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Coarse-Grained Entanglement and Operator Growth in Anomalous Dynamics
Zongping Gong1, Adam Nahum2,3, Lorenzo Piroli1,4
1Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, D-85748 Garching, Germany.
Physical Review Letters
|March 11, 2022
Summary
A nonzero chiral topological index in 2D Floquet systems causes chaotic edge dynamics, affecting entanglement and operator spreading. This study analyzes random quantum cellular automata to understand these anomalous behaviors.
Area of Science:
- Condensed Matter Physics
- Quantum Information Theory
Background:
- Two-dimensional Floquet systems exhibit many-body localization in the bulk.
- Chaotic dynamics at the edges are characterized by a nonzero chiral topological index.
- This edge dynamics differs from standard local-Hamiltonian evolution.
Purpose of the Study:
- Investigate how a nonzero chiral topological index impacts entanglement generation.
- Analyze the spreading of local operators in generic 2D Floquet systems.
- Provide a coarse-grained description of these anomalous dynamics.
Main Methods:
- Analysis of exactly solvable models of random quantum cellular automata (QCA).
- Generalization of random circuit models.
- Application of a modified entanglement membrane theory.
Main Results:
- A nonzero index leads to asymmetric butterfly velocities and different light cone broadening.
- The order of butterfly and entanglement velocities is modified.
- A spacetime entropy current, fixed by the index, influences entanglement membrane tension.
Conclusions:
- The topological index acts as a background velocity for coarse-grained entanglement dynamics.
- Results are consistent with a generalized entanglement membrane theory.
- The study offers insights into anomalous dynamics in Floquet systems.
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