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Quantum fidelity in the thermodynamic limit
1Los Alamos National Laboratory, Theoretical Division, MS B213, Los Alamos, New Mexico 87545, USA.
Physical Review Letters
|March 17, 2011
Summary
Quantum fidelity, the overlap between ground states, reveals universal information about quantum phase transitions. A drop in fidelity near critical points provides insights into these transitions, as shown in the quantum Ising chain.
Area of Science:
- Condensed matter physics
- Quantum mechanics
Background:
- Quantum many-body systems exhibit complex ground states.
- Quantum phase transitions mark significant changes in these ground states.
- Quantum fidelity quantifies the overlap between quantum states.
Purpose of the Study:
- To investigate quantum fidelity in the thermodynamic regime.
- To demonstrate how fidelity changes near quantum critical points.
- To derive general scaling results for fidelity.
Main Methods:
- Analysis of ground state overlap.
- Focus on the thermodynamic limit.
- Application to the quantum Ising chain model.
Main Results:
- A drop in quantum fidelity near critical points encodes universal information.
- General scaling relations for fidelity are established.
- A simple expression for fidelity is derived for the quantum Ising chain.
Conclusions:
- Quantum fidelity is a powerful tool for characterizing quantum phase transitions.
- The observed fidelity drop provides universal insights into critical phenomena.
- The quantum Ising chain serves as a key example illustrating these findings.
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