论文标题
双曲带理论通过希格斯束
Hyperbolic band theory through Higgs bundles
论文作者
论文摘要
双曲线晶格是一种新形式的量子物质形式，并具有潜在的量子计算和仿真应用，并且迄今为止已进行了人工设计。出现了相应的双曲带理论，以一种自然的方式扩展了二维欧几里得条带理论，以使其延伸到更高的配置空间。试图开发Bloch定理的双曲线类似物的尝试揭示了代数几何模量空间的内在作用，尤其是曲线上稳定束的空间。我们将此图片扩展到包括希格斯捆绑包，这些捆绑包在乐队理论的背景下享有自然解释。首先，它们的光谱数据编码晶体晶格和动量，为对称双曲线晶体提供了一个框架。其次，它们充当晶体动量的复杂类似物。作为应用程序，我们引起了欧几里得乐队理论的新观点。最后，我们推测了双曲线理论的潜在相互作用，这是由希格斯束促进的，以及数学和物理学领域的其他主题。
Hyperbolic lattices underlie a new form of quantum matter with potential applications to quantum computing and simulation and which, to date, have been engineered artificially. A corresponding hyperbolic band theory has emerged, extending 2-dimensional Euclidean band theory in a natural way to higher-genus configuration spaces. Attempts to develop the hyperbolic analogue of Bloch's theorem have revealed an intrinsic role for algebro-geometric moduli spaces, notably those of stable bundles on a curve. We expand this picture to include Higgs bundles, which enjoy natural interpretations in the context of band theory. First, their spectral data encodes a crystal lattice and momentum, providing a framework for symmetric hyperbolic crystals. Second, they act as a complex analogue of crystal momentum. As an application, we elicit a new perspective on Euclidean band theory. Finally, we speculate on potential interactions of hyperbolic band theory, facilitated by Higgs bundles, with other themes in mathematics and physics.
