The chiral SYK model

Abstract

We study the generalization of the Sachdev-Ye-Kitaev (SYK) model to a $1+1$ dimensional chiral SYK model of $N$ flavors of right-moving chiral Majorana fermions with all-to-all random 4-fermion interactions. The interactions in this model are exactly marginal, leading to an exact scaling symmetry. We show the Schwinger-Dyson equation of this model in the large $N$ limit is exactly solvable. In addition, we show this model is integrable for small $N\le 6$ by bosonization. Surprisingly, the two point function in the large $N$ limit has exactly the same form as that for $N=4$, although the four point functions of the two cases are quite different. The ground state entropy in the large $N$ limit is the same as that of $N$ free chiral Majorana fermions, leading to a zero ground state entropy density. The OTOC of the model in the large $N$ limit exhibits a non-trivial spacetime structure reminscent of that found by Gu and Kitaev for generic SYK-like models. Specifically we find a Lyapunov regime inside an asymmetric butterfly cone, which are signatures of quantum chaos, and that the maximal velocity dependent Lyapunov exponent approaches the chaos bound $2\pi /\beta$ as the interaction strength approaches its physical upper bound. Finally, the model is integrable for (at least) $N\le 6$ but chaotic in the large $N$ limit, leading us to conjecture that there is a transition from integrability to chaos as $N$ increases past a critical value.

arXiv comment51 pages, 13 figures, typos corrected

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• Chaos in the butterfly cone
• Exact Quantum Scars in the Chiral Non-Linear Luttinger Liquid
• Low-rank Sachdev-Ye-Kitaev models
• Pole skipping away from maximal chaos
• Dirac Fast Scramblers
• The Generalized OTOC from Supersymmetric Quantum Mechanics: Study of Random Fluctuations from Eigenstate Representation of Correlation Functions
• Complex Sachdev-Ye-Kitaev model in the double scaling limit
• Dynamics of spectral correlations in the entanglement Hamiltonian of the Aubry-André-Harper model
• A Quantum Breakdown Model: from Many-body Localization to Chaos with Scars
• Onset of Quantum Chaos in Random Field Theories
• The onset of quantum chaos in disordered CFTs
• Chiral Sachdev-Ye model: Integrability and chaos of anyons in 1+1d
• Conserved Quantities from Entanglement Hamiltonian
• Mapping SYK to the Sky
• Phase space holography with no strings attached
• Integrability of the $\nu =4/3$ fractional quantum Hall edge states
• Statistic behaviors of gauge-invariance-dominated 1D chiral current random model
• The chiral SYK model in three-dimensional holography
• Quasiparticle tunnelling in two coupled chiral SYK model