Superfluid, Supersolid, and Checkerboard Solid in Two-Component Bosons in an Optical Lattice: Study by Means of Gross–Pitaevskii Theory and Monte-Carlo Simulations

Yoshihito Kuno, Keita Suzuki, Ikuo Ichinose

arXiv:1402.0284Journal of the Physical Society of JapanJun 13, 20143 citations

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

Anne van Otterlo, Karl-Heinz Wagenblast

arXiv:cond-mat/9312034Physical Review LettersMay 30, 199478 citations

Journal of the Physical Society of Japan

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

Yukitoshi Motome, Masatoshi Imada

Published Jul 15, 1996• 1 citation

Publisher

Abstract

DOI: 10.1143/jpsj.65.2135

Related papers

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.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/9603028Mar 5, 19960 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.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/0701337Physical Review BMay 2, 200753 citations

Effect of Doublon–Holon Binding on Mott Transition–Variational Monte Carlo Study of Two-Dimensional Bose Hubbard Models

Hisatoshi Yokoyama, Tomoaki Miyagawa, Masao Ogata

To understand the mechanism of Mott transitions in case of no magnetic influence, superfluid-insulator (Mott) transitions in the S=0 Bose Hubbard model at unit filling are studied on the square and triangular lattices, using a variational Monte Carlo method. In trial many-body wave functions, we introduce various types of attractive correlation factors between a doubly-occupied site (doublon, D) and an empty site (holon, H), which play a central role for Mott transitions, in addition to the onsite repulsive (Gutzwiller) factor. By optimizing distance-dependent parameters, we study various properties of this type of wave functions. With a hint from the Mott transition arising in a completely D-H bound state, we propose an improved picture of Mott transitions, by introducing two characteristic length scales, the D-H binding length $ξ_{\rm dh}$ and the minimum D-D exclusion length $ξ_{\rm dd}$ . Generally, a Mott transition occurs when $ξ_{\rm dh}$ becomes comparable to $ξ_{\rm dd}$ . In the conductive (superfluid) state, domains of D-H pairs overlap with each other ( $ξ_{\rm dh}>ξ_{\rm dd}$ ); thereby D and H can propagate independently as density carriers by successively exchanging the partners. In contrast, intersite repulsive Jastrow (D-D and H-H) factors have little importance for the Mott transition.To understand the mechanism of Mott transitions in case of no magnetic influence, superfluid-insulator (Mott) transitions in the S=0 Bose Hubbard model at unit filling are studied on the square and triangular lattices, using a variational Monte Carlo method. In trial many-body wave functions, we introduce various types of attractive correlation factors between a doubly-occupied site (doublon, D) and an empty site (holon, H), which play a central role for Mott transitions, in addition to the onsite repulsive (Gutzwiller) factor. By optimizing distance-dependent parameters, we study various properties of this type of wave functions. With a hint from the Mott transition arising in a completely D-H bound state, we propose an improved picture of Mott transitions, by introducing two characteristic length scales, the D-H binding length $ξ_{\rm dh}$ and the minimum D-D exclusion length $ξ_{\rm dd}$. Generally, a Mott transition occurs when $ξ_{\rm dh}$ becomes comparable to $ξ_{\rm dd}$. In the conductive (superfluid) state, domains of D-H pairs overlap with each other ($ξ_{\rm dh}>ξ_{\rm dd}$); thereby D and H can propagate independently as density carriers by successively exchanging the partners. In contrast, intersite repulsive Jastrow (D-D and H-H) factors have little importance for the Mott transition.

arXiv:1104.0516Journal of the Physical Society of JapanAug 15, 201127 citations

Superfluid-insulator transitions of two-species bosons in an optical lattice

Andreas Isacsson, Min-Chul Cha, K. Sengupta +1 more

We consider the two-species bosonic Hubbard model with variable interspecies interaction and hopping strength in the grand canonical ensemble with a common chemical potential. We analyze the superfluid-insulator (SI) transition for the relevant parameter regimes and compute the ground state phase diagram in the vicinity of odd filling Mott states. We find that the superfluid-insulator transition occurs with (a) simultaneous onset of superfluidity of both species or (b) coexistence of Mott insulating state of one species and superfluidity of the other or, in the case of unit filling, (c) complete depopulation of one species. The superfluid-insulator transition can be first order in a large region of the phase diagram. We develop a variational mean-field method which takes into account the effect of second order quantum fluctuations on the superfluid-insulator transition and corroborate the mean-field phase diagram using a quantum Monte Carlo study.We consider the two-species bosonic Hubbard model with variable interspecies interaction and hopping strength in the grand canonical ensemble with a common chemical potential. We analyze the superfluid-insulator (SI) transition for the relevant parameter regimes and compute the ground state phase diagram in the vicinity of odd filling Mott states. We find that the superfluid-insulator transition occurs with (a) simultaneous onset of superfluidity of both species or (b) coexistence of Mott insulating state of one species and superfluidity of the other or, in the case of unit filling, (c) complete depopulation of one species. The superfluid-insulator transition can be first order in a large region of the phase diagram. We develop a variational mean-field method which takes into account the effect of second order quantum fluctuations on the superfluid-insulator transition and corroborate the mean-field phase diagram using a quantum Monte Carlo study.

