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首页> 外文期刊>Physical review >Phase transitions in three-dimensional topological lattice models with surface anyons
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Phase transitions in three-dimensional topological lattice models with surface anyons

机译：具有表面任意子的三维拓扑晶格模型中的相变

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We study the phase diagrams of a family of three-dimensional Walker-Wang-type lattice models, which are not topologically ordered but have deconfined anyonic excitations confined to their surfaces. We add a perturbation (analogous to that which drives the confining transition in Z_p lattice gauge theories) to the Walker-Wang Hamiltonians, driving a transition in which all or some of the variables associated with the loop-gas or string-net ground states of these models become confined. We show that in many cases the location and nature of the phase transitions involved is exactly that of a generalized Z_p lattice gauge theory, and use this to deduce the basic structure of the phase diagram. We further show that the relationship between the phases on opposite sides of the transition is fundamentally different than in conventional gauge theories: in the Walker-Wang case, the number of species of excitations that are deconfined in the bulk can increase across a transition that confines only some of the species of loops or string nets. The analog of the confining transition in the Walker-Wang models can therefore lead to bulk deconfinement and topological order.
机译：我们研究了一系列三维Walker-Wang型晶格模型的相图，这些拓扑模型的拓扑结构不是有序的，而是定义了局限于其表面的非声子激发。我们向Walker-Wang哈密顿量添加一个扰动（类似于驱动Z_p晶格规范理论中的约束转变的扰动），从而驱动一个转变，在该转变中，与以下项的回路气或弦网基态相关的所有或某些变量这些模型受到限制。我们证明，在许多情况下，所涉及的相变的位置和性质恰好是广义Z_p晶格规理论的位置和性质，并以此推论相图的基本结构。我们进一步表明，过渡相对两侧的相位之间的关系与传统规范理论有根本不同：在Walker-Wang案例中，在整个过渡范围内，被限定在主体中的激发物种数量会增加仅某些种类的环网或弦网。因此，Walker-Wang模型中的限制过渡类似物可能会导致批量限制和拓扑顺序。

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