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Bulletin of the Russian Academy of Sciences Physics

Effect of Local Correlations on Phase States in a Model of Semi-Hard-Core Bosons on a Square Lattice

V. A. Ulitko, V. V. Konev, A. A. Chikov, Yu. D. Panov

Published Sep 1, 2024• 0 citations
Publisher

Abstract

The authors consider a model of charged semi-hard-core bosons on a square lattice with possible occupation number $${{n}_{i}} = 0,1,2~$$ at each site. Temperature phase diagrams of the model are obtained using quantum Monte Carlo calculations, and the effect of local charge correlations is studied. It is shown that local charge correlations increase the role of quantum fluctuations in the formation of phase states.

DOI
10.1134/s1062873824707682

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The authors consider a model of charged semi-hard-core bosons on a square lattice with possible occupation number ni=0,1,2 {{n}_{i}} = 0,1,2~ni​=0,1,2  at each site. Temperature phase diagrams of the model are obtained using quantum Monte Carlo calculations, and the effect of local charge correlations is studied. It is shown that local charge correlations increase the role of quantum fluctuations in the formation of phase states.
The work considers a model of charged "semi-hard-core" bosons on a square lattice with a possible filling number at each node, ranging from 0 to 2. Temperature phase diagrams of the model are obtained using numerical Monte Carlo quantum simulation methods, and the influence of local charge correlations is examined. Comparison with results from mean-field methods shows that local charge correlations contribute to an increased role of quantum fluctuations in the formation of phase states.
Abstract Phase diagrams of charged “semi-hard-core” bosons are studied in the mean field approximation. An increase in the parameter of local correlations is shown to lead to the transformation of the phase diagram of the system from the form characteristic of “hard-core” bosons to the limiting form with a parabolic dependence of the critical temperature of charge ordering on the boson concentration. The evolution between these limiting cases is dependent on the ratio between the model parameters and is accompanied by various effects, such as the change in the phase transition type, the appearance of new order–order transition, and the appearance of new critical points.
Abstract Neighboring correlations are considered for a two-dimensional hard-core boson model on square lattice within Bethe approximation for the clusters consisting of two and four nodes. Explicit equations are derived for the determination of critical temperatures of charge and superfluid ordering and their solutions are considered for various ratios of the parameter of between-centers charge correlations to the transfer integral. It is demonstrated that assumption of neighboring correlations for the temperatures of charge ordering results in the appearance of the critical concentration of bosons, which restricts the existence domain of the solutions of charge ordering type. In the case of superfluid ordering with the assumption of neighboring correlations, the critical temperature is reduced up to zero values at half filling. A phase diagram of the hard-core boson model is constructed with the assumption of phase separation within Maxwell construction and it is shown that consideration of neighboring correlations within Bethe approximation quantitatively approximates the form of phase diagram to the results of Monte Carlo quantum method.
We have used the stochastic series expansion quantum Monte Carlo method to study interacting hard-core bosons on the square lattice with pair-hopping processes supplementing the standard single-particle hopping. Such pair hopping arises in effective models for frustrated quantum magnets. Our goal is to investigate the effects of the pair-hopping process on the commonly observed superfluid, insulating (Mott), and supersolid ground-state phases in the standard hard-core boson model with various interaction terms. The model is specifically motivated by the observation of finite dispersion of two-magnon bound states in neutron-diffraction experiments SrCu2(BO3)2{\mathrm{SrCu}}_{2}{({\mathrm{BO}}_{3})}_{2}SrCu2​(BO3​)2​. Our results show that the pair hopping has different effects on Mott phases at different filling fractions, ``melting'' them at different critical pair-hopping amplitudes. Thus, it appears that pair hopping may play an important role in determining which out of a potentially large number of Mott phases (stabilized by details of the charge-diagonal interaction terms) actually survive the totality of quantum fluctuations present.
We determine the finite-temperature phase diagram of the square lattice hard-core boson Hubbard model with nearest neighbor repulsion using quantum Monte Carlo simulations. This model is equivalent to an anisotropic spin-1/2 XXZ model in a magnetic field. We present the rich phase diagram with a first order transition between a solid and superfluid phase, instead of a previously conjectured supersolid and a tricritical end point to phase separation. Unusual reentrant behavior with ordering upon increasing the temperature is found, similar to the Pomeranchuk effect in 3He.
We consider the inclusion of short-range correlations for a two-dimensional model of local bosons on a square lattice in the framework of the Bethe approximation for clusters of 2 and 4 sites. Explicit equations are obtained for determining the critical temperatures of charge and superfluid ordering and their solutions are considered for various ratios of the charge-charge correlation parameter and the transfer integral. It is shown that taking into account short-range correlations for temperatures of charge ordering leads to the appearance of a critical concentration of bosons, limiting the region of existence of solutions like charge ordering. For superfluid ordering, when short-range correlations are taken into account, the critical temperature is reduced down to zero values at half-filling. The phase diagram of the model of local bosons is constructed with allowance for phase separation within the framework of Maxwell's construction, and it is shown that taking into account short-range correlations in the Bethe approximation quantitatively approximates the form of the phase diagram to the results of the quantum Monte Carlo method.