Symmetry Aspects of Quantum Phase Transitions

Symmetry plays a profound role in thermal and quantum phase transitions (QPT). The latter occur at zero temperature as a function of a coupling constant. Such ground-state energy phase transitions are a pervasive phenomenon observed in many branches in physics, and are realized empirically in nuclei as transitions between different shapes. QPT occur as a result of a competition between terms in the Hamiltonian with different symmetries which lead to considerable mixing in the eigenfunctions, especially at the critical-point where the structure changes most rapidly. In the present talk I will address the question of whether there are any symmetries (or traces of) still present at the critical points of QPT. As will be shown, unexpectedly, several types of intermediate-symmetries can survive in spite of the strong mixing. These include: "critical-point symmetries", [Iachello, PRL 85, 3580 (2000); 87, 052502 (2001)], "quasidynamical symmetries" [Rowe et al., NPA 745, 47 (2004); 759, 92 (2005)] and "partial dynamical symmetries" [Leviatan, PRL 98, 242502 (2007)].