Bridging Rokhsar-Kivelson type and generic quantum phase transitions via thermofield double states

The formalism of the Rokhsar-Kivelson (RK) model has been frequently used to study topological phase transitions in 2D in terms of the deformed wave functions, which are RK-type wave functions. A key drawback of the deformed wave functions is that the obtained quantum critical points are RK-type, in the sense that the equal-time correlation functions are described by 2D conformal field theories (CFTs). The generic Lorentz invariant quantum critical points described by (2+1)D CFTs can not be obtained from the deformed wave functions. To address this issue, we generalize the deformed wave-function approach to the deformed thermofield double (TFD) state methodology. Through this extension, we can effectively reconstruct the absent temporal dimension at the RK-type quantum critical point. We construct deformed TFD states for a (1+1)D quantum phase transition from a symmetry-protected topological phase to a symmetry-breaking phase and for generic (2+1)D topological phase transitions from a Z₂ topologically ordered phase to a trivial paramagnetic phase.