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Fidelity, dynamic structure factor, and susceptibility in critical phenomena
Wen-Long You1, Ying-Wai Li, Shi-Jian Gu
1Department of Physics and Institute of Theoretical Physics, The Chinese University of Hong Kong, Hong Kong, China.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 13, 2007
Summary
We found a general relation between quantum fidelity and the structure factor of a Hamiltonian. This simplifies fidelity evaluation using established methods like density matrix renormalization group and Monte Carlo simulations.
Area of Science:
- Quantum physics
- Condensed matter physics
Background:
- Quantum critical phenomena are crucial in understanding many-body quantum systems.
- Fidelity is a key measure for quantifying distinguishability between quantum states.
Purpose of the Study:
- To establish a general relation between quantum fidelity and the structure factor of the driving term in a Hamiltonian.
- To simplify the evaluation of fidelity in quantum critical phenomena.
Main Methods:
- Utilizing the concept of fidelity susceptibility.
- Applying density matrix renormalization group for ground states.
- Employing Monte Carlo simulations for thermal equilibrium states.
Main Results:
- A general relation between fidelity and the structure factor of the Hamiltonian's driving term is established.
- Fidelity evaluation is facilitated by relating it to fidelity susceptibility.
- Demonstrated applicability through examples using established numerical techniques.
Conclusions:
- The developed relation offers a practical approach to assess quantum fidelity.
- Leveraging fidelity susceptibility simplifies complex calculations in quantum critical phenomena.
- The findings are applicable to both ground states and thermal equilibrium states.
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