Scrambling in the Quantum Lifshitz Model

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.

arXiv comment15 pages + appendices. 12 figures

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Cited by in corpus (4)

• Scrambling in the Dicke model
• Scrambling and Lyapunov Exponent in Unitary Networks with Tunable Interactions
• Entanglement Entropy in Generalised Quantum Lifshitz Models
• Entanglement wedge method, out-of-time-ordered correlators, and pole skipping