Supersymmetry breaking and Nambu-Goldstone fermions in interacting Majorana chains

Noriaki Sannomiya and Hosho Katsura
Phys. Rev. D 99, 045002 – Published 7 February 2019

Abstract

We introduce and study a lattice fermion model in one dimension with explicit 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 wavelengths.

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  • Received 14 December 2017

DOI:https://doi.org/10.1103/PhysRevD.99.045002

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Particles & FieldsStatistical Physics & Thermodynamics

Authors & Affiliations

Noriaki Sannomiya and Hosho Katsura

  • Department of Physics, Graduate School of Science, The University of Tokyo, Hongo, Tokyo 113-0033, Japan

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Issue

Vol. 99, Iss. 4 — 15 February 2019

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