arXiv:cond-mat/0508068Physical Review BNov 15, 2005118 citations

Superfluid, Supersolid, and Checkerboard Solid in Two-Component Bosons in an Optical Lattice: Study by Means of Gross–Pitaevskii Theory and Monte-Carlo Simulations

Yoshihito Kuno, Keita Suzuki, Ikuo Ichinose

The bosonic t-J model is a strong-on-site repulsion limit of the two-component Bose-Hubbard model and is expected to be realized by experiments of cold atoms in an optical lattice. In previous papers, we studied the bosonic t-J model by both analytical methods and numerical Monte - Carlo (MC) simulations. However, in the case of finite $J_z$ , where $J_z$ is the $z$ -component coupling constant of the pseudospin interaction, the phase diagram of the model was investigated by assuming the checkerboard type of boson densities. In this study, we shall continue our previous study of the bosonic t-J model using both the Gross-Pitaevskii (GP) theory and MC simulations without assuming any pattern of boson densities. These two methods complement each other and give reliable results. We show that as $J_z$ is increased, the superfluid state evolves into a supersolid (SS), and furthermore into a genuine solid with the checkerboard symmetry. In the present study, we propose a method identifying quantum phase transitions in the GP theory. We also study finite-temperature phase transitions of the superfluidity and the diagonal solid order of the SS by MC simulations.The bosonic t-J model is a strong-on-site repulsion limit of the two-component Bose-Hubbard model and is expected to be realized by experiments of cold atoms in an optical lattice. In previous papers, we studied the bosonic t-J model by both analytical methods and numerical Monte - Carlo (MC) simulations. However, in the case of finite $J_z$, where $J_z$ is the $z$-component coupling constant of the pseudospin interaction, the phase diagram of the model was investigated by assuming the checkerboard type of boson densities. In this study, we shall continue our previous study of the bosonic t-J model using both the Gross-Pitaevskii (GP) theory and MC simulations without assuming any pattern of boson densities. These two methods complement each other and give reliable results. We show that as $J_z$ is increased, the superfluid state evolves into a supersolid (SS), and furthermore into a genuine solid with the checkerboard symmetry. In the present study, we propose a method identifying quantum phase transitions in the GP theory. We also study finite-temperature phase transitions of the superfluidity and the diagonal solid order of the SS by MC simulations.

arXiv:1402.0284Journal of the Physical Society of JapanJun 13, 20143 citations

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

Anne van Otterlo, Karl-Heinz Wagenblast

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.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.

arXiv:cond-mat/9312034Physical Review LettersMay 30, 199478 citations

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

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.

ξ_{\rm dh}

and the minimum D-D exclusion length

ξ_{\rm dd}

. Generally, a Mott transition occurs when

ξ_{\rm dh}

becomes comparable to

ξ_{\rm dd}

. In the conductive (superfluid) state, domains of D-H pairs overlap with each other (

ξ_{\rm dh}>ξ_{\rm dd}

); thereby D and H can propagate independently as density carriers by successively exchanging the partners. In contrast, intersite repulsive Jastrow (D-D and H-H) factors have little importance for the Mott transition.

J_z

, where

J_z

is the

z

-component coupling constant of the pseudospin interaction, the phase diagram of the model was investigated by assuming the checkerboard type of boson densities. In this study, we shall continue our previous study of the bosonic t-J model using both the Gross-Pitaevskii (GP) theory and MC simulations without assuming any pattern of boson densities. These two methods complement each other and give reliable results. We show that as

J_z

is increased, the superfluid state evolves into a supersolid (SS), and furthermore into a genuine solid with the checkerboard symmetry. In the present study, we propose a method identifying quantum phase transitions in the GP theory. We also study finite-temperature phase transitions of the superfluidity and the diagonal solid order of the SS by MC simulations.