Emergent spacetime supersymmetry in an interacting Kitaev chain with explicit supersymmetry

TL;DR

This paper demonstrates the emergence of spacetime supersymmetry in an interacting Kitaev chain, revealing a phase transition from a gapless phase with broken SUSY to a gapped phase with restored SUSY, characterized by distinct conformal field theories.

Contribution

It provides a concrete lattice model exhibiting explicit microscopic supersymmetry at criticality and details the phase transition and universality classes involved.

Findings

Weak-coupling phase described by Ising CFT with c=1/2

Transition belongs to tricritical Ising universality with c=7/10

Phase structure aligns with integrable CFT deformations

Abstract

We investigate the emergence of spacetime supersymmetry (SUSY) in an interacting Kitaev chain model with explicit microscopic $\mathcal{N}=1$ quantum mechanical SUSY. As the interaction strength is varied, the model transitions from a weak-coupling gapless phase with spontaneously broken SUSY to a strong-coupling phase with restored SUSY. In this paper, we numerically determine the transition point and investigate the phase structure around it. The weak-coupling phase is governed by the Ising conformal field theory (CFT) with central charge $c=1/2$ which agrees with the prediction made in our previous work and that the SUSY restoration transition which borders the strong-coupling gapped phase belongs to the $c=7/10$ tricritical Ising universality with emergent superconformal invariance. Crucially, the phase structure around the transition closely aligns with the scenario proposed by Zamolodchikov and others based on the integrable deformation of CFTs. These findings provide a concrete example of a lattice model where explicit microscopic supersymmetry at criticality, enriches the understanding of phase transitions governed by supersymmetric conformal field theories.