A Description of Phases with Induced Hybridisation at Finite Temperatures

In an extended Falicov-Kimball model, an excitonic insulator phase can be stabilised at zero temperature. With increasing temperature, the excitonic order parameter (interaction-induced hybridisation on-site, characterised by the absolute value and phase) eventually becomes disordered, which involves fluctuations of both its phase and (at higher T) its absolute value. In order to build an adequate mean field description, it is important to clarify the nature of degrees of freedom associated with the phase and absolute value of the induced hybridisation, and the corresponding phase space volume. We show that a possible description (including the phase space integration measure) is provided by the on-site density matrix parametrisation. In principle, this allows to describe both the lower-temperature regime where phase fluctuations destroy the long-range order, and the higher temperature crossover corresponding to a decrease of absolute value of the hybridisation relative to the fluctuations level. This picture is also expected to be relevant in other contexts, including the Kondo lattice model.