Conjecture on the Butterfly Velocity across a Quantum Phase Transition

TL;DR

This paper investigates quantum chaos near a quantum phase transition in an anisotropic holographic model, revealing that the butterfly velocity is not universal but the information screening length peaks at criticality, influenced by the null-energy condition.

Contribution

It introduces a holographic model of a quantum phase transition and analyzes quantum chaos, highlighting the behavior of butterfly velocity and screening length across the transition.

Findings

Butterfly velocity is not universal across the QPT.

The dimensionless screening length peaks at the quantum critical point.

Null-energy condition constrains the bounds of chaos-related quantities.

Abstract

We study an anisotropic holographic bottom-up model displaying a quantum phase transition (QPT) between a topologically trivial insulator and a non-trivial Weyl semimetal phase. We analyze the properties of quantum chaos in the quantum critical region. We do not find any universal property of the Butterfly velocity across the QPT. In particular it turns out to be either maximized or minimized at the quantum critical point depending on the direction of propagation. We observe that instead of the butterfly velocity, it is the dimensionless information screening length that is always maximized at a quantum critical point. We argue that the null-energy condition (NEC) is the underlying reason for the upper bound, which now is just a simple combination of the number of spatial dimensions and the anisotropic scaling parameter.