突现准粒子的安德森局域化：三维$\mathbb{Z}_2$规范理论中有限温度下自旋和维素相互作用
Anderson localization of emergent quasiparticles: Spinon and vison interplay at finite temperature in a $\mathbb{Z}_2$ gauge theory in three dimensions
摘要：
准粒子激发的分数阶统计在拓扑系统的检测和表征中起着重要的作用。在本文中，我们研究的情况下，一个三维（3D）Z 2规范理论，其中的激发形式的玻色子自旋准粒子和vison通量管，相互半离子统计。我们专注于一个实验相关的中间温度制度，稀疏的自旋相干跳跃密集的准静态和随机vison背景。有效哈密顿量简化为随机符号双峰紧束缚模型，其中粒子和无序都来自相同的底层量子自旋液体（QSL）自由度，两者之间的耦合纯粹由相互分数统计驱动。我们研究的本地化特性，并观察到一个流动性的边缘位于靠近带边，其过渡属于3D安德森模型普适类。允许自旋通过准静态vison背景传播似乎显示量子扩散行为。当vison被允许放松，在响应的存在下的自旋平衡，我们观察到的vison耗尽区的形成奴隶的支持的自旋波函数。我们讨论了这种行为如何可以引起可测量的影响，系统的松弛，响应和传输特性，以及如何这些可以被用来作为签名的相互半离子统计和在较低的温度下在系统中出现的QSL相的前体。
英文摘要：
Fractional statistics of quasiparticle excitations often plays an important role in the detection and characterization of topological systems. In this paper, we investigate the case of a three-dimensional (3D) Z2 gauge theory, where the excitations take the form of bosonic spinon quasiparticle and vison flux tubes, with mutual semionic statistics. We focus on an experimentally relevant intermediate temperature regime, where sparse spinons hop coherently on a dense quasistatic and stochastic vison background. The effective Hamiltonian reduces to a random-sign bimodal tight-binding model, where both the particles and the disorder are borne out of the same underlying quantum spin liquid (QSL) degrees of freedom, and the coupling between the two is purely driven by the mutual fractional statistics. We study the localization properties and observe a mobility edge located close to the band edge, whose transition belongs to the 3D Anderson model universality class. Spinons allowed to propagate through the quasistatic vison background appear to display quantum diffusive behavior. When the visons are allowed to relax, in response to the presence of spinons in equilibrium, we observe the formation of vison depletion regions slave to the support of the spinon wavefunction. We discuss how this behavior can give rise to measurable effects in the relaxation, response and transport properties of the system and how these may be used as signatures of the mutual semionic statistics and as precursors of the QSL phase arising in the system at lower temperatures.
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