Quantum correlated cluster mean-field theory applied to the transverse Ising model

TL;DR

This paper introduces a quantum correlated cluster mean-field theory (QCCMFT) that improves upon classical methods by incorporating quantum states, accurately predicting phase transitions in the transverse Ising model across various lattice structures.

Contribution

The paper proposes the quantum CCMFT, enhancing the classical CCMFT by using quantum states, and applies it successfully to the transverse Ising model.

Findings

Accurately predicts Curie temperature and critical field.

Results match exact solutions and simulations.

Effective across different lattice geometries.

Abstract

Mean-field theory (MFT) is one of the main available tools for analytical calculations entailed in investigations regarding many-body systems. Recently, there have been an urge of interest in ameliorating this kind of method, mainly with the aim of incorporating geometric and correlation properties of these systems. The correlated cluster MFT (CCMFT) is an improvement that succeeded quite well in doing that for classical spin systems. Nevertheless, even the CCMFT presents some deficiencies when applied to quantum systems. In this article, we address this issue by proposing the quantum CCMFT (QCCMFT), which, in contrast to its former approach, uses general quantum states in its self-consistent mean-field equations. We apply the introduced QCCMFT to the transverse Ising model in honeycomb, square, and simple cubic lattices and obtain fairly good results both for the Curie temperature of thermal phase transition and for the critical field of quantum phase transition. Actually, our results match those obtained via exact solutions, series expansions or Monte Carlo simulations.