard model in the superfluid phase. The finite-size effects are smaller and QMC data are already in impressive agreement with CFT at moderate large sizes.
In this dissertation I present results for lattice boson systems based on quantum Monte Carlo simulations by the Worm algorithm. Lattice bosons can be realized by ultracold gases in optical lattices and, under certain conditions, they are described by the Bose-Hubbard model. I will discuss the ground state, i.e. the phase diagram and properties of elementary excitations, as well as finite temperature thermodynamic properties of the two- and three-dimensional systems. These results provide bench-marks and guidance for experimentalists. I will also discuss the phase diagram of the one-dimensional hard-core Bose-Hubbard model with three-body interactions. The model is realized by cold polar molecules in optical lattices. The ground state presents a novel solid phase at unconventional filling, characterized by coexisting charge density wave and bond orders. Such phase has not been predicted by the preexisting mean field theory.
Motivated by a recent experiment that realizes nearest-neighbor dipolar couplings in an optical lattice [C. Lagoin et al., Nature (London) 609, 485 (2022)], we study a one-dimensional version of the two-component extended Bose-Hubbard model via the density-matrix renormalization group method. By using the nearest-neighbor and on-site interaction parameters from the experiment, we start by mapping the quantum phase diagram in the hopping parameter ${t}_{A}\text{\ensuremath{-}}{t}_{B}$ plane with boson densities ${\ensuremath{\rho}}_{A}={\ensuremath{\rho}}_{B}=1/2$. In addition to the density-wave phase reported in the experiment, we find several regimes of superfluidity when one or both hopping parameters are large enough, and interestingly there is a supercounterfluid phase at moderate and comparable hopping parameters. The universality classes of these phase transitions are analyzed from the correlation functions, excitation gaps, and entanglement entropy. In particular, a Berezinskii-Kosterlitz-Thouless type is recognized for several gapped-to-gapless transitions. In addition, we also study the quantum phase transitions by varying ${\ensuremath{\rho}}_{B}$ from 0 to 1 while keeping ${\ensuremath{\rho}}_{A}=1/2$. We identify a supersolid phase in a wide range of $1/2<{\ensuremath{\rho}}_{B}<1$. Our work paves the way for realizing exotic many-body phases in cold-atom experiments upon proper tuning of experimental parameters.
We study the ground state phases of Bose-Fermi mixtures in one-dimensional optical lattices with quantum Monte Carlo simulations using the canonical worm algorithm. Depending on the filling of bosons and fermions, and the on-site intra- and interspecies interaction, different kinds of incompressible and superfluid phases appear. On the compressible side, correlations between bosons and fermions can lead to a distinctive behavior of the bosonic superfluid density and the fermionic stiffness, as well as of the equal-time Green functions, which allow one to identify regions where the two species exhibit anticorrelated flow. We present here complete phase diagrams for these systems at different fillings and as a function of the interaction parameters.
We study Andreev-Bashkin drag interactions between the superflow of different components in the superfluid phase of a three-component Bose-Hubbard model without component-mixing interactions, relevant for cold atom systems subjected to an optical lattice. By means of directed worm algorithm path integral Monte Carlo simulations we produce the phase diagram of the superfluid drag density as a function of the nearest-neighbor hopping amplitude and the chemical potential in the case of component-symmetric parameters. In both one and two dimensions, we find an expected region of negative drag close to the tip of the first Mott lobe and a generalization of the two-component supercounterfluid phase in parts of this region. In addition, we also find a more trivial positive drag with strongest presence below the Mott lobe. Further, we investigate the dependence of the drag on the details of the intercomponent interactions strengths in the weakly-coupled regime. In accordance with mean-field results obtained by Stian Hartman, we find that, unlike in the two-component case, the drag is no longer independent of the sign of the intercomponent interaction strengths. In particular, the drag between component a and b can either be strengthened or weakened by increasing interaction strength between component a and c, depending on the sign of the interaction strength between b and c.
Recent experiments on ultracold Bose gases in two dimensions have provided evidence for the existence of the Berezinskii-Kosterlitz-Thouless (BKT) phase via analysis of the interference between two independent systems. In this work we study the two-dimensional quantum degenerate Bose gas at finite temperature using the projected Gross-Pitaevskii equation classical field method. Although this describes the highly occupied modes of the gas below a momentum cutoff, we have developed a method to incorporate the higher momentum states in our model. We concentrate on finite-sized homogeneous systems in order to simplify the analysis of the vortex pairing. We determine the dependence of the condensate fraction on temperature and compare this to the calculated superfluid fraction. By measuring the first order correlation function we determine the boundary of the Bose-Einstein condensate and BKT phases, and find it is consistent with the superfluid fraction decreasing to zero. We reveal the characteristic unbinding of vortex pairs above the BKT transition via a coarse-graining procedure. Finally, we model the procedure used in experiments to infer system correlations [Hadzibabic et al., Nature 441, 1118 (2006)], and quantify its level of agreement with directly calculated in situ correlation functions.