Supersymmetry breaking and Nambu-Goldstone fermions with cubic dispersion

TL;DR

This paper introduces a one-dimensional lattice fermion model with supersymmetry that exhibits spontaneous SUSY breaking and features Nambu-Goldstone fermions with cubic dispersion, combining analytical and numerical analysis.

Contribution

It presents a new lattice fermion model with supersymmetry, exploring its phase transition and low-energy excitations, including the novel cubic dispersion of Nambu-Goldstone fermions.

Findings

Spontaneous SUSY breaking occurs at certain parameters.

Nambu-Goldstone fermions exhibit cubic dispersion.

Model shows exponential ground state growth at g=0.

Abstract

We introduce a lattice fermion model in one spatial dimension with supersymmetry (SUSY) but without particle number conservation. The Hamiltonian is defined as the anticommutator of two nilpotent supercharges $Q$ and $Q^\dagger$. Each supercharge is built solely from spinless fermion operators and depends on a parameter $g$. The system is strongly interacting for small $g$, and in the extreme limit $g=0$, the number of zero-energy ground states grows exponentially with the system size. By contrast, in the large-$g$ limit, the system is non-interacting and SUSY is broken spontaneously. We study the model for modest values of $g$ and show that under certain conditions spontaneous SUSY breaking occurs in both finite and infinite chains. We analyze the low-energy excitations both analytically and numerically. Our analysis suggests that the Nambu-Goldstone fermions accompanying the spontaneous SUSY breaking have cubic dispersion at low energies.