J1J2 frustrated two-dimensional Heisenberg model: Random phase approximation and functional renormalization group

Johannes Reuther and Peter Wölfle
Phys. Rev. B 81, 144410 – Published 8 April 2010

Abstract

We study the ground-state properties of the two-dimensional spin-1/2 J1J2 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 random-phase approximation, demonstrating the appearance of a paramagnetic phase between the Néel-ordered and Collinear-ordered phases, at sufficiently large pseudofermion damping. Second 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 Néel order at g=J2/J1gc10.40.45 and Collinear order at ggc20.660.68, 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.

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  • Received 16 December 2009

DOI:https://doi.org/10.1103/PhysRevB.81.144410

©2010 American Physical Society

Authors & Affiliations

Johannes Reuther and Peter Wölfle

  • Institut für Theorie der Kondensierten Materie, Karlsruhe Institute of Technology, D-76128 Karlsruhe, Germany

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Vol. 81, Iss. 14 — 1 April 2010

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