Exact renormalization group for quantum spin systems

We show  that the generating functional of the time-ordered connected spin correlation functions of an  arbitrary quantum spin system satisfies an exact renormalization group flow equation [1].  Formally, this flow equation resembles  bosonic version of the so-called Wetterich equation. The SU(2) spin algebra is taken into account by integrating the renormalization group flow with a non-trivial initial condition.  Our method is closely related to a diagrammatic approach to quantum spin systems developed many years ago in a seminal work by  Vaks, Larkin, and Pikin [2].  As a first application, we show that our method gives the critical temperature of spin-S Ising models with high accuracy. We also discuss applications to quantum spin systems without long-range magnetc order.

 

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