TY - JOUR

T1 - Chiral Sachdev-Ye model

T2 - Integrability and chaos of anyons in 1+1 d

AU - Hu, Yichen

AU - Lian, Biao

N1 - Funding Information:
The authors thank Zhenbin Yang, Fabian Essler, Jeffrey C.Y. Teo, and Igor Klebanov for helpful discussions. Y.H. is supported by Grant No. EP/S020527/1 from EPSRC. B.L. acknowledges support from the Alfred P. Sloan Foundation. This paper is also supported by NSF through Princeton University's Materials Research Science and Engineering Center No. DMR-2011750.
Publisher Copyright:
© 2022 American Physical Society.

PY - 2022/3/15

Y1 - 2022/3/15

N2 - 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 a 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 1NM 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.

AB - 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 a 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 1NM 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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U2 - 10.1103/PhysRevB.105.125109

DO - 10.1103/PhysRevB.105.125109

M3 - Article

AN - SCOPUS:85127089585

SN - 2469-9950

VL - 105

JO - Physical Review B

JF - Physical Review B

IS - 12

M1 - 125109

ER -