On Hastings factorization for quantum many-body systems in the infinite volume setting

TL;DR

This paper provides detailed proofs of Hastings factorization and an area law for quantum many-body systems, extending their applicability to infinite quantum spin and fermion chains.

Contribution

It offers comprehensive proofs of Hastings factorization and the area law in a broader setting, including infinite quantum spin and fermion chains.

Findings

Proofs of Hastings factorization for infinite systems

Establishment of a 1D area law in a wider context

Applicability to quantum spin and fermion chains

Abstract

We will give self-contained and detailed proofs of the (multidimensional) Hastings factorization as well as a (1-dimensional) area law in a wider setup than previous works. Especially, they are applicable to both quantum spin and fermion chains of infinite volume as special cases.