Exceptional points near first- and second-order quantum phase transitions

Abstract

We study impact of quantum phase transitions (QPTs) on the distribution of exceptional points (EPs) of the Hamiltonian in complex-extended parameter domain. Analyzing first- and second-order QPTs in the Lipkin model, we find an exponentially and polynomially close approach of EPs to the respective critical point with an increasing size of the system. If the critical Hamiltonian is subject to random perturbations of various kinds, the averaged distribution of EPs close to the critical point still carries decisive information on the QPT type. We therefore claim that properties of the EP distribution represent a parametrization-independent signature of criticality in quantum systems.

14 pages, 8 figures

References in corpus (7)

• Nonlinear atom interferometer surpasses classical precision limit
• Excited state quantum phase transitions in many-body systems
• Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections
• Quantum phase transitions in the interacting boson model
• Entanglement and spin squeezing in non-Hermitian phase transitions
• Coulomb analogy for nonhermitian degeneracies near quantum phase transitions
• A scalar two-level boson model to study the IBM phase diagram in the Casten triangle