Supersymmetry Breaking and Nambu-Goldstone Fermions in Interacting Majorana Chains

TL;DR

This paper introduces a one-dimensional lattice fermion model with explicit supersymmetry, exploring its phases, spontaneous SUSY breaking, and the emergence of gapless Nambu-Goldstone fermions with cubic dispersion.

Contribution

It constructs and analyzes a supersymmetric Majorana chain model, revealing phases with unbroken and spontaneously broken SUSY, and characterizes the low-energy excitations.

Findings

SUSY is unbroken at g=1 with ground states matching Kitaev chains

SUSY is restored in certain parameter regimes

SUSY is spontaneously broken for large g with gapless Nambu-Goldstone fermions

Abstract

We introduce and study a lattice fermion model in one dimension with explicit $\mathcal{N}=1$ supersymmetry (SUSY). The Hamiltonian of the model is defined by the square of a supercharge built from Majorana fermion operators. The model describes interacting Majorana fermions and its properties depend only on a single parameter $g$. When $g=1$, we find that SUSY is unbroken and the ground states are identical to those of the frustration-free Kitaev chains. We also find a parameter regime in which SUSY is restored in the infinite volume limit. For sufficiently large $g$, we prove that SUSY is spontaneously broken and the low-lying excitations are gapless, which can be thought of as Nambu-Goldstone fermions. We then show numerically that these gapless modes have cubic dispersion at long wavelength.