Black-Hole Signatures in the Finite-Temperature Critical Ising Chain

TL;DR

This paper shows that the finite-temperature critical Ising chain exhibits black-hole-like signatures in its dual gravitational description, linking quantum criticality with black-hole physics via the AdS/CFT correspondence.

Contribution

It provides the first detailed analysis of black-hole signatures in a quantum spin chain at finite temperature, connecting many-body physics with gravitational phenomena.

Findings

Universal temperature-dependent excitation transport curve

Exponential relaxation governed by black hole quasi-normal modes

Pronounced minimum in entropy derivative at Hawking-Page transition

Abstract

We demonstrate that the finite-temperature critical transverse-field Ising chain exhibits quantitative signatures of black-hole physics in its dual gravitational description within the AdS/CFT correspondence. Its finite-temperature dynamics and thermodynamics are consistently captured by a mixed thermal-AdS/BTZ black hole saddle, leading to three mutually compatible observations. First, antipodal excitation transport collapses onto a universal temperature-dependent curve determined by the relative AdS and BTZ contributions to the gravitational partition function, reflecting horizon absorption. Second, in the high-temperature regime, the retarded response exhibits exponential relaxation governed by the lowest quasi-normal mode of the dual black hole. Third, the temperature derivative of the von Neumann entropy develops a pronounced minimum at a temperature consistent with the Hawking-Page transition. These results identify critical quantum spin chains as minimal and experimentally accessible platforms for probing dynamical and thermodynamic aspects of quantum black holes in controllable many-body systems.