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

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• Integrable nonlocal vector nonlinear Schrödinger equation with self-induced parity-time-symmetric Potential
• On Symmetries and Exact Solutions of a Class of Non-local Non-linear Schrodinger Equations with Self-induced PT-symmetric Potential
• Exactly Solvable Quasi-hermitian Transverse Ising Model
• Level statistics of a pseudo-Hermitian Dicke model
• A note on topological insulator phase in non-hermitian quantum systems
• Probing phase transitions in non-Hermitian systems with Multiple Quantum Coherences
• On the construction of pseudo-hermitian quantum system with a pre-determined metric in the Hilbert space
• On regular and chaotic dynamics of a non-$\mathcal{P}\mathcal{T}$-symmetric Hamiltonian system of a coupled Duffing oscillator with balanced loss and gain
• Deconstructing non-Dirac-hermitian supersymmetric quantum systems
• Supersymmetric Many-particle Quantum Systems with Inverse-square Interactions
• Deconstructing non-dissipative non-Dirac-hermitian relativistic quantum systems
• Edge states and persistent current in a PT-symmetric extended Su-Schrieffer-Heeger model with generic boundary conditions