Excited-state quantum phase transitions and their manifestations in an extended Dicke model

Abstract

Abstract. An Excited-State Quantum Phase Transition (esqpt) is a singularity observed in quantum energy spectra in the infinitesize limit of the system. It originates in the existence of stationary points in the semiclassical Hamiltonian function. We review the classification of esqpts and present a case study in an extended Dicke model. Finally, we show some preliminary results on the dynamical effect induced by esqpts.

Critical Phenomena in Light–Matter Systems with Collective Matter Interactions

“…While in the TC model and the new phase is equal to the standard one; in the Dicke model, , so it becomes not observable. The ESPQTs predicted in the Dicke model persist in the generalized one; the only difference is that the ESQPT changes its type from a logarithmic singularity in the derivative of the smooth DoS to a step function with a downward jump from lower to higher energies in the interval [ 4 , 6 , 70 ]. On the other hand, in the absence of light–matter interaction, the boson is decoupled from the collective spin.…”

“…A finite value of leads to the generalized or extended Dicke model instead [ 6 , 45 , 61 , 69 ]. There, a new superradiant phase appears whose critical point occurs at [ 62 , 69 , 70 ]. While in the TC model and the new phase is equal to the standard one; in the Dicke model, , so it becomes not observable.…”

“…In the absence of qubit interactions, the main difference with those limits is the presence of two different superradiant domains that can coexist for some values of the light–matter coupling. Hence, three phases separated by the critical values of the light–matter coupling appear , such that [ 6 , 62 , 69 , 70 ]. Given that , in the interval , one finds the standard effect of the Dicke model that we will call here superradiance- .…”

“…As discussed before, the phenomenology of this result is similar to what is found in absence of interactions but for arbitrary , as shown in Refs. [ 6 , 62 , 69 , 70 ]. The main difference is the modification of the critical coupling of the superradiant- phase by , the critical coupling of the superradiant- phase by and the direct shift of the energy and intervals of validity by .…”

“…This classification is tied to the properties of the Hessian matrix describing the local dependence of the Hamiltonian around the fixed points of the energy surface, so it is valid only if the Hessian does not have zero or singular eigenvalues. r determines the type of singularity: for even f systems, a logarithmic-type singularity, while indicates a jump-type one [ 6 , 68 , 70 ]. As the Dicke model has only two degrees of freedom (the collective spin and the boson), it has .…”