Thermodynamic Analogy for Structural Phase Transitions

We investigate the relationship between ground-state (zero-temperature) quantum phase transitions in systems with variable Hamiltonian parameters and classical (temperature-driven) phase transitions in standard thermodynamics. An analogy is found between (i) phase-transitional distributions of the ground-state related branch points of quantum Hamiltonians in the complex parameter plane and (ii) distributions of zeros of classical partition functions in complex temperatures. Our approach properly describes the firstand second-order quantum phase transitions in the interacting boson model and can be generalized to finite temperatures.