Entanglement growth in diffusive systems

TL;DR

This paper investigates how conservation laws influence entanglement growth in diffusive quantum systems, revealing a generally linear growth with specific exceptions, supported by numerical simulations of Clifford circuits.

Contribution

It provides a theoretical prediction of entanglement growth in diffusive systems with U(1) symmetry across dimensions and qudit sizes, including a special case for qubit chains.

Findings

Entanglement growth is generally linear in time for diffusive systems.

In qubit chains, entanglement growth follows a square-root of time.

Numerical simulations confirm theoretical predictions using Clifford circuits.

Abstract

We study the influence of conservation laws on entanglement growth. Focusing on systems with U(1) symmetry, i.e., conservation of charge or magnetization, that exhibits diffusive dynamics, we theoretically predict the growth of entanglement, as quantified by the Renyi entropy, in lattice systems in any spatial dimension d and for any local Hilbert space dimension q (qudits). We find that the growth depends both on d and q, and is in generic case first linear in time, similarly as for generic systems without any conservation laws. Exception to this rule are chains of 2-level systems where the dependence is a square-root of time at all times. Predictions are numerically verified by simulations of diffusive Clifford circuits with upto 10^5 qubits. Such efficiently simulable circuits should be a useful tool for other many-body problems.