Exact renormalization group for quantum spin systems

TL;DR

This paper introduces a novel non-perturbative method for quantum spin systems by embedding a diagrammatic approach into the functional renormalization group framework, enabling exact flow equations for spin correlations.

Contribution

It develops a general, exact renormalization group approach for quantum spin systems that incorporates the $SU(2)$ algebra through specific initial conditions, extending previous diagrammatic methods.

Findings

Derives an exact RG flow equation for quantum spin correlation functions.

Shows the RG flow resembles that of interacting bosons.

Provides a new non-perturbative framework for analyzing quantum spin systems.

Abstract

We show that the diagrammatic approach to quantum spin systems developed in a seminal work by Vaks, Larkin, and Pikin [Sov. Phys. JETP 26, 188 (1968)] can be embedded in the framework of the functional renormalization group. The crucial insight is 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 which resembles the corresponding flow equation of a system of interacting bosons. The $SU (2)$ spin algebra is implemented via a non-trivial initial condition for the renormalization group flow. Our method is rather general and offers a new non-perturbative approach to quantum spin systems.