  We show 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 BTZ black hole, an exact solution to
specific semi-classical 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.
