论文标题
浆果曲率的高维概括
Higher-dimensional generalizations of the Berry curvature
论文作者
论文摘要
一个有限维量子系统的家族具有非降级基态的量子系统，导致了参数空间的封闭2形：浆果连接的曲率。它的共同学课是家庭的拓扑不变。我们寻求将浆果曲率概括为在空间维度中的多体系统的家庭。田间理论预测，在空间维度D中，浆果曲率的类似物是参数空间（Wess-Zumino-witten形式）的封闭（D+2）。我们在各个维度上为互动晶格系统的任意家庭构建了此类封闭形式。在一个维度的自由费米斯系统的特殊情况下，我们表明这些形式可以用布里鲁因区域和参数空间的乘积上的bloch-berry连接表示。对于短距离纠缠系统的家族，我们认为对球形周期的形式的积分进行了量化。
A family of finite-dimensional quantum systems with a non-degenerate ground state gives rise to a closed 2-form on the parameter space: the curvature of the Berry connection. Its cohomology class is a topological invariant of the family. We seek generalizations of the Berry curvature to families of gapped many-body systems in D spatial dimensions. Field theory predicts that in spatial dimension D the analog of the Berry curvature is a closed (D+2)-form on the parameter space (the Wess-Zumino-Witten form). We construct such closed forms for arbitrary families of interacting lattice systems in all dimensions. In the special case of systems of free fermions in one dimension, we show that these forms can be expressed in terms of the Bloch-Berry connection on the product of the Brillouin zone and the parameter space. In the case of families of Short-Range Entangled systems, we argue that integrals of our forms over spherical cycles are quantized.
