Strong Coupling Expansion of the Extended Hubbard Model with Spin-Orbit Coupling

TL;DR

This paper develops a strong coupling analytical approach to the extended Hubbard model with spin-orbit coupling, focusing on topological phases and superconductivity, using variational methods and topology analysis.

Contribution

It introduces a canonical transformation and variational analysis for the strong coupling regime of the extended Hubbard model with spin-orbit coupling, including topology characterization.

Findings

Identification of topological phases in the model

Comparison of Gutzwiller approximation with Monte Carlo results

Mapping of the topological phase diagram

Abstract

We study the strong coupling limit of the extended Hubbard model in two dimensions. The model consists of hopping, on-site interaction, nearest-neighbor interaction, spin-orbit coupling and Zeeman spin splitting. While the study of this model is motivated by a search for topological phases and in particular a topological superconductor, the methodology we develop may be useful for a variety of systems. We begin our treatment with a canonical transformation of the Hamiltonian to an effective model which is appropriate when the (quartic) interaction terms are larger than the (quadratic) kinetic and spin-orbit coupling terms. We proceed by analyzing the strong coupling model variationally. Since we are mostly interested in a superconducting phase we use a Gutzwiller projected BCS wavefunction as our variational state. To continue analytically we employ the Gutzwiller approximation and compare the calculated energy with Monte-Carlo calculations. Finally we determine the topology of the ground state and map out the topology phase diagram.