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arXiv · 1802.07268

Scrambling in the Quantum Lifshitz Model

Eugeniu Plamadeala·Eduardo Fradkin
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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.

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Eugeniu Plamadeala, Eduardo Fradkin. 2018-02-20. Scrambling in the Quantum Lifshitz Model. https://doi.org/10.1088/1742-5468%2Faac136

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