Numerical Simulation of Critical Quantum Dynamics without Finite Size Effects

TL;DR

This paper introduces a tensor network-based method to simulate critical quantum dynamics in infinite one-dimensional systems, avoiding finite-size effects and enabling precise determination of universal critical exponents.

Contribution

It extends classical cellular automata advantages to quantum systems, allowing direct infinite-lattice simulations of critical phenomena using non-unitary quantum cellular automata.

Findings

Accurate universal exponents for a quantum model were obtained.

The method effectively avoids finite-size and boundary effects.

It provides a new tool for classifying non-equilibrium quantum universality.

Abstract

Classical $(1+1)D$ cellular automata, as for instance Domany-Kinzel cellular automata, are paradigmatic systems for the study of non-equilibrium phenomena. Such systems evolve in discrete time-steps, and are thus free of time-discretisation errors. Moreover, information about critical phenomena can be obtained by simulating the evolution of an initial seed that, at any finite time, has support only on a finite light-cone. This allows for essentially numerically exact simulations, free of finite-size errors or boundary effects. Here, we show how similar advantages can be gained in the quantum regime: The many-body critical dynamics occurring in $(1+1)D$ quantum cellular automata with an absorbing state can be studied directly on an infinite lattice when starting from seed initial conditions. This can be achieved efficiently by simulating the dynamics of an associated one-dimensional, non-unitary quantum cellular automaton using tensor networks. We apply our method to a model introduced recently and find accurate values for universal exponents, suggesting that this approach can be a powerful tool for precisely classifying non-equilibrium universal physics in quantum systems.