标题： 拓扑相的朗道-金兹堡范式 显示英文标题

标题： Landau-Ginzburg Paradigm of Topological Phases

摘要： 拓扑有序物质相一直被视为超越物质相的朗道-金兹堡对称性破缺范式的。然而，最近对拓扑相中任意子凝聚的研究可能使拓扑相重新符合朗道-金兹堡范式。为了真正实现这一点，我们意识到拓扑相的弦网模型实际上在进行两项修改后，是一种与任意子物质耦合的有效格点规范理论：(1) 我们将任意子重新解释为与格点规范场耦合的物质场，从而将HGW模型扩展为真正的哈密顿格点规范理论。(2) 通过明确地包含任意子的内部自由度，我们构建了一个扩展的希尔伯特空间，该空间支持定义良好的规范变换和协变耦合，恢复了与传统格点规范场理论的类比。在这个修改后的弦网模型中，由任意子凝聚引起的拓扑相变及其后续现象，如序参量场、相干态、戈德斯通模和禁带规范自由度，可以精确地表述为希格斯机制的朗道有效理论。为了便于理解，我们还将任意子凝聚与电弱理论中的希格斯玻色子凝聚和库珀对凝聚进行了比较。 显示英文摘要

摘要： Topologically ordered matter phases have been regarded as beyond the Landau-Ginzburg symmetry breaking paradigm of matter phases. Recent studies of anyon condensation in topological phases, however, may fit topological phases back in the Landau-Ginzburg paradigm. To truly do so, we realized that the string-net model of topological phases is in fact an effective lattice gauge theory coupled with anyonic matter once two modifications are made: (1) We reinterpret anyons as matter fields coupled to lattice gauge fields, thus extending the HGW model to a genuine Hamiltonian lattice gauge theory. (2) By explicitly incorporating the internal degrees of freedom of anyons, we construct an enlarged Hilbert space that supports well-defined gauge transformations and covariant coupling, restoring the analogy with conventional lattice gauge field theory. In this modified string-net model, topological phase transitions induced by anyon condensation and their consequent phenomena, such as order parameter fields, coherent states, Goldstone modes, and gapping gauge degrees of freedom, can be formulated exactly as Landau's effective theory of the Higgs mechanism. To facilitate the understanding, we also compare anyon condensation to/with the Higgs boson condensation in the electroweak theory and the Cooper pair condensation.