Dynamic critical exponent in quantum long-range models

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.