Empirical signatures of quantum phase transitions and universal properties of critical point descriptions and dynamical symmetries

Abstract

Recently, a new signature for quantum phase transitional regions has been discussed. This signature, based on degeneracies of yrast and intrinsic excitations, can distinguish first and second order phase transitions, and is valid not only at or near the analytic critical points described by X(5) and E(5), but along the phase transitional line connecting them as well. In addition, a study of a number of recent analytic solutions to the Bohr Hamiltonian and of the dynamical symmetries of the IBA Hamiltonian has revealed a set of extremely simple and general analytic formulas that describe the energies of 0+ states. For the case of flat‐bottomed geometrical potentials, the formula depends solely on the number of relevant dimensions. For the IBA (large boson number limit) a single formula describes all three dynamical symmetries.