Entanglement Entropy of Coupled Conformal Field Theories and Fermi Liquids

TL;DR

This paper investigates how entanglement entropy scales in coupled gapless systems, including conformal field theories and Fermi liquids, across various dimensions and coupling strengths, using multiple analytical methods.

Contribution

It provides a comprehensive analysis of entanglement entropy in coupled gapless systems with a unified approach across different models and dimensions.

Findings

Entanglement entropy scales with system size and coupling strength.

Exact, perturbative, and scaling methods yield consistent results.

Results applicable to both conformal field theories and Fermi liquids.

Abstract

In this paper we calculate the entanglement entropy of two coupled gapless systems in general spatial dimension d. The gapless systems can be either conformal field theories (CFT), or Fermi liquids. We assume the two systems are coupled uniformly in a h-dimensional submanifold of the space, with 0 <= h <= d. We will focus on the scaling of the entanglement entropy with the size of the system, and its scaling with the inter-system coupling constant g. Three approaches will be used for our calculation: (1) exact calculation with ground state wave-functional, (2) perturbative calculation with functional path integral, (3) scaling argument.