Bridging Rokhsar-Kivelson Type and Generic Quantum Phase Transitions via Thermofield Double States
arxiv(2023)
摘要
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 ℤ_2 topologically ordered phase to a trivial paramagnetic
phase.
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