Murciano Sara, Vitale Vittorio, Dalmonte Marcello, Calabrese Pasquale
SISSA, via Bonomea 265, 34136 Trieste, Italy.
INFN Sezione di Trieste, via Bonomea 265, 34136 Trieste, Italy.
Phys Rev Lett. 2022 Apr 8;128(14):140502. doi: 10.1103/PhysRevLett.128.140502.
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 quasilocal functional form, that is captured by simple functional relations.
在量子多体系统的基态背景下，空间相连区域之间纠缠的局域性与相应纠缠哈密顿量的局域性直接相关：后者由局部的少体项主导。在这项工作中，我们引入负性哈密顿量作为描述多体系统部分转置对数的（非厄米）有效哈密顿算符。这使我们能够在二分纯系统范式之外探讨纠缠与算符局域性之间的联系。作为朝这个方向迈出的第一步，我们研究了费米子共形场论和自由费米子链的负性哈密顿量的结构：在这两种情况下，我们都表明负性哈密顿量具有准局域泛函形式，可由简单的函数关系来描述。
