Non-equilibrium almost-stationary states and linear response for gapped quantum systems

TL;DR

This paper establishes linear response theory at zero temperature for gapped quantum systems with perturbations that may close the spectral gap, using a novel adiabatic theorem extension to non-equilibrium states.

Contribution

It introduces a new adiabatic theorem for situations where perturbations close the spectral gap, enabling linear response analysis in more general gapped quantum systems.

Findings

Validates linear response at zero temperature for a broad class of perturbations.

Provides formulas for higher order response coefficients.

Constructs explicit non-equilibrium almost-stationary states (NEASS).

Abstract

We prove the validity of linear response theory at zero temperature for perturbations of gapped Hamiltonians describing interacting fermions on a lattice. As an essential innovation, our result requires the spectral gap assumption only for the unperturbed Hamiltonian and applies to a large class of perturbations that close the spectral gap. Moreover, we prove formulas also for higher order response coefficients. Our justification of linear response theory is based on a novel extension of the adiabatic theorem to situations where a time-dependent perturbation closes the gap. According to the standard version of the adiabatic theorem, when the perturbation is switched on adiabatically and as long as the gap does not close, the initial ground state evolves into the ground state of the perturbed operator. The new adiabatic theorem states that for perturbations that are either slowly varying potentials or small quasi-local operators, once the perturbation closes the gap, the adiabatic evolution follows non-equilibrium almost-stationary states (NEASS) that we construct explicitly.