Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk

TL;DR

This paper proves a generalized adiabatic theorem for extended fermionic systems with a bulk spectral gap, showing that finite systems approximate the infinite system's adiabatic behavior with errors decreasing faster than any inverse power of size.

Contribution

It establishes an adiabatic theorem assuming only a bulk spectral gap, even when finite systems lack a spectral gap, extending previous results to more general conditions.

Findings

Adiabatic theorem holds in the bulk of finite systems with vanishing errors

Finite systems approximate infinite system behavior faster than any inverse power of size

Spectral gap in the bulk suffices for adiabatic evolution, even without a gap in finite volumes

Abstract

We prove a generalised super-adiabatic theorem for extended fermionic systems assuming a spectral gap only in the bulk. More precisely, we assume that the infinite system has a unique ground state and that the corresponding GNS-Hamiltonian has a spectral gap above its eigenvalue zero. Moreover, we show that a similar adiabatic theorem also holds in the bulk of finite systems up to errors that vanish faster than any inverse power of the system size, although the corresponding finite volume Hamiltonians need not have a spectral gap.