Hawking-Page transition on a spin chain

The accessibility of the Hawking-Page transition in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi>AdS</a:mi><a:mn>5</a:mn></a:msub></a:math> through a one-dimensional (1D) Heisenberg spin chain is demonstrated. We use the random matrix formulation of the Loschmidt echo for a set of spin chains, and randomize the ferromagnetic spin interaction. It is shown that the thermal Loschmidt echo, when averaged, detects the predicted increase in entropy across the Hawking-Page transition. This suggests that a 1D spin chain exhibits characteristics of black hole physics in <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mn>4</b:mn><b:mo>+</b:mo><b:mn>1</b:mn></b:mrow></b:math> dimensions. We show that this approach is equally applicable to free fermion systems with a general dispersion relation.