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Numerical Verification of the Fluctuation-Dissipation Theorem for Isolated Quantum Systems
Jae Dong Noh1, Takahiro Sagawa2, Joonhyun Yeo3
1Department of Physics, University of Seoul, Seoul 02504, Korea.
Physical Review Letters
|August 16, 2020
Summary
Isolated quantum systems in energy eigenstates obey the fluctuation-dissipation theorem (FDT) in the infinite size limit. Finite size corrections to the FDT were derived and confirmed numerically for the XXZ spin chain model.
Area of Science:
- Quantum statistical mechanics
- Condensed matter physics
Background:
- The fluctuation-dissipation theorem (FDT) is fundamental for systems in thermal equilibrium.
- Its validity in isolated quantum systems, particularly energy eigenstates, remains an open question.
Purpose of the Study:
- To investigate whether isolated quantum systems in energy eigenstates adhere to the FDT.
- To derive theoretical expressions for correlation functions and analyze finite-size effects.
Main Methods:
- Utilizing the eigenstate thermalization hypothesis framework.
- Deriving formal expressions for two-time correlation functions in energy eigenstates.
- Performing extensive numerical simulations on the XXZ spin chain model.
Main Results:
- Demonstrated that energy eigenstates satisfy the Kubo-Martin-Schwinger condition, a necessary and sufficient condition for FDT, in the infinite system size limit.
- Derived analytical expressions for finite-size corrections to the FDT.
- Numerical results for the XXZ model confirm the theoretical predictions.
Conclusions:
- The FDT is applicable to isolated quantum systems in energy eigenstates under specific conditions (infinite size limit).
- The derived finite-size corrections are crucial for understanding FDT in realistic, finite experimental systems.
- The findings provide a theoretical and numerical basis for experimental investigations of FDT in quantum systems.
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