On adiabatic theory for extended fermionic lattice systems

TL;DR

This paper reviews recent advances in adiabatic theory for ground states of extended fermionic lattice systems, focusing on super-adiabatic theorems applicable to finite and infinite systems with spectral gaps.

Contribution

It provides a comprehensive overview of generalized super-adiabatic theorems for extended fermionic systems under various gap assumptions.

Findings

Extended super-adiabatic theorems established for finite and infinite systems

Results applicable under uniform and bulk spectral gap conditions

Outline of key ideas and techniques in proofs of adiabatic theorems

Abstract

We review recent results on adiabatic theory for ground states of extended gapped fermionic lattice systems under several different assumptions. More precisely, we present generalized super-adiabatic theorems for extended but finite as well as infinite systems, assuming either a uniform gap or a gap in the bulk above the unperturbed ground state. The goal of this note is to provide an overview of these adiabatic theorems and briefly outline the main ideas and techniques required in their proofs.