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Bulletin of the American Physical Society

Geometry and black holes in periodically driven critical quantum systems

Bastien Lapierre, Kenny Choo, Per Moosavi, Apoorv Tiwari, Clément Tauber, Titus Neupert, R. Chitra

Published Mar 18, 2021• 0 citations
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While driven interacting quantum matter is generically subject to heating and scrambling, certain classes of systems evade this paradigm. We study such an exceptional class in periodically driven critical (1+1)-dimensional systems with a spatially modulated but disorder-free time evolution operator. Instead of complete scrambling, the excitations of the system remain well defined. Their propagation is analogous to the evolution along light cones in a curved spacetime obtained by two black holes. The Hawking temperature serves as an order parameter which distinguishes between heating and nonheating phases. Beyond a timescale determined by the inverse Hawking temperature, excitations are absorbed by the black holes resulting in a singular concentration of energy at their horizon. We obtain these results analytically within conformal field theory, capitalizing on a mapping to sine-squared deformed field theories. Furthermore, by means of numerical calculations for an interacting XXZ spin-12 chain, we demonstrate that our findings survive lattice regularization.
In the curved spacetime of a black hole, quantum physics gives rise to distinctive effects such as Hawking radiation and maximally fast scrambling. Here, we present a scheme for an analogue quantum simulation of (1 + 1) and (2 + 1)-dimensional black holes using ultracold atoms in a locally Floquet-driven optical lattice. We show how the effective dynamics of the driven system can generate position-dependent tunnelling amplitudes that encode the curved geometry of the black hole. Moreover, we provide a simple and robust scheme to determine the Hawking temperature of a (1+1)D simulated black hole based solely on on-site atom population measurements. Combined with the highly tunable onsite atom-atom interactions typical for cold atoms, our simulator provides a powerful and feasible platform to probe the scrambling of quantum information in black holes. We illustrate the ergodicity of our (2+1)D black-hole simulator by showing numerically that its level statistics in the hard-core limit approaches the ergodic regime faster than a globally homogeneous Hamiltonian.
A bstract We consider holographic entanglement entropy in AdS black hole backgrounds by using the limit of large number of dimensions. By dividing the geometry to two patches (with one patch covering the vicinity of the black hole horizon and another covering the other regions), we are able to obtain fully analytic expressions for the entropy when the entanglement region is a strip. We argue that apart from conformal field theories at finite temperature in high number of dimensions, our method works for nearly critical theories in 3+1 dimensions. In the case of extremal black holes, dual to quantum critical systems, the results take a particularly simple form. We also comment on the case of soliton geometries. Finally, we analyze entanglement entropy for wide strips, and propose a general formula for the first subleading term in the expansion of the entropy in (inverse) system size for generic entanglement regions.