Renormalization group analysis of competing quantum phases in the J1-J2 Heisenberg model on the kagome lattice

TL;DR

This study uses the pseudofermion functional renormalization group to map the quantum phases of the S=1/2 Heisenberg kagome model, identifying various magnetic orders and disordered regions relevant to experimental materials.

Contribution

It provides a detailed phase diagram of the kagome Heisenberg model, revealing multiple magnetic orders and disordered phases, and analyzes susceptibility features linked to experimental observations.

Findings

Identified four magnetic quantum orders including q=0 and cuboc.

Reconciled susceptibility features of Herbertsmithite with small J2 coupling.

Rejection of valence bond crystal order in the disordered regime.

Abstract

Recent discoveries in neutron scattering experiments for Kapellasite and Herbertsmithite as well as theoretical calculations of possible spin liquid phases have revived interest in magnetic phenomena on the kagome lattice. We study the quantum phase diagram of the S=1/2 Heisenberg kagome model as a function of nearest neighbor coupling J1 and second neighbor coupling J2. Employing the pseudofermion functional renormalization group, we find four types of magnetic quantum order (q=0 order, cuboc order, ferromagnetic order, and Sqrt{3}x\Sqrt{3} order) as well as extended magnetically disordered regions by which we specify the possible parameter regime for Kapellasite. In the disordered regime J2/J1<<1, the flatness of the magnetic susceptibility at the zone boundary which is observed for Herbertsmithite can be reconciled with the presence of small J2>0 coupling. In particular, we analyze the dimer susceptibilities related to different valence bond crystal (VBC) patterns, which are strongly inhomogeneous indicating the rejection of VBC order in the RG flow.