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Physica Scripta

Two-component bosonic mixtures on the three-dimensional cubic lattice

Dian-Cheng Zhang, Shi-Jie Yang

Published Jan 29, 2026• 0 citations
Publisher

Abstract

Abstract We investigate the extended Bose–Hubbard model of two bosonic components, on a cubic lattice. Utilizing the dynamical Gutzwiller mean-field theory, we discover the counterflow supersolid state, characterized by the modulated checkerboard order, critically coexisting with a characteristic of the counterflow superfluid. The standard supersolid state of checkerboard order is further identified. And it could be governed by the phase-separation, via an adjustment of the inter-component interaction. Finally, we also chart out the relevant phase diagram.

DOI
10.1088/1402-4896/ae3a54

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Abstract We investigate the extended Bose–Hubbard model of two bosonic components, on a cubic lattice. Utilizing the dynamical Gutzwiller mean-field theory, we discover the counterflow supersolid state, characterized by the modulated checkerboard order, critically coexisting with a characteristic of the counterflow superfluid. The standard supersolid state of checkerboard order is further identified. And it could be governed by the phase-separation, via an adjustment of the inter-component interaction. Finally, we also chart out the relevant phase diagram.
Abstract We theoretically investigate the extended Bose–Hubbard model using a three-dimensional cubic lattice. In the framework of the dynamical Gutzwiller mean-field theory, we identify a checkerboard supersolid phase. By considering the repulsive interactions between next-nearest-neighbor lattice sites, we further discover an exotic type of supersolid state, whose site occupancies show a stereoscopically arrayed and staggered distribution rather than checkerboard ordering. Intriguingly, if the physical observations of two neighboring layers were superimposed, they would give rise to a checkerboard configuration. This novel structure is convincingly induced by the simultaneous existence of nearest-neighbor and next-nearest-neighbor interactions. We also identify arrayed stripes in the ground state, as well as arrayed holes in the pattern of occupancies.
We investigate quantum phases of the Bose-Bose mixtures in a two dimensional (2D) square lattice under artificial magnetic flux. Our analysis employs the inhomogeneous Dynamical Gutzwiller Mean-Field Theory (DGMFT) to investigate ground state within the two-component Bose-Hubbard model. The results based on various inter-component interactions and magnetic flux. In the case of weak inter-component interaction (wherein the inter-component interactions remain subordinate to intra-component interactions, symbolically expressed as |Uab|≤U), we observe a multitude of captivating quantum phases within the Bose-Bose mixtures. These include the emergence of the jagged density-wave supersolid(SS) phase, the latticed-like density-wave SS phase, and counterflow superfluid (CFSF) phase. Notably, the introduction of artificial magnetic flux expands the range of existence for CFSF phase. In the case of strong inter-component interaction(wherein the inter-component interactions surpass intra-component interactions, symbolically expressed as Uab>U), we delve deeper into the classification of the spatially separated phase, aptly termed the phase separated supersolid (P-SS).
We introduce an inhomogeneous bosonic mixture composed of two kinds of hard-core and semi-hard-core bosons with different nilpotency conditions and demonstrate that in contrast with the standard hard-core Bose-Hubbard model, our bosonic mixture with nearest- and next-nearest-neighbor interactions on a square lattice develops the checkerboard supersolid phase characterized by the simultaneous superfluid and checkerboard solid orders. Our bosonic mixture is created from a two-orbital Bose-Hubbard model including two kinds of bosons: a single-orbital boson and a two-orbital boson. By mapping the bosonic mixture to an anisotropic inhomogeneous spin model in the presence of a magnetic field, we study the ground-state phase diagram of the model by means of cluster mean field theory and linear spin-wave theory and show that various phases such as solid, superfluid, supersolid, and Mott insulator appear in the phase diagram of the mixture. Competition between the interactions and magnetic field causes the mixture to undergo different kinds of first- and second-order phase transitions. By studying the behavior of the spin-wave excitations, we find the reasons of all first- and second-order phase transitions. We also obtain the temperature phase diagram of the system using cluster mean field theory. We show that the checkerboard supersolid phase persists at finite temperature comparable with the interaction energies of bosons.
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 JzJ_zJz​, where JzJ_zJz​ is the zzz-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 JzJ_zJz​ 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.
In the present paper, we study finite-temperature phase structure of two-component hard-core bosons in a cubic optical lattice. The system that we study in the present paper is an effective model for the Bose-Hubbard model with strong on-site repulsions and is called bosonic t-J model. This model is a bosonic counterpart of the t-J model for the strongly-correlated electron systems like the high-temperature superconducting materials. We study the model by means of path-integral methods and Monte-Carlo simulations. We found that this system has a very rich phase structure including checkerboard-type "insulating" state, superfluid, phase-separated state, inhomogeneous cloudlet state, etc. We are also interested in the possible supersolid phase with both the checkerboard order and superfluidity and found that additional nearest-neighbor inter-species attractive force induces the supersolid state. In the supersolid state, paired superfluid appears in addition to the superfluid of single atom. This result gives important insight into mechanism of the high-temperature superconductivity of the cuprate.
We study the finite temperature properties of the extended Bose-Hubbard model on a cubic lattice. This model exhibits the so-called supersolid state. To start with, we investigate the ground-state phase diagram and find the supersolid state in the region of underdoped (less than the half-filled) density in contrast to the cases of one- and two-dimensional systems where the superfluid state and the solid state show the phase separation. Next, we investigate ordering processes at finite temperatures by quantum Monte Carlo simulations and find successive superfluid and solid phase transitions. There, we find that the two order parameters compete with each other. We establish a finite temperature phase diagram, which contains the superfluid, the solid, the supersolid, and the disordered phases. We develop a mean-field theory to analyze the ordering processes and compare the result with that obtained by simulations and discuss the mechanism of the competition of these two orders. We also study how the supersolid region shrinks as the on-site repulsion becomes strong.