Scrambling in the quantum Lifshitz model

Eugeniu Plamadeala, Eduardo Fradkin

Research output: Contribution to journalArticlepeer-review


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 a uniform ground state to another one with spontaneously broken 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.

Original languageEnglish (US)
Article number063102
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number6
StatePublished - Jun 8 2018


  • quantum chaos
  • quantum criticality
  • quantum thermalization
  • thermalization

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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