Abstract We investigate a model closely related to both the original Sachdev-Ye-Kitaev (SYK) model and the $$ \mathcal{N} $$ N = 1 supersymmetric SYK model. It consists of N real Majorana fermions and M auxiliary bosons with Yukawa interactions. We consider the large N and M limit and keep the ratio M/N fixed. The model has two branches characterized by the conformal dimensions of fields, which we compute as a function of the ratio M/N. One of the branches contains the supersymmetric saddle for M = N. As we take the limit M/N → ∞ both branches coincide and we obtain the same conformal dimensions as SYK. Furthermore, we determine the Lyapunov exponent of the model and find maximal chaos independent of M/N.
Abstract We investigate a model closely related to both the original Sachdev-Ye-Kitaev (SYK) model and the N N = 1 supersymmetric SYK model. It consists of N real Majorana fermions and M auxiliary bosons with Yukawa interactions. We consider the large N and M limit and keep the ratio M/N fixed. The model has two branches characterized by the conformal dimensions of fields, which we compute as a function of the ratio M/N. One of the branches contains the supersymmetric saddle for M = N. As we take the limit M/N → ∞ both branches coincide and we obtain the same conformal dimensions as SYK. Furthermore, we determine the Lyapunov exponent of the model and find maximal chaos independent of M/N.
We investigate a model closely related to both the original Sachdev-Ye-Kitaev (SYK) model and the mathcalN=1 supersymmetric SYK model. It consists of N real Majorana fermions and M auxiliary bosons with Yukawa interactions. We consider the large N and M limit and keep the ratio M/N fixed. The model has two branches characterized by the conformal dimensions of fields, which we compute as a function of the ratio M/N. One of the branches contains the supersymmetric saddle for M=N. Furthermore, we determine the Lyapunov exponent of the model and find maximal chaos independent of M/N.
Abstract We study the chaos exponent of some variants of the Sachdev-Ye-Kitaev (SYK) model, namely, the N N = 1 supersymmetry (SUSY)-SYK model and its sibling, the (N|M)-SYK model which is not supersymmetric, for arbitrary interaction strength. We find that for large q the chaos exponent of these variants, as well as the SYK and the N N = 2 SUSY-SYK model, all follow a single-parameter scaling law. By quantitative arguments we further make a conjecture, i.e. that the found scaling law might hold for general one-dimensional (1D) SYK-like models with large q. This points out a universal route from maximal chaos towards completely regular or integrable motion in the SYK model and its 1D variants.
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 ≤ 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 [1] 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 2π/β as the interaction strength approaches its physical upper bound. Finally, the model is integrable for (at least) N ≤ 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.
The Sachdev-Ye-Kitaev (SYK) model shows chaotic behavior with a maximal Lyapunov exponent. In this paper, we investigate the four-point function of a SYK-type model numerically, which gives us access to its Lyapunov exponent. The model consists of two sets of Majorana fermions, called A and B, and the interactions are restricted to being exclusively pairwise between the two sets, not within the sets. We find that the Lyapunov exponent is still maximal at strong coupling. Furthermore, we show that even though the conformal dimensions of the A and B fermions change with the population ratio, the Lyapunov exponent remains constant, not just in the conformal limit where it is maximal, but also in the intermediate and weak coupling regimes.
We study a class of Sachdev, Ye, and Kitaev (SYK) models with N = 2 supersymmetry, described by N fermions in chiral Fermi multiplets, as well as α N first-order bosons in chiral multiplets. The interactions are characterized by two integers ( p , q ) . We focus on the large N and low energy limit of these models. Despite the presence of dynamical bosons, we find conformal behavior akin to the standard SYK model. We use I -extremization of a Witten index to study the supersymmetric solutions. In particular, we find an exact expression for the entropy, which matches the numerical solutions to the Schwinger-Dyson equations. We further solve the model both in the large p and large p , q limits. Numerically, we verify our analytical results and obtain estimates for the Schwarzian coupling in the near zero-temperature limit. We also study the low-lying spectrum of operators to determine the parameter ranges where the Schwarzian mode dominates the IR dynamics. Lastly, we study out-of-time-ordered correlators to show that the model is maximally chaotic.
The SYK model: fermions with a q-body, Gaussian-random, all-to-all interaction, is the first of a fascinating new class of solvable large N models. We generalize SYK to include f flavors of fermions, each occupying N a sites and appearing with a q a order in the interaction. Like SYK, this entire class of models generically has an infrared fixed point. We compute the infrared dimensions of the fermions, and the spectrum of singlet bilinear operators. We show that there is always a dimension-two operator in the spectrum, which implies that, like in SYK, there is breaking of conformal invariance and maximal chaos in the infrared four-point function of the generalized model. After a disorder average, the generalized model has a global O(N 1) × O(N 2) × … × O(N f ) symmetry: a subgroup of the O(N) symmetry of SYK; thereby giving a richer spectrum. We also elucidate aspects of the large q limit and the OPE, and solve q = 2 SYK at finite N.