Entanglement Entropy in Lifshitz Theories

Abstract

We discuss and compute entanglement entropy (EE) in (1+1)-dimensional free Lifshitz scalar field theories with arbitrary dynamical exponents. We consider both the subinterval and periodic sublattices in the discretized theory as subsystems. In both cases, we are able to analytically demonstrate that the EE grows linearly as a function of the dynamical exponent. Furthermore, for the subinterval case, we determine that as the dynamical exponent increases, there is a crossover from an area law to a volume law. Lastly, we deform Lifshitz field theories with certain relevant operators and show that the EE decreases from the ultraviolet to the infrared fixed point, giving evidence for a possible c-theorem for deformed Lifshitz theories.

24 pages, 8 figures; v2: Clarified discussions in Subsection 3.3 and appendix; v3: Major extension of results, including an analytic computation of subinterval entanglement in massless scalar Lifshitz theories; v4: Added footnote 4 for clarification, version to appear in SciPost

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