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

• URL: http://arxiv.org/abs/2201.03989v1
• Date: Tue, 11 Jan 2022 15:08:41 GMT
• Title: The Negativity Hamiltonian: An operator characterization of mixed-state entanglement
• Authors: Sara Murciano, Vittorio Vitale, Marcello Dalmonte, Pasquale Calabrese
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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