Scrambling with conservation laws

Brian Swingle,Gong Cheng

doi:10.1007/jhep11(2021)174

Abstract

In this article we discuss the impact of conservation laws, specifically U(1) charge conservation and energy conservation, on scrambling dynamics, especially on the approach to the late time fully scrambled state. As a model, we consider a d + 1 dimensional (d ≥ 2) holographic conformal field theory with Einstein gravity dual. Using the holographic dictionary, we calculate out-of-time-order-correlators (OTOCs) that involve the conserved U(1) current operator or energy-momentum tensor. We show that these OTOCs approach their late time value as a power law in time, with a universal exponent frac{d}{2} . We also generalize the result to compute OTOCs between general operators which have overlap with the conserved charges.

Highlights

1.1 MotivationQuantum information scrambling [1,2,3] is a fundamental phenomenon in chaotic manybody systems that has been under wide discussion in recent years
We will see that due to the hydrodynamical property of the conserved current, the particle sourced by these operators in the bulk spreads over a large region of space-time
We expect the OTOC to have the same power law tail as in the photon case. Another interesting regime for the sound mode is at early time, where we have the shockwave that propagates at the butterfly velocity vB as well as the hydrodynamical mode that propagates at the sound speed vs. For the gravity model we considered in this work, vB > vs for physically sensible spatial dimension

Summary

Introduction

1.1 MotivationQuantum information scrambling [1,2,3] is a fundamental phenomenon in chaotic manybody systems that has been under wide discussion in recent years. This activity focused on the study of out-of-time-order correlators (OTOCs) [4,5,6,7,8,9,10,11,12,13,14,15,16]. For a chaotic system with large N number of degrees of freedom per unit volume, the OTOC displays an exponentially increasing deviation from its initial value which is characterized by a quantum Lyapunov exponent. This period of growth occurs after local equilibrium is achieved but before the scrambling time, when the system approaches global equilibrium.

Results

Discussion

Conclusion