超越拓扑量子场论的拓扑序
Topological Orders Beyond Topological Quantum Field Theories
AI总结：
该研究突破拓扑量子场论范畴，提出一类含任意子距离依赖相互作用的拓扑序模型，通过朗道序系统严格对偶变换分析，给出朗道型理论到同维拓扑序对偶模型的通用映射，且模型低能子空间抗热效应能力优于表面码。
摘要：
展现量子拓扑序的系统具有鲁棒特性，这类特性对量子计算方案极具吸引力。拓扑量子场论（Topological Quantum Field Theories）已被证明能有效捕捉拓扑序系统的核心属性，尤其是其任意子激发。本文研究了超出这一常见范畴的系统，提出了一类丰富的模型，这类模型展现出任意子之间存在距离依赖相互作用的拓扑序。正如我们所阐释的，在某些情况下，有能隙的最低能量激发由密集覆盖整个系统的任意子构成，这会产生拓扑量子场论通常无法描述的行为。我们通过与展现常规（即朗道（Landau））序的系统进行严格对偶变换来研究这些模型。我们的方法提供了一种通用方法，可将任意朗道型理论映射为相同空间维度下具有拓扑序的对偶模型。我们的模型的低能子空间对热效应的抵御能力可优于表面码（surface codes）的低能子空间。
英文摘要：
Systems displaying quantum topological order feature robust characteristics that are very attractive to quantum computing schemes. Topological quantum field theories have proven to be powerful in capturing the quintessential attributes of systems displaying topological order including, in particular, their anyon excitations. Here, we investigate systems that lie outside this common purview, and present a rich class of models exhibiting topological orders with distance-dependent interactions between anyons. As we illustrate, in some instances, the gapped lowest-energy excitations are comprised of anyons that densely cover the entire system. This leads to behaviors not typically described by topological quantum field theories. We examine these models by performing exact dualities to systems displaying conventional (i.e., Landau) orders. Our approach enables a general method for mapping generic Landau-type theories to dual models with topological order of the same spatial dimension. The low-energy subspaces of our models can be made more resilient to thermal effects than those of surface codes.
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