Entanglement of two disjoint intervals in conformal field theory and the 2D Coulomb gas on a lattice

TL;DR

This paper links entanglement measures in conformal field theories to classical Coulomb gas models on lattices, providing a new perspective on quantum entanglement through statistical mechanics.

Contribution

It demonstrates that moments of reduced density matrices in certain CFTs can be represented as Coulomb gas partition functions on lattices, revealing a novel connection between quantum entanglement and classical statistical models.

Findings

Partition functions correspond to Coulomb gas models at specific couplings.

Entanglement measures relate to grand canonical partition functions of Coulomb gases.

Provides a new computational approach for entanglement in CFTs.

Abstract

In the conformal field theories given by the Ising and Dirac models, when the system is in the ground state, the moments of the reduced density matrix of two disjoint intervals and of its partial transpose have been written as partition functions on higher genus Riemann surfaces with $\mathbb{Z}_n$ symmetry. We show that these partition functions can be expressed as the grand canonical partition functions of the two-dimensional two component classical Coulomb gas on certain circular lattices at specific values of the coupling constant.