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Finite-temperature fidelity susceptibility for one-dimensional quantum systems
1Department of Physics and Research Center OPTIMAS, University of Kaiserslautern, D-67663 Kaiserslautern, Germany.
Physical Review Letters
|September 28, 2010
Summary
We found a universal temperature-dependent contribution to fidelity susceptibility in quantum systems. Our new lattice path integral algorithm calculates fidelity in the thermodynamic limit, validated for Luttinger models and quantum chains.
Area of Science:
- Condensed matter physics
- Quantum information theory
- Statistical mechanics
Background:
- Fidelity susceptibility quantifies the sensitivity of a quantum system's ground state to parameter changes.
- Understanding quantum phase transitions and system behavior at finite temperatures is crucial.
Purpose of the Study:
- To calculate the fidelity susceptibility (χf) for the Luttinger model, revealing universal behavior.
- To develop a novel algorithm for computing fidelity (F(T)) in the thermodynamic limit for 1D quantum systems.
- To investigate fidelity susceptibility at quantum phase transitions.
Main Methods:
- Analytical calculation of fidelity susceptibility for free spinless fermions.
- Numerical computation of fidelity susceptibility for the XXZ chain.
- Development of a lattice path integral algorithm for fidelity calculations.
Main Results:
- A universal contribution to fidelity susceptibility, linear in temperature (T) or inverse length (1/L), was identified.
- The Luttinger model predictions were successfully verified through analytical and numerical calculations.
- Fidelity susceptibility was studied across two phase transitions in the XXZ model.
Conclusions:
- The study establishes a universal feature of fidelity susceptibility in 1D quantum systems.
- The developed lattice path integral algorithm provides a powerful tool for analyzing quantum systems in the thermodynamic limit.
- The findings offer insights into quantum criticality and the behavior of quantum matter under thermal and system size variations.
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