Abstract
We introduce and study a lattice fermion model in one dimension with explicit 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 . When , 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 , 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 wavelengths.
- Received 14 December 2017
DOI:https://doi.org/10.1103/PhysRevD.99.045002
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