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Ising spin system with three-site four-spin and four-site four-spin interactions

Takashi Iwashita, Kakuko Uragami, Yui Ito

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

Sz SizSjzSkzSlz CM S ! ! # $ J1SizSjz J3SizSjzSkz J4SizSjzSkzSlz DSiz # # % & ' ( ! ! ( ) ! ! # ! ! ( Sz SizSjzSkzSlz J3 /J1 J4 /J1(

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PRSM•Jan 12, 2012•0 citations
We introduce three novel cluster-based methods to describe the ground states of strongly-correlated systems such as iron-sulfur clusters, conjugated hydrocarbons, and superconductors. These methods utilize a spatial tiling of sites as their core principle. The first approach employs unrestricted cluster mean-field theory (UcMF), with clusters of Sz eigenstates. Correlations between tiles are accounted for using perturbation theory (cPT2) and coupled-cluster (cCCSD). The second approach, generalized cluster mean-field theory (GcMF), allows Sz to break in each cluster, partially including missing intercluster correlations. A projection scheme, Sz GcMF, restores global Sz symmetry for further improvement. The third approach, a non-orthogonal configuration interaction-based theory (LC-cMF) which is still in development, is based on linear combinations of different system tilings. Various criteria, such as translational symmetry and spatial proximity, guide the selection of these tilings. Benchmark calculations on one- and two-dimensional spin models show the promise of these methods. GcMF and Sz GcMF provide a qualitative improvement over UcMF, while cPT2, cCCSD, and LC-cMF can quantitatively capture inter-cluster interactions in some systems. Overall, cluster-based methods offer valuable tools for investigating strongly-correlated spin systems with potential for further advancement.
The two dimensional mixed spin system consisting of spin-1/2 and spin-1 with four-spin interactions exhibits tricritical behaviour. The influence of a transverse field on this behaviour is studied with the finite cluster approximation based on a single-site cluster theory. The state equations are derived for the square lattice. It has been shown that the system keeps its tricritical behaviour, but when the strength of the transverse field approaches a critical value, all transitions become of second-order for any value of four-spin interaction.