Slow thermalization and subdiffusion in $U(1)$ conserving Floquet random circuits

TL;DR

This paper investigates how certain charge-conserving quantum circuits exhibit slow thermalization and subdiffusive behavior, identifying conditions that lead to robust thermalization versus slow dynamics.

Contribution

It demonstrates that minimal charge-conserving Floquet circuits do not thermalize quickly, and shows how small modifications can induce robust thermalization.

Findings

Minimal models show slow subdiffusive dynamics and lack robust thermalization.

Extensions like longer-range interactions or larger local Hilbert space promote thermalization.

Proximate localized and integrable regimes explain slow dynamics.

Abstract

Random quantum circuits are paradigmatic models of minimally structured and analytically tractable chaotic dynamics. We study a family of Floquet unitary circuits with Haar random $U(1)$ charge conserving dynamics; the minimal such model has nearest-neighbor gates acting on spin 1/2 qubits, and a single layer of even/odd gates repeated periodically in time. We find that this minimal model is not robustly thermalizing at numerically accessible system sizes, and displays slow subdiffusive dynamics for long times. We map out the thermalization dynamics in a broader parameter space of charge conserving circuits, and understand the origin of the slow dynamics in terms of proximate localized and integrable regimes in parameter space. In contrast, we find that small extensions to the minimal model are sufficient to achieve robust thermalization; these include (i) increasing the interaction range to three-site gates (ii) increasing the local Hilbert space dimension by appending an additional unconstrained qubit to the conserved charge on each site, or (iii) using a larger Floquet period comprised of two independent layers of gates. Our results should inform future numerical studies of charge conserving circuits which are relevant for a wide range of topical theoretical questions.