The relationship is established between the Berry phase and spin crossover in condensed matter physics induced by high pressure. It is shown that the geometric phase has topological origin and can be considered as the order parameter for such transition.
The relationship between quantum phase transition and complex geometric phase for open quantum system governed by the non-Hermitian effective Hamiltonian with the accidental crossing of the eigenvalues is established. In particular, the geometric pha
se associated with the ground state of the one-dimensional dissipative Ising model in a transverse magnetic field is evaluated, and it is demonstrated that related quantum phase transition is of the first order.
