Nambu-Goldstone fermions in supersymmetric lattice fermion models

The relation between spontaneous symmetry breaking and gapless excitations
called Nambu-Goldstone (NG) bosons has been well understood in
both relativistic and non-relativistic systems. On the other hand,
less is known about the relation between spontaneous supersymmetry (SUSY)
breaking and NG modes in non-relativistic systems. To close this gap, we
introduce and study two lattice fermion models with SUSY in (1+1) dimension
[1,2], which are generalizations of the Nicolai model [3].
In each model, the Hamiltonian is built from two supercharges. The
supercharges have one adjustable parameter, and are comprised solely of
fermion operators. Under certain conditions, we prove that SUSY is
spontaneously broken in both finite and the infinite systems. Then, by
combining analytical and numerical methods, we show that there exist
gapless modes that can be thought of as NG fermions associated with
spontaneous SUSY breaking. We also discuss the dispersion relation of the
NG fermions in each model.

[1] N. Sannomiya, H. Katsura and Y. Nakayama, Phys. Rev. D 94, 045014 (2016).
[2] N. Sannomiya, H. Katsura and Y. Nakayama, Phys. Rev. D 95, 065001 (2017).
[3] H. Nicolai, J. Phys. A 9, 1497 (1976).