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

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.

28 pages, 7 figures included

References in corpus (3)

• Magnetization plateaus of SrCu_2(BO_3)_2 from a Chern-Simons theory
• Jordan-Wigner fermionization for spin-1/2 systems in two dimensions: A brief review
• Quantum Phase Transition in Coupled Spin Ladders

Cited by in corpus (5)

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• Dissipative Preparation of Antiferromagnetic Order in the Fermi-Hubbard Model
• Numerical Jordan-Wigner approach for two dimensional spin systems
• Dynamics of zz spin correlations in the square-lattice spin-1/2 isotropic XY model
• Fermionic Approach to Elementary Excitations and Magnetization Plateaus in an S=1/2 XX Hybrid Trimer-Dimer Chain