  In the framework of braneworld holography, we construct a quantum charged
black hole that is localized on a three-dimensional anti-de Sitter brane and
incorporates quantum backreaction effects from the boundary field theory. The
field on the brane consists of higher curvature gravitation coupled with a
nonlinear electromagnetic field, and it does not exhibit conformal symmetry. We
also investigate the thermodynamics of these quantum charged black holes from
three distinct perspectives: a pure bulk description, where the bulk
gravitation interacts with a brane; a brane description, where local dynamical
gravitation is subject to quantum backreaction from the dual quantum conformal
field; a boundary description, where the degrees of freedom for defect quantum
conformal matters are considered. In so doing we obtain doubly holographic
formulations of both the first law of thermodynamics and the Smarr (energy)
relations.
