Dynamical phase transitions in spin models and automata

Johannes Richter, S E Kreuger, DAMIAN J. J. FARNELL +1 more

Hanchen Liu, Xiao Chen

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.

van Kah Ton Leeuwen

Konstantinos Sfairopoulos

This thesis studies a selection of time-independent phase transitions in lattice spin models and of dynamical phase transitions in stochastic dynamics. First, we explore the quantum phase transitions of some old and some newly introduced plaquette spin models. The classical zero-temperature ground states of these plaquette spin models can be equally constructed through a mapping to the dynamical evolution of the respective cellular automata, thus manifesting a relation between dynamical and static processes. We describe in detail the quantum phase transitions of those plaquette models whose cellular automaton constraint is linear when in the presence of quantum fluctuation fields. We also introduce and study paradigmatic models from the nonlinear cellular automaton class. We study frustration effects and effective lattice gauge theories for extensions of the models with linear constraints, thus relating disparate areas of classical and quantum many-body theory with gauge theories, classical satisfiability problems, and glasses. At the same time, we study kinetically constrained spin models whose constraints are implemented dynamically. Specifically, we focus on relating concepts of quantum dualities with classical biased stochastic models and present whole classes with multicritical points and non-invertible symmetries.

Konstantinos Sfairopoulos, Luke Causer, Jamie F. Mair +1 more

We show how the trajectories of d-dimensional cellular automata (CA) can be used to systematically construct the ground states of (d+1)-dimensional classical spin models, and we characterize their quantum phase transition, when in the presence of a transverse magnetic field. For each of the 256 one-dimensional elementary CA we explicitly construct the simplest local two-dimensional classical spin model associated to the given CA, and we also describe this method for d>1 through selected examples. We illustrate our general observations with detailed studies of: (i) the d=1 CA Rule 150 and its d=2 four-body plaquette spin model, (ii) the d=2 CA whose associated model is the d=3 square-pyramid plaquette model, and (iii) two counterpropagating d=1 Rule 60 CA that correspond to the two-dimensional Baxter-Wu spin model. For the quantum spin models, we show that the connection to CAs implies a sensitivity on the approach to the thermodynamic limit via finite-size scaling for their quantum phase transitions.

Masuo Suzuki