随机磁场下Toric码中拓扑序与自旋玻璃化的相互作用
Interplay of Topological Order and Spin Glassiness in the Toric Code under Random Magnetic Fields
摘要：
我们分析了通过不同类型的随机磁场引入的淬火无序存在下的复曲面编码模型。在一般情况下，接近一个量子相变之间的自旋极化阶段和拓扑有序的，我们发现，增加无序的数量有利于拓扑阶段。对于无序的某些实现，拓扑序可以抵抗任意强的磁场。在随机\pm h场中的复曲面编码的情况下，我们证明了在适当的对偶变量描述下，系统表现出到自旋玻璃相的量子相变。自旋玻璃相中拓扑有序的存在与Edwards-Anderson双峰自旋玻璃模型中刚性晶格的逾渗性质直接相关。根据该模型最近的数值结果[Phys.Rev.B82，214401（2010）]，很可能刚性晶格不渗透，因此，在随机场复曲面码中出现新的中间量子相位。在这个中间量子阶段，拓扑有序与自旋玻璃化共存。
英文摘要：
We analyze the toric code model in the presence of quenched disorder, which is introduced via different types of random magnetic fields. In general, close to a quantum phase transition between a spin polarized phase and a topologically ordered one, we find that increasing the amount of disorder favors the topological phase. For some realizations of disorder, topological order can be robust against arbitrarily strong magnetic fields. In the case of the toric code in a random \pm h field, we show that the system exhibits a quantum phase transition to a spin glass phase in an appropriate dual variables description. The survival of topological order in the spin glass phase is directly related to the percolation properties of the rigid lattice in the Edwards-Anderson bimodal spin glass model. According to recent numerical results for this model [Phys. Rev. B 82, 214401 (2010)], it is likely that the rigid lattice does not percolate and, as a result, a new intermediate quantum phase appears in the random-field toric code. In this intermediate quantum phase, topological order coexists with spin glassiness.
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