Jordan-Wigner fermionization for spin-1/2 systems in two dimensions: A brief review

Abstract

We review the papers on the Jordan-Wigner transformation in two dimensions to comment on a possibility of examining the statistical mechanics properties of two-dimensional spin-1/2 models. We discuss in some detail the two-dimensional spin-1/2 isotropic XY and Heisenberg models.

19 pages, 10 figures included

Cited by in corpus (12)

• Interacting spinless fermions in a diamond chain
• Jordan-Wigner approach to dynamic correlations in spin-ladders
• Quantum field theory from a quantum cellular automaton in one spatial dimension and a no-go theorem in higher dimensions
• Dissipative Preparation of Antiferromagnetic Order in the Fermi-Hubbard Model
• Numerical Jordan-Wigner approach for two dimensional spin systems
• Probing Anderson Localization using the Dynamics of a Qubit
• Numerical simulation of non-abelian anyons
• Square-lattice s=1/2 XY model and the Jordan-Wigner fermions: The ground-state and thermodynamic properties
• Spin-1/2 $XX$ chain in a transverse field with regularly alternating $g$-factors: Static and dynamic properties
• Dynamics of zz spin correlations in the square-lattice spin-1/2 isotropic XY model
• Jordan-Wigner fermionization for the one-dimensional Bariev model of three coupled XY chains
• Non-equilibrium variational cluster perturbation theory: quench dynamics of the quantum Ising model