Quantum Phase Transition in a Pseudo-hermitian Dicke model

Abstract

We show that a Dicke-type pseudo-hermitian Hamiltonian undergoes quantum phase transition by mapping it to the "Dressed Dicke Model" through a similarity transformation. We find the positive-definite metric in the Hilbert space of the pseudo-hermitian Hamiltonian so that it is unitary and allows a consistent quantum description. Further, we obtain the limit in which the pseudo-hermitian Hamiltonian is exactly solvable.

10 pages, RevTeX, no figures(v1); Two column, 5 pages, Added discussions, Version to appear in Physical Review E