Reentrant phase transitions of quantum black holes

We show that backreaction of quantum fields on black hole geometries can trigger new thermal phase transitions. Specifically, we study the phase behavior of the three-dimensional quantum-corrected static Bañados-Teitelboim-Zanelli black hole, an exact solution to specific semiclassical gravitational equations due to quantum conformal matter, discovered through braneworld holography. Focusing on the canonical ensemble, for large backreaction, we find novel reentrant phase transitions as the temperature monotonically increases, namely, from thermal anti–de Sitter space to the black hole and back to thermal anti–de Sitter. The former phase transition is first-order, a quantum analog of the classical Hawking-Page phase transition, while the latter is zeroth order and has no classical counterpart. Published by the American Physical Society 2024