Scrambling in the Quantum Lifshitz Model

TL;DR

This paper investigates chaos in the quantum Lifshitz model using out-of-time ordered correlators, revealing a temperature-dependent Lyapunov exponent and insights into the model's chaotic dynamics across different interaction regimes.

Contribution

It provides the first numerical analysis of chaos in the quantum Lifshitz model, demonstrating a non-zero Lyapunov exponent and characterizing its dependence on temperature and interaction strength.

Findings

Non-zero Lyapunov exponent observed across various temperatures.

Lyapunov exponent weakly depends on temperature and saturates at strong interactions.

Butterfly velocity increases with interaction strength but remains below the interaction-induced velocity.

Abstract

We study signatures of chaos in the quantum Lifshitz model through out-of-time ordered correlators (OTOC) of current operators. This model is a free scalar field theory with dynamical critical exponent $z=2$. It describes the quantum phase transition in 2D systems, such as quantum dimer models, between a phase with an uniform ground state to another one with a spontaneously translation invariance. At the lowest temperatures the chaotic dynamics are dominated by a marginally irrelevant operator which induces a temperature dependent stiffness term. The numerical computations of OTOC exhibit a non-zero Lyapunov exponent (LE) in a wide range of temperatures and interaction strengths. The LE (in units of temperature) is a weakly temperature-dependent function; it vanishes at weak interaction and saturates for strong interaction. The Butterfly velocity increases monotonically with interaction strength in the studied region while remaining smaller than the interaction-induced velocity/stiffness.