Exactly solvable two-dimensional quantum spin models

TL;DR

This paper introduces a method for constructing exact ground-state wave functions for two-dimensional spin-1/2 models, revealing nondegenerate singlet states with exponential decay of correlations, applicable to various lattice types.

Contribution

It presents a novel approach to analytically solve a class of two-dimensional quantum spin models with exact ground states.

Findings

Ground state is a nondegenerate singlet.

Spin correlation functions decay exponentially.

Method applicable to different lattice geometries.

Abstract

A method is proposed for constructing an exact ground-state wave function of a two-dimensional model with spin 1/2. The basis of the method is to represent the wave function by a product of fourth-rank spinors associated with the sites of a lattice and the metric spinors corresponding to bonds between nearest neighbor sites. The function so constructed is an exact wave function of a 14-parameter model. The special case of this model depending on one parameter is analyzed in detail. The ground state is always a nondegenerate singlet, and the spin correlation functions decay exponentially with distance. The method can be generalized for models with spin 1/2 to other types of lattices.