J_1-J_2 frustrated two-dimensional Heisenberg model: Random phase approximation and functional renormalization group

TL;DR

This paper investigates the phase diagram of the 2D J_1-J_2 Heisenberg model using diagrammatic approximations, revealing a paramagnetic phase with enhanced quantum fluctuations between magnetic orders, and compares methods including RPA and functional renormalization group.

Contribution

It introduces a combined approach using RPA and an improved functional renormalization group to analyze ground state phases of the J_1-J_2 model, emphasizing the importance of self-energy renormalizations.

Findings

Identification of a paramagnetic phase between magnetic orders.

Agreement of phase boundaries with numerical studies.

Observation of enhanced quantum fluctuations in the paramagnetic phase.

Abstract

We study the ground state properties of the two-dimensional spin-1/2 J_1-J_2-Heisenberg model on a square lattice, within diagrammatic approximations using an auxiliary fermion formulation with exact projection. In a first approximation we assume a phenomenological width of the pseudofermion spectral function to calculate the magnetization, susceptibilities and the spin correlation length within RPA, demonstrating the appearance of a paramagnetic phase between the Neel ordered and Collinear ordered phases, at sufficiently large pseudo fermion damping. Secondly we use a Functional Renormalization Group formulation. We find that the conventional truncation scheme omitting three-particle and higher order vertices is not sufficient. We therefore include self-energy renormalizations in the single-scale propagator as recently proposed by Katanin, to preserve Ward identities in a better way. We find Neel order at g = J_2/J_1 < 0.4 ... 0.45 and Collinear order at g > 0.66 ... 0.68, which is in good agreement with results obtained by numerical studies. In the intervening quantum paramagnetic phase we find enhanced columnar dimer and plaquette fluctuations of equal strength.