Out-of-Time-Order correlators in driven conformal field theories

Abstract

We compute Out-of-Time-Order correlators (OTOCs) for conformal field theories (CFTs) subjected to either continuous or discrete periodic drive protocols. This is achieved by an appropriate analytic continuation of the stroboscopic time. After detailing the general structure, we perform explicit calculations in large-c CFTs where we find that OTOCs display an exponential, an oscillatory and a power-law behaviour in the heating phase, the non-heating phase and on the phase boundary, respectively. In contrast to this, for the Ising CFT representing an integrable model, OTOCs never display such exponential growth. This observation hints towards how OTOCs can demarcate between integrable and chaotic CFT models subjected to a periodic drive. We further explore properties of the light-cone which is characterized by the corresponding butterfly velocity as well as the Lyapunov exponent. Interestingly, as a consequence of the spatial inhomogeneity introduced by the drive, the butterfly velocity, in these systems, has an explicit dependence on the initial location of the operators. We chart out the dependence of the Lyapunov exponent and the butterfly velocities on the frequency and amplitude of the drive for both protocols and discuss the fixed point structure which differentiates such driven CFTs from their undriven counterparts.

Entanglement and geometry from subalgebras of the Virasoro

“…21 The techniques and the dual bulk geometries in our work can serve as building blocks for the holographic understanding of the quench dynamics in those deformed models or related questions with excited states. Some progress in this direction has been already reported in [84][85][86][87][88] and more will be presented in the future work [89].…”

JT gravity and near-extremal thermodynamics for Kerr black holes in AdS4,5 for rotating perturbations

“…Since we would be interested in taking the near horizon near extremal limits we choose to work with the {r, τ, θ, z} coordinates using the relation (2.12). In these 9 gτ ∼ O(r − r+) at the outer horizon, hence θ was not in need of redefinition.…”

“…This bound was shown to be saturated for the Nambu-Goto dynamics of a string stretched in BTZ [7] and for the case of critical quenches in CFT 2 with large central charge [8]. Explicit results for both the Lyapunov index and the butterfly velocity(v B )-the corresponding spread in the spatial direction, have been recently computed for a driven large-c CF T 2 [9]. Here λ L and v B depend on the characteristics of the drive protocol.…”

“…Note, as the future (past) horizon is defined at U = 0 (V=0), the line element h τ dτ does not blow up at the horizon as the z coordinate had been specifically chosen so that h τ ∼ O(r − r + ) ∼ O(U V ) at the outer horizon. 9 The above form of the metric is well suited to study the Dray-'tHooft solutions which account for the back reaction caused due to an in-falling null shockwave at very late time [44]. Since we would be interested in taking the near horizon near extremal limits we choose to work with the {r, τ, θ, z} coordinates using the relation (2.12).…”

Floquet's Refrigerator: Conformal Cooling in Driven Quantum Critical Systems

“…The Floquet unitary evolution is generated by spatially deformed Hamiltonians, as studied extensively in recent works on Floquet CFTs [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. There are dynamically generated hot spots serving as the reservoir, which are depicted as the black dots (heating regions) in Fig.…”