Numerical Jordan-Wigner approach for two-dimensional spin systems

Abstract

We present a numerical self consistent variational approach based on the Jordan-Wigner transformation for two dimensional spin systems. We apply it to the study of the well known quantum (S = 1/2) antiferromagnetic XXZ system as a function of the easy-axis anisotropy ∆ on a periodic square lattice. For the SU (2) case the method converges to a Néel ordered ground state irrespectively of the input density profile used and in accordance with other studies. This shows the potential utility of the proposed method to investigate more complicated situations like frustrated or disordered systems.

Kohn's localization in disordered fermionic systems with and without interactions

“…We restrict our analysis to paramagnetic phases (allowing charge-density waves), and we determine the phase boundary separating the metallic and the insulating ground-states. In the regime of relatively strong disorder and weak interactions the Hartree approximation is expected to provide reliable results 43,44 . Within this approximation, the Hamiltonian (10) is simplified using a mean-field decoupling of the interaction term, obtaining:…”

Comparison between disordered quantum spin-12chains

“…We first review the procedure proposed in Ref. 15 and then apply it to the present case. In terms of the fermion operators in Eq.…”

“…In a second step we implement a numerical self-consistent method based on a mean-field approximation, 15 which allows for analyzing quantum XX spin-1 2 chains with NN and NNN interactions, to be applied in the antiferromagnetic case. Finally, common features found in these spin systems are discussed.…”

Saturated Ferromagnetism from Statistical Transmutation in Two Dimensions

“…Here we follow a prescription introduced in Ref. [23], although this prescription unavoidably breaks translation invariance of a periodic cluster. The order parameter for the condensation of the composite bosons may be defined by…”