Square-lattice 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, squarelattice 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.

Dissipative preparation of antiferromagnetic order in the Fermi-Hubbard model

“…Such a procedure is similar to the 'mean-field' treatment of the strings applied, e.g. in [76,78,89]. As a result, the hopping between rows is expressed in the same way as in equations (B .2) and (B.3), which is visualized in figure 5(d).…”

Two-Dimensional Spin-1/2 J1 – J'1 – J2 Heisenberg Model within Jordan–Wigner Transformation

“…For the four-fermionic terms in (7), the used mean-field-like approximation (see works [34,37,56,59]) reads…”

“…For the first time, the one-dimensional Jordan-Wigner transformation, which makes it possible to change from spin operators to Fermi ones, was implemented for the one-dimensional spin-1/2 chain [35]. Later, various generalizations of fermionization onto twoand three-dimensional cases were intensively applied to the study of both the thermodynamic and dynamic properties of various systems [36][37][38][39][40][41][42][43][44][45].…”

“…Here, we performed the Jordan-Wigner fermionization, which was proposed in work [56] for a two-dimensional Heisenberg model, but with the nearest-neighbor interaction only. In the meanfield-like approximation, similarly to what was done in works [37,56], we consider two possible types of antiferromagnetic ordering. The thermodynamic functions are obtained, and the magnetic order parameter in the ground state is calculated.…”

Numerical Jordan-Wigner approach for two-dimensional spin systems

“…More recently this technique was used to obtain a theoretical magnetization curve for the Shashtry-Sutherland model, reproducing at the mean field level some of the experimentally observed features for the material SrCu 2 (BO 3 ) 2 which is assumed to be described by such model 8 . Also the J 1 − J 2 model, in relation to Li 2 VOSiO 4 and Li 2 VOGeO 4 compounds 9 , and the XY model 10 were analyzed with the same technique. All the studies performed have been based on a mean field decoupling scheme as the starting point to deal with the non-local interactions introduced by the JW transformation.…”