Interplay of topological order and spin glassiness in the toric code under random magnetic fields
Interplay of topological order and spin glassiness in the toric code under random magnetic fields
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DOI：
10.1103/physrevb.83.075124
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发表时间：
2011-02-28
影响因子：
3.7
通讯作者：
Castelnovo, Claudio
中科院分区：
文献类型：
--
作者：
Tsomokos, Dimitris I.;Osborne, Tobias J.;Castelnovo, Claudio
我们分析了存在猝灭无序的Toric码模型，该模型是通过不同类型的随机磁场引入的。一般而言，在接近自旋极化相和拓扑有序相之间的量子相变时，我们发现无序量的增加有利于拓扑相的形成。对于无序的某些实现，拓扑有序在任意强磁场下都是健壮的。在随机的+/-h场中使用Toric码的情况下，在适当的对偶变量描述下，系统表现出向自旋玻璃相的量子相变。在Edwards-Anderson双峰自旋玻璃模型中，自旋玻璃相中拓扑有序的存留与刚性晶格的渗流性质直接相关。根据该模型的最新数值结果[F.Roma等人，Phys.Rev.B82,214401(2010年)]，很可能刚性晶格不会渗漏，因此，新的中间量子相出现在随机场Toric码中。在这一中间量子阶段，拓扑有序性与自旋玻璃性共存。
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 +/- 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 [ F. Roma et al., 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.