Quantum Phase Transition in a Pseudo-hermitian Dicke model

TL;DR

This paper demonstrates a quantum phase transition in a pseudo-hermitian Dicke model by mapping it to a known model, establishing a positive-definite metric for a consistent quantum description, and identifying solvable limits.

Contribution

It introduces a method to analyze pseudo-hermitian Hamiltonians via similarity transformations and constructs a positive-definite metric for their quantum consistency.

Findings

Identification of quantum phase transition in the pseudo-hermitian Dicke model

Construction of a positive-definite metric for the model

Exact solvable limit of the pseudo-hermitian Hamiltonian

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.