Topological properties of a chain of interacting electrons

TL;DR

This paper investigates the topological phases of a one-dimensional interacting electron system, identifying distinct topological and trivial phases, and characterizing phase transitions using exact solutions and numerical methods.

Contribution

It provides an exact analytical study of topological properties and phase diagram of a 1D interacting electron model, including Majorana edge states and topological invariants.

Findings

Identification of two topological phases with different winding numbers

Existence of a topologically trivial Mott insulator phase

Numerical confirmation of analytical phase diagram and edge states

Abstract

Within the framework of a one-dimensional model of interacting electrons, the ground state of an electron liquid is studied. Using the exact solution of the model, the ground state phase diagram and zero-energy Majorana edge functions in a finite chain are calculated. The winding number invariant reflects the topological nature of the electron liquid. The phase diagram includes two topological phases with different winding number invariants, the topologically trivial Mott insulator phase, and three critical phase transition points. Numerical calculations confirm and illustrate the analytical results.