Conformal field theory and the web of quantum chaos diagnostics

Abstract

We study three prominent diagnostics of chaos and scrambling in the context of two-dimensional conformal field theory: the spectral form factor, out-of-time-ordered correlators, and unitary operator entanglement. With the observation that all three quantities may be obtained by different analytic continuations of the torus partition function, we address the connections and distinctions between the information that each quantity provides us. In this process, we study the emergence of irrationality from "large-N" limits of rational conformal field theories (RCFTs) as well as the explicit breakdown of rationality for theories with central charges greater than the number of their conserved currents. Our analysis begins to elucidate the intermediate dynamical behavior of theories that bridge the gap between integrable RCFTs and maximally chaotic holographic CFTs.

Correlation measures and the entanglement wedge cross-section after quantum quenches in two-dimensional conformal field theories

“…Their entanglement content may also be extracted from GGE thermodynamic entropy by considering appropriate pure state limits. We will have more to say on this issue in future work [39]. Similar to the Alba and Calabrese relation, we will find a simple relation within the quasi-particle picture among the Rényi mutual information, negativity, odd-entropy, and reflected entropy,…”

“…An interesting future direction is to determine how these quantities behave for theories that lie somewhere in between RCFTs and the irrational CFTs discussed in Section III, such as the compactified boson at irrational squared radius [47,78,79]. Other interesting intermediate theories that are not conformal include chaotic spin chains and random unitary circuits at finite q.…”

Spectral form factors of clean and random quantum Ising chains

“…This expression for the partition function at the critical point (after factoring out the diverging piece) is in agreement with the modular invariant partition function of the Ising CFT [18]. In fact, the periodic behavior of the SFF at the Ising critical point can be predicted directly from its correspondence with the Ising CFT.…”

Heavy operators and hydrodynamic tails

“…In the thermodynamic limit, thermal correlation functions are trivial and there is no room for a hydrodynamic description. However they still exhibit thermalization after a quench [95] (towards a generalized Gibbs ensemble for the KdV charges [96][97][98][99][100]), non-trivial non-equilibrium behavior [101], and chaos [102][103][104]. It would be interesting to see if out of equilibrium methods can be used to determine heavyheavy-light OPE coefficients, comparing against results obtained from other methods [105][106][107][108][109], see in particular [110][111][112] for discussions on the off-diagonal part of ETH in this context.…”