Coherence dynamics in quantum many-body systems with conservation laws

TL;DR

This paper investigates how conservation laws influence the spreading and relaxation of quantum coherence in many-body systems, revealing distinct dynamical behaviors and linking coherence to thermalization processes.

Contribution

It provides a comprehensive analysis of coherence dynamics under various conservation laws using multiple computational methods, highlighting new relaxation mechanisms.

Findings

Conservation laws replace logarithmic saturation with slow hydrodynamic relaxation.

Symmetry constraints cause a rise-peak-fall coherence pattern with algebraic peak growth.

Ergodic Hamiltonians produce extended coherence plateaus at larger subsystem sizes.

Abstract

We study how conservation laws shape the spreading of quantum coherence in many-body dynamics. Focusing on $U(1)$-symmetric random circuits, charge-and-dipole conserving circuits, as well as ergodic Hamiltonian dynamics, we probe coherences both globally, via the participation entropy, and locally, via the relative entropy of coherence. Combining exact vector evolution, matrix product state simulations, and replica tensor networks methods, we find that conservation laws replace the logarithmic saturation of unconstrained circuits with slow hydrodynamic relaxation of the global coherence measures. Locally, symmetry-constrained circuits show a clean rise-peak-fall structure whose peak time grows algebraically with subsystem size. In contrast, ergodic Hamiltonians broaden the peak into an extended plateau at larger subsystems, highlighting a qualitatively distinct mechanism. Coherence thus emerges as a sensitive probe of symmetry-constrained thermalization, linking quantum resource dynamics to many-body transport.