A method to treat strongly correlated topological superconductors in one and two dimensions

TL;DR

This paper introduces a novel method using $su(2|1)$ superalgebra to analyze strongly correlated topological superconductors in one and two dimensions, effectively handling electron fractionalization and occupation constraints.

Contribution

The paper presents a general approach employing $su(2|1)$ coherent states to solve models with strong electron-electron interactions and topological properties.

Findings

Successfully applied to 1D Kitaev chain showing topological phases

Extended to 2D BCS-Hubbard model revealing topological features

Method accounts for electron fractionalization and occupation constraints

Abstract

In the strong electron-electron (e-e) interaction limit each atomic site is constrained to be either empty or singly occupied. One can treat this scenario by fractionalizing the electrons into spin and charge degrees of freedom. We use the coherent state symbols associated with the lowest irreducible representation of the $su(2|1)$ superalgebra spanned by the Hubbard operators to solve the proposed models, as they implicitly take into account both the single particle occupation constraint and the fractionalization of the electrons. As an example, using the proposed method we solve the one dimensional Kitaev chain and two-dimensional BCS-Hubbard model to show the emergence of topological properties. The proposed procedure is quite general and can be used to analyze different lattice Hamiltonian, provided strong e-e correlation excludes doubly occupied states.