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arXiv · 2310.19493

Interacting Kitaev Chain with $\mathcal{N}=1$ Supersymmetry

Urei Miura·Kenji Shimomura·Keisuke Totsuka
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Abstract

Lattice models with supersymmetry are known to exhibit a variety of remarkable properties that do not exist in the relativistic models. In this paper, we introduce an interacting generalization of the Kitaev chain of Majorana fermions with $\mathcal{N} = 1$ supersymmetry and investigate its low-energy properties, paying particular attention to the ground-state degeneracy and low-lying fermionic excitations. First, we establish the existence of a phase with spontaneously broken supersymmetry and a phase transition out of it with the help of variational arguments and the exact ground state. We then develop, based on the superfield formalism, a simple mean-field theory, in which the order parameters detect supersymmetry-breaking, to understand the ground-state phases and low-lying Nambu-Goldstone fermions. At the solvable point ({\em frustration-free point}), the exact ground state of an open chain exhibits large degeneracy of the order of the system size, which is attributed to the existence of a zero-energy domain wall (dubbed kink or skink) separating the topological and trivial states of Majorana fermions. Our results may shed new light on the intriguing ground-state properties of supersymmetric lattice models.

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Urei Miura, Kenji Shimomura, Keisuke Totsuka. 2023-10-30. Interacting Kitaev Chain with $\mathcal{N}=1$ Supersymmetry. https://arxiv.org/abs/2310.19493

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