Entanglement Wedge Cross Section Growth During Thermalization

Abstract

Motivated by exploring the thermalization process in relativistic and non-relativistic holographic field theories after a non-local quench, we investigate some features in the time evolution of the entanglement wedge cross section (EWCS). This quantity is a possible holographic dual to some non-local information measures such as entanglement of purification. In particular, we focus on the time dependence of EWCS during black hole formation in D+2 dimensional AdS spacetime as well as geometries with Lifshitz and hyperscaling violating exponents. A combination of analytic and numerical results for large symmetric strip shaped boundary subregions shows that the scaling of EWCS at early times only depends on the Lifshitz exponent. In addition, this early growth regime is followed by a linear growth regime whose velocity depends on the dimensions of spacetime, the Lifshitz exponent, and the hyperscaling parameter. This velocity is the same as the entanglement velocity and for nontrivial dynamical exponent depends on the temperature of the final equilibrium state.

22 pages, 7 figures, references added, updated to match the published version

References in corpus (10)

• Thermalization of Strongly Coupled Field Theories
• Holographic Evolution of Entanglement Entropy
• Evolution of Holographic Entanglement Entropy after Thermal and Electromagnetic Quenches
• Charged Black Branes with Hyperscaling Violating Factor
• Some Aspects of Entanglement Wedge Cross-Section
• Aspects of Hyperscaling Violating Geometries at Finite Cutoff
• Balanced Partial Entanglement and Mixed State Correlations
• Evolution of Entanglement Wedge Cross Section Following a Global Quench
• Holographic study of entanglement and complexity for mixed states
• Entanglement wedge cross-section in shock wave geometries