Chiral Sachdev-Ye model: Integrability and chaos of anyons in 1+1d
Chiral Sachdev-Ye model: Integrability and chaos of anyons in 1+1d
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DOI：
10.1103/physrevb.105.125109
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发表时间：
2021-09
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影响因子：
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通讯作者：
Yichen Hu;Biao Lian
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作者：
Yichen Hu;Biao Lian
构造并研究了由N个具有电流-电流相互作用的手征SU（M）1 Wess-ZuminoWitten（WZW）模型组成的手征Sachdev-Ye（SY）模型，将0+1d混沌SY自旋模型推广到具有任意子激发的1+1d手征系统.每一个WZW模型都有阿贝尔任意子作为电荷激发，并可能作为2+1d带隙拓扑相的手征边理论而出现。我们解决了手征SY模型在两个极限，表现出不同的量子动力学。第一个极限是在任意整数N和M处的均匀相互作用的情况，这是可积的，并且分解为具有不同“光速”的手征SU（M）N WZW模型及其陪集。当N = M = 2时，该模型映射到一个自由的马约拉纳费米子模型。第二个极限是具有随机相互作用的大N和M极限，它可解到前导1 NM阶，并且在任意子的无序关联中表现出多体量子混沌。当相互作用强度接近保持手征性的上限时，模型的主导速度依赖的李雅普诺夫指数在温度β−1处饱和最大混沌界2π/β。
We construct and study a chiral Sachdev-Ye (SY) model consisting of N chiral SU(M)1 Wess-ZuminoWitten (WZW) models with current-current interactions among each other, which generalizes the 0+1d quantum chaotic SY spin model into 1+1d chiral system with anyon excitations. Each WZW model hosts Abelian anyons as charge excitations, and may arise as the chiral edge theory of 2+1d gapped topological phases. We solve the chiral SY model in two limits which show distinct quantum dynamics. The first limit is the case with uniform interactions at any integers N and M , which is integrable and decomposes into a chiral SU(M)N WZW model and its coset with different “speed of light”. When N = M = 2, the model maps to a free Majorana fermion model. The second limit is the large N and M limit with random interactions, which is solvable to the leading 1 NM order, and exhibits many-body quantum chaos in the out-of-time-ordered correlation of anyons. As the interaction strength approaches the upper limit preserving the chirality, the leading velocity-dependent Lyapunov exponent of the model saturates the maximal chaos bound 2π/β at temperature β−1.