论文标题
Luttinger系统中电子和晶格的纠缠
Entanglement of electrons and the lattice in a Luttinger system
论文作者
论文摘要
电子和晶格自由度之间的耦合在于固体许多重要特性的核心。然而，令人惊讶的是，对这些自由程度之间的纠缠知之甚少。我们在这里计算零温度的纠缠熵，以及在电子和一维链的晶格之间的有限温度下的相互信息和纠缠负效率。这些电子在Luttinger-liquid理论中描述。我们的结果表明，当人们接近稳定性的极限时，纠缠熵会发散。我们发现，互信息和纠缠负性随温度而降低。相互信息在无限温度极限中达到有限值，这是Luttinger理论的无限线性电子光谱的结果。纠缠负性在一定温度（即晶格和电子都在该温度上方的非输入）中完全零变为零。如果电子 - 电子相互作用被释放或弱筛选，则该特征温度随系统尺寸而异。但是，如果对相互作用进行了强烈筛选，则特征温度是有限的，并且与系统尺寸无关。
The coupling between electronic and lattice degrees of freedom lies at the core of many important properties of solids. Nevertheless, surprisingly little is know about the entanglement between these degrees of freedom. We here calculate the entanglement entropy at zero temperature as well as the mutual information and the entanglement negativity at finite temperatures between the electrons and the lattice of a one-dimensional chain. The electrons are described within Luttinger-liquid theory. Our results show that the entanglement entropy diverges when one approaches the limit of stability, the so-called Wentzel-Bardeen singularity. We have found that the mutual information and the entanglement negativity decrease with the temperature. The mutual information reaches a finite value in the infinite-temperature limit, which is the consequence of the infinite linear electron spectrum of Luttinger theory. The entanglement negativity becomes exactly zero above a certain temperature, i.e., the lattice and the electrons become non-entangled above this temperature. If the electron-electron interaction is unscreened or weakly screened, this characteristic temperature diverges with the system size. However, if the interaction is strongly screened the characteristic temperature is finite and independent of the system size.
