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arXiv · 1712.01148

Supersymmetry Breaking and Nambu-Goldstone Fermions in Interacting Majorana Chains

Noriaki Sannomiya·Hosho Katsura
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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.

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Noriaki Sannomiya, Hosho Katsura. 2017-12-04. Supersymmetry Breaking and Nambu-Goldstone Fermions in Interacting Majorana Chains. https://doi.org/10.1103/physrevd.99.045002

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