Functional renormalization group for the anisotropic triangular antiferromagnet

Abstract

We present a functional renormalization group scheme that allows us to calculate frustrated magnetic systems of arbitrary lattice geometry beyond $O(200)$ sites from first principles. We study the magnetic susceptibility of the antiferromagnetic (AFM) spin-$1/2$ Heisenberg model ground state on the spatially anisotropic triangular lattice, where ${J}^{\ensuremath{'}}$ denotes the coupling strength of the intrachain bonds along one lattice direction and $J$ the coupling strength of the interchain bonds. We identify three distinct phases of the Heisenberg model. Increasing $\ensuremath{\xi}={J}^{\ensuremath{'}}/J$ from the effective square lattice $\ensuremath{\xi}=0$, we find an AFM N\'eel order to spiral order transition at ${\ensuremath{\xi}}_{c1}~0.6--0.7$, with an indication that it is of second order. In addition, above the isotropic point at ${\ensuremath{\xi}}_{c2}~1.1$, we find a first-order transition to a magnetically disordered phase with collinear AFM stripe fluctuations.