Plaquette Models, Cellular Automata, and Measurement-induced Criticality

TL;DR

This paper introduces randomized plaquette models in 2D that exhibit phase transitions in symmetry operators, connecting classical spin models, cellular automata, and measurement-induced entanglement transitions in quantum circuits.

Contribution

It demonstrates the universality class of certain plaquette models with multi-body interactions, linking them to measurement-induced entanglement phase transitions.

Findings

Five-body interaction model shares universality with 1+1D Clifford dynamics.

Phase transition from extensive to localized symmetry operator.

Connection established between classical models, cellular automata, and quantum circuits.

Abstract

We present a class of two-dimensional randomized plaquette models, where the multi-spin interaction term, referred to as the plaquette term, is replaced by a single-site spin term with a probability of $1-p$. By varying $p$, we observe a ground state phase transition, or equivalently, a phase transition of the symmetry operator. We find that as we vary $p$, the symmetry operator changes from being extensive to being localized in space. These models can be equivalently understood as 1+1D randomized cellular automaton dynamics, allowing the 2D transition to be interpreted as a 1+1D dynamical absorbing phase transition. In this paper, our primary focus is on the plaquette term with three or five-body interactions, where we explore the universality classes of the transitions. Specifically, for the model with five-body interaction, we demonstrate that it belongs to the same universality class as the measurement-induced entanglement phase transition observed in 1+1D Clifford dynamics, as well as the boundary entanglement transition of the 2D cluster state induced by random bulk Pauli measurements. This work establishes a connection between transitions in classical spin models, cellular automata, and hybrid random circuits.