Dynamics of Rényi entanglement entropy in diffusive qudit systems

Abstract

My previous work [arXiv:1902.00977] studied the dynamics of Rényi entanglement entropy $R_{\alpha }$ in local quantum circuits with charge conservation. Initializing the system in a random product state, it was proved that $R_{\alpha }$ with Rényi index $\alpha >1$ grows no faster than "diffusively" (up to a sublogarithmic correction) if charge transport is not faster than diffusive. The proof was given only for qubit or spin-$1/2$ systems. In this note, I extend the proof to qudit systems, i.e., spin systems with local dimension $d\ge 2$.

arXiv commentv2: title changed and abstract expanded

References in corpus (20)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Measuring entanglement entropy through the interference of quantum many-body twins
• A class of quantum many-body states that can be efficiently simulated
• Matrix product states represent ground states faithfully
• Operator Spreading in Random Unitary Circuits
• Ballistic spreading of entanglement in a diffusive nonintegrable system
• 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
• Does a single eigenstate encode the full Hamiltonian?
• Measuring entanglement entropy of a generic many-body system with a quantum switch
• Canonical Typicality of Energy Eigenstates of an Isolated Quantum System
• Subsystem ETH
• Sub-ballistic growth of Rényi entropies due to diffusion
• Renyi Entropy of Chaotic Eigenstates
• Quantum circuit complexity of one-dimensional topological phases
• Entanglement growth in diffusive systems
• Diffusive scaling of Rényi entanglement entropy

Cited by in corpus (10)

• Entanglement and charge-sharpening transitions in U(1) symmetric monitored quantum circuits
• Efficient classical simulation of random shallow 2D quantum circuits
• Sub-ballistic growth of Rényi entropies due to diffusion
• The entanglement membrane in chaotic many-body systems
• Finite-size scaling of out-of-time-ordered correlators at late times
• Correlations in Perturbed Dual-Unitary Circuits: Efficient Path-Integral Formula
• Information Scrambling with Conservation Laws
• Two-dimensional local Hamiltonian problem with area laws is QMA-complete
• Comment on "Entanglement growth in diffusive systems"
• Entanglement Dynamics From Random Product States: Deviation From Maximal Entanglement