Holographic Butterfly Effect at Quantum Critical Points

TL;DR

This paper proposes using butterfly velocity, derived from holographic chaos models, as a diagnostic tool for quantum phase transitions, supported by evidence from an anisotropic holographic model exhibiting metal-insulator transitions.

Contribution

It introduces a novel approach to identify quantum critical points via butterfly velocity derivatives in holographic theories, linking chaos phenomena with quantum phase transitions.

Findings

Butterfly velocity derivatives signal quantum critical points.

Holographic models show local extrema at quantum critical points.

Experimental tests are feasible through OTOC measurements.

Abstract

When the Lyapunov exponent $\lambda_L$ in a quantum chaotic system saturates the bound $\lambda_L\leqslant 2\pi k_BT$, it is proposed that this system has a holographic dual described by a gravity theory. In particular, the butterfly effect as a prominent phenomenon of chaos can ubiquitously exist in a black hole system characterized by a shockwave solution near the horizon. In this paper we propose that the butterfly velocity can be used to diagnose quantum phase transition (QPT) in holographic theories. We provide evidences for this proposal with an anisotropic holographic model exhibiting metal-insulator transitions (MIT), in which the derivatives of the butterfly velocity with respect to system parameters characterizes quantum critical points (QCP) with local extremes in zero temperature limit. We also point out that this proposal can be tested by experiments in the light of recent progress on the measurement of out-of-time-order correlation function (OTOC).