Dynamic critical exponent in quantum long-range models

Abstract: Quantum long-range models at zero temperature can be described by fractional Lifshitz field theories, that is, anisotropic models whose actions are short-range in time and long-range in space. In this paper we study the renormalization of fractional Lifshitz field theories with weakly relevant cubic or quartic self-interactions. Their nontrivial infrared fixed points exhibit Lifshitz scale invariance, and we compute the lowest-order corrections to the dynamic critical exponent.