Thermodynamics of quantum isolated horizons with model Hamiltonians

Following a recent proposal, we consider the most general structure possible for the Hamiltonian operator associated with the quantum isolated horizon (QIH) with explanations of the underlying physical motivations. After a brief overview of the microcanonical ensemble results, thermodynamic analysis with this model Hamiltonian is presented considering the usual canonical energy ensemble for a fixed number of punctures. It is shown that for a quantum spacetime admitting a thermodynamically stable QIH as its internal boundary, there must exist a specific bound on the Barbero-Immirzi parameter if the entropy of the QIH obeys the Bekenstein-Hawking area law. Arguing that the known classical results must follow in the correspondence limit, the model is fixed, yielding the energy spectrum of the QIH.