Chiral Sachdev-Ye model: Integrability and chaos of anyons in 1+1d

• URL: http://arxiv.org/abs/2109.13263v3
• Date: Thu, 10 Mar 2022 01:24:36 GMT
• Title: Chiral Sachdev-Ye model: Integrability and chaos of anyons in 1+1d
• Authors: Yichen Hu and Biao Lian
• Abstract summary: We 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. Each WZW model hosts Abelian anyons as charge excitations, and may arise as the chiral edge theory of 2+1d gapped topological phases.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 $2\pi/\beta$ at temperature $\beta^{-1}$.

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