Dynamics of Renyi entanglement entropy in local quantum circuits with charge conservation

Abstract

In local quantum circuits with charge conservation, we initialize the system in random product states and study the dynamics of the Renyi entanglement entropy $R_{\alpha }$. We rigorously prove that $R_{\alpha }$ with Renyi index $\alpha >1$ at time $t$ is $\le O(\sqrt{t\ln t})$ if the transport of charges is diffusive. Very recent numerical results of Rakovszky et al. show that this upper bound is saturated (up to the sub-logarithmic correction) in random local quantum circuits with charge conservation.

References in corpus (13)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• A class of quantum many-body states that can be efficiently simulated
• Matrix product states represent ground states faithfully
• Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
• Entropy scaling and simulability by Matrix Product States
• Measuring entanglement growth in quench dynamics of bosons in an optical lattice
• Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
• Diffusive hydrodynamics of out-of-time-ordered correlators with charge conservation
• Measuring entanglement entropy of a generic many-body system with a quantum switch
• Sub-ballistic growth of Rényi entropies due to diffusion
• Renyi Entropy of Chaotic Eigenstates
• Entanglement growth in diffusive systems
• Diffusive scaling of Rényi entanglement entropy

Cited by in corpus (8)

• Entanglement and charge-sharpening transitions in U(1) symmetric monitored quantum circuits
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• Sub-ballistic growth of Rényi entropies due to diffusion
• The entanglement membrane in chaotic many-body systems
• Correlations in Perturbed Dual-Unitary Circuits: Efficient Path-Integral Formula
• Information Scrambling with Conservation Laws
• Comment on "Entanglement growth in diffusive systems"
• Entanglement Dynamics From Random Product States: Deviation From Maximal Entanglement