# Exotic $Z_2$ Symmetry Breaking Transitions in 2D Correlated Systems

## TL;DR

This paper identifies an exotic universality class for $Z_2$ symmetry breaking in 2D correlated systems, characterized by a central charge of 1 and super-linear order parameter onset, challenging traditional Landau theory.

## Contribution

It reveals a new $Z_2$ symmetry breaking universality class with fractionalized order parameters and super-linear onset, expanding understanding beyond the Landau paradigm.

## Key findings

- Discovery of a $Z_2$ transition with central charge c=1
- Observation of super-linear order parameter onset
- Application to recent pseudo-gap phase experiments

## Abstract

The Landau paradigm of phase transitions is one of the backbones in critical phenomena. With a $Z_2$ symmetry, it describes the Ising universality class whose central charge is one half (c = 1=2) in two spatial dimensions (2D). Recent experiments in strongly correlated systems, however, suggest intriguing possibilities beyond the Landau paradigm. We uncover an exotic universality class of a $Z_2$ symmetry breaking transition with c = 1. It is shown that fractionalization of discrete symmetry order parameters may realize the exotic class. In addition to novel critical exponents, we find that the onset of an order parameter may be super-linear in contrast to the sub-linear onset of the Ising class. We argue that a super-linear onset of a $Z_2$ order parameter without breaking a bigger symmetry than $Z_2$ is evidence of exotic phenomena, and our results are applied to recent experiments in phase transitions at pseudo-gap temperatures.