Sufficient symmetry conditions for Topological Quantum Order
Sufficient symmetry conditions for Topological Quantum Order
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DOI：
10.1073/pnas.0803726105
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发表时间：
2006-05
期刊：
影响因子：
--
通讯作者：
Z. Nussinov;G. Ortiz
中科院分区：
文献类型：
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作者：
Z. Nussinov;G. Ortiz
我们证明了零温度和有限温度下拓扑量子序的充分条件。证明的关键在于低维类规范对称性的存在，从而提供了一个统一的框架，基于对称性原则。这些对称性可能是系统的实际不变性，也可能出现在低能区。拓扑量子序的突出例子显示规范样对称性。表现出这种对称性的新系统包括描述轨道相关自旋交换和过渡金属轨道化合物中的Jahn-Teller效应的哈密顿量，短程受抑的Klein自旋模型和p+ip超导阵列。我们分析了规范对称性（包括拓扑项和电荷）的物理后果，指出了能谱、拓扑纠缠熵、最大弦算符和分数化在建立拓扑量子序中的不足。一般的对称性考虑表明，不承受光谱间隙，热波动可能会对建议的量子计算方案施加限制。我们的研究结果使我们能够超越标准的拓扑场论，并设计具有拓扑量子序的系统。
We prove sufficient conditions for Topological Quantum Order at zero and finite temperatures. The crux of the proof hinges on the existence of low-dimensional Gauge-Like Symmetries, thus providing a unifying framework based on a symmetry principle. These symmetries may be actual invariances of the system, or may emerge in the low-energy sector. Prominent examples of Topological Quantum Order display Gauge-Like Symmetries. New systems exhibiting such symmetries include Hamiltonians depicting orbital-dependent spin exchange and Jahn–Teller effects in transition metal orbital compounds, short-range frustrated Klein spin models, and p+ip superconducting arrays. We analyze the physical consequences of Gauge-Like Symmetries (including topological terms and charges) and show the insufficiency of the energy spectrum, topological entanglement entropy, maximal string correlators, and fractionalization in establishing Topological Quantum Order. General symmetry considerations illustrate that not withstanding spectral gaps, thermal fluctuations may impose restrictions on suggested quantum computing schemes. Our results allow us to go beyond standard topological field theories and engineer systems with Topological Quantum Order.