Plaquette Models, Cellular Automata, and Measurement-induced Criticality
- URL: http://arxiv.org/abs/2405.08286v2
- Date: Sat, 24 Aug 2024 17:20:15 GMT
- Title: Plaquette Models, Cellular Automata, and Measurement-induced Criticality
- Authors: Hanchen Liu, Xiao Chen,
- Abstract summary: We present a class of two-dimensional randomized plaquette models.
We observe a ground state phase transition, or equivalently, a phase transition of the symmetry operator.
These models can be equivalently understood as 1+1D randomized cellular automaton dynamics.
- Score: 3.074411226628252
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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