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Excited-state quantum phase transitions (ESQPTs) are quantum phase transitions that take place at excited levels. They have been shown for different systems with few degrees of freedom. One of such models is the Lipkin-Meshkov-Glick (LMG) model, which has one degree of freedom and is equivalent to a spin-1/2 model with infinite-range interaction. Here, we examine whether the precursors of the ESQPT in the LMG model can still be captured when the long-range interaction in this spin system becomes finite and the Hilbert space exponentially large in system size. [ABSTRACT FROM AUTHOR]

The modeling of coupled vibrational bending degrees of freedom within the two-dimensional limit of the Vibron Model is presented. The new aspects that arise in this case, in comparison to the single bender case, are examined, with special emphasis on the different geometrical limits embedded in a simple model Hamiltonian and the phase diagram associated to this two-fluid bosonic model. [ABSTRACT FROM AUTHOR]