Chiral spin liquids with crystalline Z2 gauge order in a three-dimensional Kitaev model
Chiral spin liquids with crystalline Z2 gauge order in a three-dimensional Kitaev model
复制标题
三维 Kitaev 模型中具有结晶 Z2 规范级的手性自旋液体
DOI：
10.1103/physrevb.101.045118
复制
发表时间：
2020
影响因子：
3.7
通讯作者：
Motome Yukitoshi
中科院分区：
文献类型：
--
作者：
Mishchenko Petr A.;Kato Yasuyuki;O'Brien Kevin;Bojesen Troels A.;Eschmann Tim;Hermanns Maria;Trebst Simon;Motome Yukitoshi
手性自旋液体(CSL)是受挫量子磁体的时间反转对称破缺基态，它没有表现出长程磁有序，而是表现出拓扑有序和分数激发。然而，它们在简单易处理的微观模型中的实现在近20年来一直是一个开放的挑战，直到人们意识到，具有奇数长度环的晶格上的Kitaev模型是这种状态的自然宿主，即使在没有时间反转对称破坏磁场的情况下也是如此。在这里，我们报道了在由九位环组成的超非四边形晶格上的三维Kitaev模型中CSL的形成，这与被广泛研究的二维CSL不同，即它们显示出规范通量的结晶有序，从而破坏了一些潜在的晶格对称性。我们通过大量的量子蒙特卡罗模拟研究了这些非常规CSL的形成，并证明了它们在高温下通过时间反转和晶格对称性同时被破坏的单一一级相变从无特征的顺磁网中分离出来。利用基态的变分方法，我们研究了不同的Kitaev耦合效应，发现至少有五个不同的CSL相，它们都具有规范通量的晶态有序。对于其中的一些位相，互补巡回Majorana费米子表现出无间隙能带结构，具有拓扑特征，如体态和费米弧态或鼓面表面态的Weyl节点或节线。
Chiral spin liquids (CSLs) are time-reversal-symmetry-breaking ground states of frustrated quantum magnets that show no long-range magnetic ordering but instead exhibit topological order and fractional excitations. Their realization in simple and tractable microscopic models has, however, remained an open challenge for almost two decades until it was realized that Kitaev models on lattices with odd-length loops are natural hosts for such states, even in the absence of a time-reversal-symmetry-breaking magnetic field. Here we report on the formation of CSLs in a three-dimensional Kitaev model on a hypernonagon lattice composed of nine-site loops, which differ from their widely studied two-dimensional counterparts; namely, they exhibit a crystalline ordering of thegauge fluxes and thereby break some of the underlying lattice symmetries. We study the formation of these unconventional CSLs via extensive quantum Monte Carlo simulations and demonstrate that they are separated from the featureless paramagnet at high temperatures by a single first-order phase transition at which both time-reversal and lattice symmetries are simultaneously broken. Using variational approaches for the ground state, we explore the effect of varying the Kitaev couplings and find at least five distinct CSL phases, all of which possess crystalline ordering of thegauge fluxes. For some of these phases, the complementary itinerant Majorana fermions exhibit gapless band structures with topological features such as Weyl nodes or nodal lines in the bulk and Fermi arc or drumhead surface states.