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Center for Nonlinear Studies |
A quantum phase transition (QPT) is characterized by qualitative changes of the ground state of a many-body system and occurs at zero temperature. The QPT, being a purely quantum phenomenon driven by quantum fluctuations, is associated with energy level crossing and implies a loss of analyticity in the energy spectrum at the critical points. Since the QPT is accomplished by changing some parameter in the Hamiltonian of the system, but not the temperature, its description in the standard framework of Landau-Ginzburg theory of phase transitions fails and identification of an order parameter is still an open problem. In this connection, an issue of a great interest is the recently established relationship between geometric phases and quantum phase transitions. This relation is expected since the geometric phase associated with the energy level crossings has a peculiar behavior near the degeneracy point. It is supposed that the geometric phase, being a measure of the curvature of the Hilbert space, is able to capture drastic changes in the properties of the ground state in the presence of a QPT. In our talk we discuss the relation between the geometric phase and the QPT in an open quantum system governed by a non-Hermitian Hamiltonian. We found that the QPT is closely connected with the geometric phase and the latter may be considered as a universal order parameter for description of the QPT. In particular, the geometric phase associated with the ground state of the one-dimensional dissipative Ising model in a transverse magnetic field is evaluated, and its relationship with the QPT is established.
Host: Gennady Berman