Abstract
We study correlation functions in the complex fermion SYK model. We focus, specifically, on the h=2 mode which explicitly breaks conformal invariance and exhibits the chaotic behaviour. We numerically explore a fermion six-point OTOC, with two and three real-time folds, respectively. While our approach is expected to yield an early-time chaotic growth, we nevertheless observe a near-maximal value. Following the program of Gross-Rosenhaus, we estimate the triple short time limit of the six point function. Unlike the conformal modes with high values of h, the h=2 mode has contact interaction dominating over the planar in the large q limit.
Highlights
We took triple short time limit of this correlation function so that it appears as a three point function of fermion bilinears
We show that the three point function of fermion bilinears, for h = 2 modes, have the scaling property of conformal field theory three point function, as is expected as a generalisation of the results of [41] to the complex fermion case
Like in [41], we find that the contribution of the contact three point graphs in the large q limit is subleading compared to that of the planar graphs
Summary
A generic dynamical system is inherently chaotic [1]. For classical systems, chaos can be characterized by the sensitivity of trajectories with respect to initial conditions. In the large N limit, further, the four-point correlator can be explicitly calculated, which yields the corresponding Lyapunov exponent: λL = 2πT , where T is the temperature of the thermal state. In keeping with the theme, in this article, we further compute higher point OTOC for complex fermion SYK-model, with a non-vanishing chemical potential. After computing the fermion six point function with a non-vanishing chemical potential, we take the triple short time limit to estimate the the bulk three point correlator, away from the conformal limit. We carry out this computation in the presence of a chemical potential μ. We conclude with the discussion of our results, and possible future directions
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