A supersymmetric multicritical point in a model of lattice fermions

TL;DR

This paper investigates a supersymmetric lattice fermion model, demonstrating it is a multicritical point described by a superconformal minimal model with central charge 3/2, using entanglement entropy to overcome finite-size effects.

Contribution

It confirms the continuum limit of a supersymmetric lattice model as a superconformal minimal model and highlights the role of entanglement entropy in analyzing quantum phase transitions.

Findings

Finite-size corrections are due to marginal operators breaking Lorentz invariance.

Entanglement entropy calculations significantly reduce finite-size effects.

The supersymmetric model is identified as a multicritical point.

Abstract

We study a model of spinless fermions with infinite nearest-neighbor repulsion on the square ladder which has microscopic supersymmetry. It has been conjectured that in the continuum the model is described by the superconformal minimal model with central charge c=3/2. Thus far it has not been possible to confirm this conjecture due to strong finite-size corrections in numerical data. We trace the origin of these corrections to the presence of unusual marginal operators that break Lorentz invariance, but preserve part of the supersymmetry. By relying mostly on entanglement entropy calculations with the density-matrix renormalization group, we are able to reduce finite-size effects significantly. This allows us to unambiguously determine the continuum theory of the model. We also study perturbations of the model and establish that the supersymmetric model is a multicritical point. Our work underlines the power of entanglement entropy as a probe of the phases of quantum many-body systems.