Thermal and quantum phase transitions in atom-field systems: a microcanonical analysis

Abstract

Abstract. The thermodynamical properties of a generalized Dicke model are calculated and related with the critical properties of its energy spectrum, namely the quantum phase transitions (QPT) and excited state quantum phase transitions (ESQPT). The thermal properties are calculated both in the canonical and the microcanonical ensembles. The latter deduction allows for an explicit description of the relation between thermal and energy spectrum properties. While in an isolated system the subspaces with different pseudo spin are disconnected, and the whole energy spectrum is accesible, in the thermal ensamble the situation is radically different. The multiplicity of the lowest energy states for each pseudo spin completely dominates the thermal behavior, making the set of degenerate states with the smallest pseudo spin at a given energy the only ones playing a role in the thermal properties, making the positive energy states thermally inaccesible. Their quantum phase transitions, from a normal to a superradiant phase, are closely associated with the thermal transition. The other critical phenomena, the ESQPTs occurring at excited energies, have no manifestation in the thermodynamics, although their effects could be seen in finite sizes corrections. A new superradiant phase is found, which only exists in the generalized model, and can be relevant in finite size systems.

From thermal to excited-state quantum phase transition: The Dicke model

“…So, ESQPTs and thermal phase transitions appear for different asymptotic regimes of N and f . (We notice that, during the progress of this work, a similar analysis, but with a different aim, was performed in the generalized Dicke model, showing that it shows two different kinds of superradiance [25]. )…”

“…(2), (5), and (6) is expected to work provided that N is large enough. On the contrary, it is also true that x max → 0 when N → ∞, suggesting that the maximally degenerated sector, and the one responsible for the behavior of the full Dicke Hamiltonian, is j → 0, or that corresponding to the lower value of j compatible with the given energy [25]. The solution of this apparent paradox is that g(N,x) becomes noncontinuous in the thermodynamical limit.…”

“…[25], as we pointed out above), were done in the subspace with maximum pseudospin sector j = N/2, in which the ground state is included. This restriction is enough to properly describe the recent experimental results [31] and also to study all the consequences of the QPT.…”

Monodromy in Dicke superradiance

“…We use a slightly extended version of the Dicke Hamiltonian [37][38][39][40], which can be written in the following form:…”

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

“…This singularity is present in the spectral level density and in related quantities, e.g., in the flow rate, which is an average slope of the quantum spectrum when λ is varied. The existence of an esqpt also influences the canonical and microcanonical thermodynamics [9,10,11,12], decoherence and relaxation processes [13,14,15], driven and dissipative dynamics [16,17], and entanglement properties [18].…”