Partial-state fidelity and quantum phase transitions induced by continuous level crossing

Abstract

The global-state fidelity cannot characterize those quantum phase transitions (QPTs) induced by continuous level crossing due to its collapse around each crossing point. In this paper, we take the isotropic Lipkin-Meshkov-Glick (LMG) model and the antiferromagnetic one-dimensional Heisenberg model as examples to show that the partial-state fidelity can signal such level-crossing QPTs. Extending to the thermodynamic limit we introduce the partial-state fidelity susceptibility and study its scaling behavior. The maximum of the partial-state fidelity susceptibility goes like $N$ for the LMG model and $N^3$ for the Heisenberg model.

5 pages, 4 figures

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• Berry phase and fidelity susceptibility of the three-qubit Lipkin-Meshkov-Glick ground state
• Finite-Temperature Fidelity-Metric Approach to the Lipkin-Meshkov-Glick Model
• Simulating continuous symmetry models with discrete ones
• Dynamical quantum phase transition of a two-component Bose-Einstein condensate in an optical lattice