Coarse-grained Entanglement and Operator Growth in Anomalous Dynamics

Abstract

In two-dimensional Floquet systems, many-body localized dynamics in the bulk may give rise to a chaotic evolution at the one-dimensional edges that is characterized by a nonzero chiral topological index. Such anomalous dynamics is qualitatively different from local-Hamiltonian evolution. Here we show how the presence of a nonzero index affects entanglement generation and the spreading of local operators, focusing on the coarse-grained description of generic systems. We tackle this problem by analyzing exactly solvable models of random quantum cellular automata (QCA) which generalize random circuits. We find that a nonzero index leads to asymmetric butterfly velocities with different diffusive broadening of the light cones, and to a modification of the order relations between the butterfly and entanglement velocities. We propose that these results can be understood via a generalization of the recently-introduced entanglement membrane theory, by allowing for a spacetime entropy current, which in the case of a generic QCA is fixed by the index. We work out the implications of this current on the entanglement "membrane tension" and show that the results for random QCA are recovered by identifying the topological index with a background velocity for the coarse-grained entanglement dynamics.

6 + 11 pages, 4 + 6 figures, published version

References in corpus (6)

• Operator space entanglement entropy in transverse Ising chain
• Chiral Floquet Phases of Many-body Localized Bosons
• Scrambling in Random Unitary Circuits: Exact Results
• Operator entanglement entropy of the time evolution operator in chaotic systems
• Floquet Topological Order in Interacting Systems of Bosons and Fermions
• Topological lower bound on quantum chaos by entanglement growth

Cited by in corpus (12)

• Random Quantum Circuits
• Bounds in Nonequilibrium Quantum Dynamics
• Non-equilibrium dynamics of charged dual-unitary circuits
• Quantum information spreading in generalised dual-unitary circuits
• The entanglement membrane in exactly solvable lattice models
• Entanglement asymmetry dynamics in random quantum circuits
• Exactly solvable many-body dynamics from space-time duality
• Quantum many-body spin ratchets
• Giant rectification in strongly-interacting driven tilted systems
• Quantum cellular automata and categorical dualities of spin chains
• Integrability and charge transport in asymmetric quantum-circuit geometries
• Tensor Product Structure Geometry under Unitary Channels