RG flow of entanglement entropy to thermal entropy

TL;DR

This paper uses holographic methods to study how entanglement entropy evolves along the RG flow, showing it approaches thermal entropy in the IR limit universally across different theories.

Contribution

It introduces a generalized temperature satisfying thermodynamics-like laws in the IR and demonstrates the universal IR behavior of entanglement entropy across various geometries.

Findings

IR entanglement entropy approaches thermal entropy

Generalized temperature satisfies thermodynamics law in IR

Universality of IR entanglement behavior across geometries

Abstract

Utilizing the holographic technique, we investigate how the entanglement entropy evolves along the RG flow. After introducing a new generalized temperature which satisfies the thermodynamics-like law even in the IR regime, we find that the renormalized entropy and the generalized temperature in the IR limit approach the thermal entropy and thermodynamic temperature of a real thermal system. This result implies that the microscopic quantum entanglement entropy in the IR region leads to the thermodynamic relation up to small quantum corrections caused by the quantum entanglement near the entangling surface. Intriguingly, this IR feature of the entanglement entropy universally happens regardless of the detail of the dual field theory and the shape of the entangling surface. We check this IR universality with a most general geometry called the hyperscaling violation geometry which is dual to a relativistic non-conformal field theory.