Ground State Degeneracy of Interacting Spinless Fermions

TL;DR

This paper rigorously proves the ground state degeneracy properties of an interacting spinless fermion lattice model using a novel eigen-operator approach and reflection positivity in Majorana fermion representation.

Contribution

It introduces a new eigen-operator scheme and demonstrates hidden reflection positivity to analyze ground state degeneracy in various lattice structures.

Findings

Ground state is either unique or doubly degenerate for even N.

Ground state is always doubly degenerate for odd N.

Results hold across all dimensions and lattice types.

Abstract

We propose an eigen-operator scheme to study the lattice model of interacting spinless fermions at half filling and show that this model possesses a hidden form of reflection positivity in its Majorana fermion representation. Based on this observation, we prove rigourously that the ground state of this model is either unique or doubly degenerate if the lattice size $N$ is even, and is always doubly degenerate if $N$ is odd. This proof holds in all dimensions with arbitrary lattice structures.