论文标题
量子几何形状的区域法律纠缠
Area-law entanglement from quantum geometry
论文作者
论文摘要
包括浆果曲率和量子度量的量子几何形状在多波段相互作用的电子系统中起关键作用。我们研究了具有非平凡量子几何形状的Fermion Systems的线性大小$ \ Ell $区域的纠缠熵，即其Bloch状态具有非平凡的$ K $依赖性。我们表明，纠缠熵的比例为$ s =α\ ell^{d-1} \ ln \ ell +β\ ell^{d-1} + \ cdots $，其中第一个项是违反fermions的众所周知的区域法律，$β$包含来自Quantum demoter的领先贡献。我们为均匀的量子几何形状和立方结构域的情况进行计算，并为Su-Schrieffer-Heeger模型，2D大型Dirac Cone和2D Chern带提供数值结果。提出了使用粒子数波动的量子几何纠缠熵的实验探针。我们提供了与最大局部威尼斯功能传播有关的区域法纠缠的直观叙述。
Quantum geometry, which encompasses both Berry curvature and the quantum metric, plays a key role in multi-band interacting electron systems. We study the entanglement entropy of a region of linear size $\ell$ in fermion systems with nontrivial quantum geometry, i.e. whose Bloch states have nontrivial $k$ dependence. We show that the entanglement entropy scales as $S = α\ell^{d-1} \ln\ell + β\ell^{d-1} + \cdots$ where the first term is the well-known area-law violating term for fermions and $β$ contains the leading contribution from quantum geometry. We compute this for the case of uniform quantum geometry and cubic domains and provide numerical results for the Su-Schrieffer-Heeger model, 2D massive Dirac cone, and 2D Chern bands. An experimental probe of the quantum geometric entanglement entropy is proposed using particle number fluctuations. We offer an intuitive account of the area-law entanglement related to the spread of maximally localized Wannier functions.
