  The most important feature of two-dimensional quantum Rokhsar-Kivelson (RK)
type models is that their ground state wavefunction norms can be mapped into
the partition functions of two-dimensional statistical models so that the
quantum phase transitions become the thermal phase transitions of the
corresponding statistical models. For a generic quantum critical point, we
generalize the framework of RK wavefunctions by introducing the concept of the
thermofield double (TFD) state, which is a purification of the equilibrium
density operator. Moreover, by expressing the TFD state in terms of the
projected entangled pair state, its $N$-order of R\'{e}nyi entropy results in a
three-dimensional statistical model in Euclidian spacetime, describing the
generic quantum phase transitions. Using the toric code model with two parallel
magnetic fields as an example, we explain these ideas and derive the partition
function of the three-dimensional $Z_2$ lattice gauge-Higgs model, where the
phase transitions are characterized by the three-dimensional universality
classes.
