# Topological states in chain of interacting electrons

## TL;DR

This paper studies the topological properties of a one-dimensional chain of interacting electrons and identifies different phases based on their topological invariants.

## Contribution

The paper presents an exact solution revealing two topological phases and critical transitions in an interacting electron chain.

## Key findings

- The ground state phase diagram includes two topological phases with distinct winding number invariants.
- Numerical calculations confirm the existence of zero-energy Majorana edge functions in finite chains.
- Three critical phase transition points are identified between topological and trivial phases.

## Abstract

Within the framework of an one-dimension 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.