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Adiabatic Evolution of Low-Temperature Many-Body Systems
Rafael L Greenblatt1, Markus Lange2, Giovanna Marcelli3
1Mathematics Department, University of Rome "Tor Vergata", viale della Ricerca Scientifica 1, 00133 Rome, Italy.
Communications in Mathematical Physics
|March 11, 2024
Summary
This study analyzes fermionic lattice models under perturbations, deriving a convergent expansion for thermal equilibrium state evolution. This rigorously establishes linear response theory and state closeness to instantaneous Gibbs states at low temperatures.
Area of Science:
- Condensed Matter Physics
- Quantum Many-Body Systems
- Statistical Mechanics
Background:
- Understanding the dynamics of quantum systems out of equilibrium is crucial.
- Fermionic lattice models are fundamental to condensed matter physics.
- Perturbations can drive systems away from their equilibrium states.
Purpose of the Study:
- To derive a convergent expansion for the evolution of thermal equilibrium states in fermionic lattice models under weak, time-dependent perturbations.
- To rigorously establish the validity of linear response theory for these systems.
- To prove the closeness of the time-evolved state to the instantaneous Gibbs state.
Main Methods:
- Derivation of a convergent expansion in the perturbation strength.
- Application of a rigorous Wick rotation to relate real-time dynamics to Euclidean correlation functions.
- Utilizing fermionic cluster expansion for precise decay estimates.
Main Results:
- A convergent expansion for the average evolution of local observables was derived for small temperatures.
- Convergence is uniform in system size and, under a spectral gap assumption, in temperature.
- The time-evolved state is shown to be close to the instantaneous Gibbs state.
- The validity of linear response theory is established.
Conclusions:
- The developed expansion provides a rigorous framework for studying non-equilibrium dynamics in fermionic lattice models.
- The results confirm theoretical predictions about system behavior under perturbations.
- This work advances the understanding of thermalization and response in quantum many-body systems.
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