Black Hole States in Quantum Spin Chains

Abstract

We define a black hole state in a spin chain by studying thermal correlators in holography. Focusing on the Heisenberg model we investigate the thermal and complexity properties of the black hole state by evaluating its entanglement entropy, emptiness formation probability and Krylov complexity. The entanglement entropy grows logarithmically with effective central charge c=5.2. We find evidence for thermalization at infinite temperature.

Figures (5)

• Figure 1: (a) Rumer relation. (b) Recursion relation defining the black-hole states.
• Figure 2: The entanglement entropy as a function of $\ell$ for the integrable and black hole states at $L=20$.
• Figure 3: The von Neumann entanglement entropy as a function of $\ell$ for the black hole state for $L=20$ and the corresponding fit to the functional form given in eqn. (\ref{['eescaling']}).
• Figure 4: Time-averaged emptiness formation probability computed with the diagonal ensemble whose Boltzmann weights are $\left\langle {\rm BH}\right.\!\left|n \right\rangle^2$ (dots), compared to the statistical average at infinite temperature defined by the density matrix (\ref{['beta=0-ensemble']}): the solid line represents (\ref{['th-exponent']}).
• Figure 5: The time averaged Krylov complexity for respective the integrable and the black hole state for $L=16$.