Local reversibility and entanglement structure of many-body ground states

TL;DR

This paper introduces 'local reversibility' as a new way to characterize the locality of quantum many-body ground states, revealing fundamental features beyond traditional entanglement and correlation properties.

Contribution

It defines local reversibility, proves it for gapped ground states, and uses it to distinguish between microscopic and macroscopic quantum phenomena.

Findings

Unique gapped ground states are locally reversible.

Local reversibility distinguishes microscopic from macroscopic quantum states.

Properties of ground states at critical and non-critical points are characterized.

Abstract

The low-temperature physics of quantum many-body systems is largely governed by the structure of their ground states. Minimizing the energy of local interactions, ground states often reflect strong properties of locality such as the area law for entanglement entropy and the exponential decay of correlations between spatially separated observables. In this letter we present a novel characterization of locality in quantum states, which we call `local reversibility'. It characterizes the type of operations that are needed to reverse the action of a general disturbance on the state. We prove that unique ground states of gapped local Hamiltonian are locally reversible. This way, we identify new fundamental features of many-body ground states, which cannot be derived from the aforementioned properties. We use local reversibility to distinguish between states enjoying microscopic and macroscopic quantum phenomena. To demonstrate the potential of our approach, we prove specific properties of ground states, which are relevant both to critical and non-critical theories.