From supersymmetric sine-Gordon equation to the superconformal minimal model

TL;DR

This paper introduces a lattice model that realizes emergent supersymmetric criticality in the universality class of superconformal minimal models, connecting topological phase transitions with supersymmetry via a generalized sine-Gordon framework.

Contribution

It proposes a generalized lattice model demonstrating supersymmetric criticality and elucidates the transition from Landau-Ginzburg to sine-Gordon descriptions using bosonization and RG techniques.

Findings

Realizes supersymmetric criticality in a lattice model.

Shows the transition from Landau-Ginzburg to sine-Gordon description.

Connects topological phase transitions with supersymmetry.

Abstract

We propose a generalization of the Grover-Sheng-Vishwanath model which, as solved by the density-matrix renormalization group, realizes the emergent supersymmetric criticality in the universality class of the even series of the $\mathcal{N}\!=\!1$ superconformal minimal models characterized by a central charge $5/4$. This chain model describes the topological phase transition of the propagating Majorana edge mode in topological superconductors coupled with the two-flavour Ising magnetic fluctuations (or the $XZ$ type). Using bosonization and perturbative renormalization group, we show that the augmented degrees of freedom trigger a paradigm shift from the supersymmetric Landau-Ginzburg action to the variant of the supersymmetric sine-Gordon equation, which, in the massless case, can flow towards the supersymmetric minimal series upon a generalized Feigin-Fuchs construction. Therefore, the present lattice model comprises a concrete system that exhibits the spacetime supersymmetry through the distinct route.