Emergent superconformal symmetry in the phase diagram of a 1D $\mathbb{Z}_{2}$ lattice gauge theory

TL;DR

This paper explores the phase diagram of a 1D $ ext{Z}_2$ lattice gauge theory, revealing emergent superconformal symmetry at a multi-critical point through analytical and numerical methods.

Contribution

It provides an exact gauge-invariant mapping and identifies emergent superconformal symmetry in a minimal lattice gauge-matter system.

Findings

Phase diagram mapped using analytical and numerical methods

Emergent superconformal symmetry found at a multi-critical line

Provides a minimal lattice model for superconformal criticalities

Abstract

We investigate the phase diagram and critical properties of a one-dimensional $\mathbb{Z}_{2}$ lattice gauge theory describing an orthogonal metal, where spinless fermions and Ising spins are minimally coupled to a deconfined $\mathbb{Z}_{2}$ gauge field. Working at half-filling of fermions, we derive an exact gauge-invariant formulation that maps the model onto decoupled XXZ and transverse-field Ising chains. This mapping enables a controlled low-energy field-theory description in terms of a perturbed Luttinger liquid and Ising conformal field theories. Combining analytical arguments with numerical simulations, we determine the full phase diagram and identify various critical and multi-critical regimes. Along a specific multi-critical line, where the fermionic and bosonic velocities coincide, we find strong evidence for an emergent superconformal symmetry. Our results establish a minimal lattice realization of emergent superconformal criticalities in a gauge-matter system and provide a route toward its exploration in quantum simulators.