Phase transitions in generalized spin-boson (Dicke) models

We consider a class of generalized single mode Dicke Hamiltonians with arbitrary boson coupling in the pseudo-spin $x\text{−}z$ plane. We find exact solutions in the thermodynamic, large-spin limit as a function of the coupling angle, which allows us to continuously move between the simple dephasing and the original Dicke Hamiltonians. Only in the latter case (orthogonal static and fluctuating couplings) does the parity-symmetry induced quantum phase transition occur.

Figure 1

The two displacement parameters $\sqrt{\alpha }$ and $\sqrt{\beta }$ as a function of the coupling $\lambda$ for various different angles $\theta$. The Hamiltonian is on scaled resonance, $\omega =\Omega =1$, ${\lambda }_c=0.5$.

Figure 2

The two displacement parameters $\sqrt{\alpha }$ and $\sqrt{\beta }$ as a function of the $\theta$ for representative couplings. The Hamiltonian is on scaled resonance, $\omega =\Omega =1$, ${\lambda }_c=0.5$.

Figure 3

The excitation energies of the system as a function of the coupling $\lambda$ for various different angles $\theta$. The Hamiltonian is on scaled resonance, $\omega =\Omega =1$, ${\lambda }_c=0.5$.

Figure 4

The excitation energies of the system as a function of angle $\theta$ for representative values of coupling $\lambda$. The Hamiltonian is on scaled resonance, $\omega =\Omega =1$, ${\lambda }_c=0.5$.

Figure 5

The ground-state energy, atomic inversion and mean photon number of the ground state as a function of the coupling $\lambda$ for various different angles $\theta$. The Hamiltonian is on scaled resonance, $\omega =\Omega =1$, ${\lambda }_c=0.5$.