手征Sachdev-Ye模型：1+1d中任意子的可积性和混沌
Chiral Sachdev-Ye model: Integrability and chaos of anyons in 1+1d
摘要：
构造并研究了由$N$手征SU $(M)_1$ Wess-Zumino-Witten（WZW）模型组成的具有电流-电流相互作用的手征Sachdev-Ye（SY）模型，将0+1d量子混沌SY自旋模型推广到1+1d任意子激发手征系统.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，模型映射到自由马约拉纳费米子模型。第二个极限是随机相互作用下的大$N$和$M$极限，它可解到主导的$\frac{1}{NM}$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，模型的速度依赖的李雅普诺夫指数在温度$β^{-1}$下饱和最大混沌界$2π/β$。
英文摘要：
We construct and study a chiral Sachdev-Ye (SY) model consisting of $N$ chiral SU$(M)_1$ Wess-Zumino-Witten (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 $\frac{1}{NM}$ 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 $β^{-1}$.
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