AdS/CFT Correspondence with a 3D Black Hole Simulator

TL;DR

This paper introduces a lattice-based simulator for 3D black holes that models their entanglement entropy via AdS/CFT correspondence, enabling numerical and experimental studies of black hole quantum properties.

Contribution

It develops a novel fermionic lattice simulator for 3D black holes, facilitating direct numerical and potential experimental analysis of their entanglement entropy.

Findings

Identifies parameter regimes where 2D CFT describes black hole entropy

Demonstrates similar entropy behavior across a family of 3D black holes

Enables experimental realization with optical lattice technology

Abstract

One of the key applications of AdS/CFT correspondence is the duality it dictates between the entanglement entropy of Anti-de Sitter (AdS) black holes and lower-dimensional conformal field theories (CFTs). Here we employ a square lattice of fermions with inhomogeneous tunneling couplings that simulate the effect rotationally symmetric 3D black holes have on Dirac fields. When applied to 3D BTZ black holes we identify the parametric regime where the theoretically predicted 2D CFT faithfully describes the black hole entanglement entropy. With the help of the universal simulator we further demonstrate that a large family of 3D black holes exhibit the same ground state entanglement entropy behavior as the BTZ black hole. The simplicity of our simulator enables direct numerical investigation of a wide variety of 3D black holes and the possibility to experimentally realize it with optical lattice technology.