论文标题
在任何维度上用于翻译不变的汉密尔顿人的Jordan-Wigner二重性
Jordan-Wigner Dualities for Translation-Invariant Hamiltonians in Any Dimension: Emergent Fermions in Fracton Topological Order
论文作者
论文摘要
受到最新发展的启发，我们使用代数形式主义来开发了一种二元性的框架，用于翻译不变的汉密尔顿人，由Haah提出。我们证明，鉴于具有一般$ q $ body互动的翻译不变的费米尼系统，其中$ q $甚至是一个本地映射，将保存全球费米恩奇偶校验与双重Pauli旋转模型存在，并且是独特的，可以选择基础。此外，双自旋模型具有建设性，我们提供了这些二元性的各种例子。作为一种应用程序，我们巩固了不存在自由屈服术语（$ q \ ge 4 $）的费米子系统，而费米昂的奇偶校验是在诸如更高形式，线，平面或分形对称性之类的子序列上保存的。在某些情况下，在3+1d中，实现这样的系统会产生分裂模型，在这种模型中，出现的颗粒是不动的，但可以以某些方式行事，例如费米子。这些模型可能是新的非杂志't Hooft异常的示例。此外，在各种Majorana稳定器代码（例如颜色代码或棋盘板模型）中，费米子亚系统对称性也存在，我们给出了示例，其中它们的双重二元组为群集状态或新的fracton模型，这些模型与其双倍的CSS代码不同。
Inspired by recent developments generalizing Jordan-Wigner dualities to higher dimensions, we develop a framework of such dualities using an algebraic formalism for translation-invariant Hamiltonians proposed by Haah. We prove that given a translation-invariant fermionic system with general $q$-body interactions, where $q$ is even, a local mapping preserving global fermion parity to a dual Pauli spin model exists and is unique up to a choice of basis. Furthermore, the dual spin model is constructive, and we present various examples of these dualities. As an application, we bosonize fermionic systems where free-fermion hopping terms are absent ($q \ge 4$) and fermion parity is conserved on submanifolds such as higher-form, line, planar or fractal symmetry. For some cases in 3+1D, bosonizing such a system can give rise to fracton models where the emergent particles are immobile but yet can behave in certain ways like fermions. These models may be examples of new nonrelativistic 't Hooft anomalies. Furthermore, fermionic subsystem symmetries are also present in various Majorana stabilizer codes, such as the color code or the checkerboard model, and we give examples where their duals are cluster states or new fracton models distinct from their doubled CSS codes.
