  In quantum systems with many degrees of freedom the replica method is a
useful tool to study the entanglement of arbitrary spatial regions. We apply it
in a way which allows them to back-react. As a consequence, they become
dynamical subsystems whose position, form and extension is determined by their
interaction with the whole system. We analyze in particular quantum spin chains
described at criticality by a conformal field theory (CFT). Its coupling to the
Gibbs' ensemble of all possible subsystems is relevant and drives the system
into a new fixed point which is argued to be that of the 2D quantum gravity
coupled to this system. Numerical experiments on the critical Ising model show
that the new critical exponents agree with those predicted by the formula of
Knizhnik, Polyakov and Zamolodchikov.
