Adiabatic Evolution of Low-Temperature Many-Body Systems
Abstract
We consider finite-range, many-body fermionic lattice models and we study the evolution of their thermal equilibrium state after introducing a weak and slowly varying time-dependent perturbation. Under suitable assumptions on the external driving, we derive a representation for the average of the evolution of local observables via a convergent expansion in the perturbation, for small enough temperatures. Convergence holds for a range of parameters that is uniform in the size of the system. Under a spectral gap assumption on the unperturbed Hamiltonian, convergence is also uniform in temperature. As an application, our expansion allows us to prove closeness of the time-evolved state to the instantaneous Gibbs state of the perturbed system, in the sense of expectation of local observables, at zero and at small temperatures. As a corollary, we also establish the validity of linear response. Our strategy is based on a rigorous version of the Wick rotation, which allows us to represent the Duhamel expansion for the real-time dynamics in terms of Euclidean correlation functions, for which precise decay estimates are proved using fermionic cluster expansion.
Cite
@article{arxiv.2211.16836,
title = {Adiabatic Evolution of Low-Temperature Many-Body Systems},
author = {Rafael L. Greenblatt and Markus Lange and Giovanna Marcelli and Marcello Porta},
journal= {arXiv preprint arXiv:2211.16836},
year = {2024}
}
Comments
The introduction and the discussion after the main result have been improved, minor corrections. We added a new corollary, about the stronger adiabatic convergence for switch functions with derivatives vanishing at zero. 61 pages