Plaquette Models, Cellular Automata, and Measurement-induced Criticality

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.

References in corpus (37)

• Measurement-based quantum computation with cluster states
• Measurement-Induced Phase Transitions in the Dynamics of Entanglement
• Quantum Zeno Effect and the Many-body Entanglement Transition
• Measurement-driven entanglement transition in hybrid quantum circuits
• Dynamics on the Way to Forming Glass: Bubbles in Space-time
• Theory of the phase transition in random unitary circuits with measurements
• Measurement-induced criticality in random quantum circuits
• Instantaneous non-local computation of low T-depth quantum circuits
• The Heisenberg Representation of Quantum Computers
• Unitary-projective entanglement dynamics
• Quantum Error Correction in Scrambling Dynamics and Measurement-Induced Phase Transition
• Dynamical purification phase transitions induced by quantum measurements
• Exotic topological order in fractal spin liquids
• Entanglement Transitions from Holographic Random Tensor Networks
• Statistical mechanics of quantum error correcting codes
• Subsystem symmetry protected topological order
• Conformal invariance and quantum non-locality in critical hybrid circuits
• Glassy dynamics and aging in an exactly solvable spin model
• A Quantum to Classical Phase Transition in Noisy Quantum Computers
• Entanglement Negativity at Measurement-Induced Criticality
• Fractal Symmetric Phases of Matter
• Measurement-induced phase transitions in quantum automaton circuits
• Glassiness and constrained dynamics of a short-range non-disordered spin model
• Entanglement in the stabilizer formalism
• Caging and mosaic lengthscales in plaquette spin models of glasses
• Glassiness through the emergence of effective dynamical constraints in interacting systems
• Entanglement phase transitions in random stabilizer tensor networks
• Coherence requirements for quantum communication from hybrid circuit dynamics
• Transfer-matrix DMRG for stochastic models: The Domany-Kinzel cellular automaton
• Measurement-induced phase transition in a classical, chaotic many-body system
• Measurement induced entanglement transition in two dimensional shallow circuit
• Measurement-induced phase transitions in the toric code
• Exact solutions to plaquette Ising models with free and periodic boundaries
• Scaling Exponents of Rough Surfaces Generated by the Domany-Kinzel Cellular Automaton
• Entanglement structure in the volume-law phase of hybrid quantum automaton circuits
• A universal crossover in quantum circuits governed by a proximate classical error correction transition
• Anomaly inflow, dualities, and quantum simulation of abelian lattice gauge theories induced by measurements