Square-lattice s=1/2 XY model and the Jordan-Wigner fermions: The ground-state and thermodynamic properties

TL;DR

This paper reformulates the 2D s=1/2 XY model using Jordan-Wigner fermions to analyze ground-state and thermodynamic properties, exploring anisotropy effects and quantum phase transitions with comparisons to exact and approximate methods.

Contribution

It introduces a fermionic reformulation of the 2D XY model and investigates anisotropy effects on quantum phase transitions and magnetization.

Findings

Identification of quantum phase transition driven by exchange anisotropy

Analysis of zero-temperature magnetization in quasi-1D limit

Comparison of approximate results with exact solutions and numerical data

Abstract

Using the 2D Jordan-Wigner transformation we reformulate the square-lattice s=1/2 XY (XZ) model in terms of noninteracting spinless fermions and examine the ground-state and thermodynamic properties of this spin system. We consider the model with two types of anisotropy: the spatial anisotropy interpolating between 2D and 1D lattices and the anisotropy of the exchange interaction interpolating between isotropic XY and Ising interactions. We compare the obtained (approximate) results with exact ones (1D limit, square-lattice Ising model) and other approximate ones (linear spin-wave theory and exact diagonalization data for finite lattices of up to N=36 sites supplemented by finite-size scaling). We discuss the ground-state and thermodynamic properties in dependence on the spatial and exchange interaction anisotropies. We pay special attention to the quantum phase transition driven by the exchange interaction anisotropy as well as to the appearance/disappearance of the zero-temperature magnetization in the quasi-1D limit.