The Negativity Hamiltonian: An operator characterization of mixed-state entanglement

TL;DR

This paper introduces the negativity Hamiltonian as a new operator to characterize mixed-state entanglement in many-body quantum systems, extending the understanding of entanglement locality beyond pure states.

Contribution

It defines the negativity Hamiltonian for mixed states and demonstrates its quasi-local structure in fermionic conformal field theories and free fermion chains.

Findings

Negativity Hamiltonian is quasi-local in studied models.

Functional relations capture the structure of the negativity Hamiltonian.

Extends entanglement analysis beyond bipartite pure states.

Abstract

In the context of ground states of quantum many-body systems, the locality of entanglement between connected regions of space is directly tied to the locality of the corresponding entanglement Hamiltonian: the latter is dominated by local, few-body terms. In this work, we introduce the negativity Hamiltonian as the (non hermitian) effective Hamiltonian operator describing the logarithm of the partial transpose of a many-body system. This allows us to address the connection between entanglement and operator locality beyond the paradigm of bipartite pure systems. As a first step in this direction, we study the structure of the negativity Hamiltonian for fermionic conformal field theories and a free fermion chain: in both cases, we show that the negativity Hamiltonian assumes a quasi-local functional form, that is captured by simple functional relations.