Spontaneous SUSY breaking and NG modes in interacting Majorana chains

The relation between spontaneous symmetry breaking and Nambu-Goldstone (NG) modes has been well studied for conventional bosonic symmetries. On the other hand, the corresponding relation for spontaneous supersymmetry (SUSY) breaking in non-relativistic systems is less understood. To fill this gap, we have studied the properties of non-relativistic systems with N=2 SUSY in [1, 2]. However, properties of N=1 SUSY are still elusive.

We thus introduce and study interacting Majorana chains with N = 1 SUSY [3]. The Hamiltonian is defined by the square of a supercharge with a parameter, which is constructed solely by Majorana fermions. In the parameter space of the model, we find a particular point at which SUSY is unbroken and the ground states can be obtained analytically. We also find that SUSY is restored in the thermodynamic limit for modest values of the parameter. We prove, for large enough parameter values, that the system exhibits spontaneous SUSY breaking. We also prove the existence of NG fermions associated with this SUSY breaking, the dispersion of which is found to be cubic in momentum.

[1] N.S., H. Katsura and Y. Nakayama, Phys. Rev. D 94, 045014.
[2] N.S., H. Katsura and Y. Nakayama, Phys. Rev. D 95, 065001.
[3] N.S. and H. Katsura, arXiv:1712.01148.