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

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.

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Cited by in corpus (7)

• Spin liquid and infinitesimal-disorder-driven cluster spin glass in the kagome lattice
• Cluster mean field study of the Heisenberg model for CuInVO${}_5$
• Multiple phase transitions and high-field quadrupolar order in a model for $\beta$-TeVO${}_4$
• The Quantum Cluster Variational Method and the Phase Diagram of the quantum ferromagnetic $J_1$-$J_2$ model
• Disentanglement Approach to Quantum Spin Ground States: Field Theory and Stochastic Simulation
• Quantum mean-field approximation for lattice quantum models: truncating quantum correlations, and retaining classical ones
• Interplay of frustration and quantum fluctuations in a spin-1/2 anisotropic square lattice