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 wavefunctions, which are RK-type wavefunctions. A key drawback of the deformed wavefunctions 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 wavefunctions. To address this issue, we generalize the deformed wavefunction 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 $\mathbb{Z}_2$ topologically ordered phase to a trivial paramagnetic phase.