Erratum: Spin waves in a triangular lattice antiferromagnet: Decays, spectrum renormalization, and singularities [Phys. Rev. B79, 144416 (2009)

Abstract

Spin-waves in triangular lattice antiferromagnet: decays, spectrum renormalization, and singularities A. L. Chernyshev Department of Physics, University of California, Irvine, California 92697, USA and Max-Planck-Institut f¨ ur Physik komplexer Systeme, 01187 Dresden, Germany M. E. Zhitomirsky Commissariat a ` l’Energie Atomique, DSM/INAC/SPSMS, F-38054 Grenoble, France (Dated: June 12, 2015) We present a comprehensive study of the dynamical properties of the quantum Heisenberg an- tiferromagnet on a triangular lattice within the framework of spin-wave theory. The distinct fea- tures of spin-wave excitations in the triangular-lattice antiferromagnet are (i) finite lifetime at zero temperature due to spontaneous two-magnon decays, (ii) strong renormalization of magnon ener- gies e k with respect to the harmonic result, and (iii) logarithmic singularities in the decay rate Γ k . Quantum corrections to the magnon spectrum are obtained using both the on-shell and off- shell solutions of the Dyson equation with the lowest-order magnon self-energy. At low-energies magnon excitations remain well-defined albeit with the anomalous decay rate Γ k ∝ k 2 at k → 0 and Γ k ∝ |k − Q AF | 7/2 at k → Q AF . At high energies, magnons are heavily damped with the decay rate reaching (2Γ k /e k ) ∼ 0.3 for the case S = 1/2. The on-shell solution shows logarithmic singularities in Γ k with the concomitant jump-like discontinuities in Re[e k ] along certain contours in the momen- tum space. Such singularities are even more prominent in the magnon spectral function A(k, ω). Although the off-shell solution removes such log-singularities, the decay rates remain strongly en- hanced. We also discuss the role of higher-order corrections and show that such singularities may lead to complete disappearance of the spectrum in the vicinity of certain k-points. The kinematic conditions for two-magnon decays are analyzed for various generalizations of the triangular-lattice antiferromagnet as well as for the XXZ model on a kagom´e lattice. Our results suggest that decays and singularities in the spin-wave spectra must be ubiquitous in all these systems. In addition, we give a detailed introduction in the spin-wave formalism for noncollinear Heisenberg antiferromagnets and calculate several quantities for the triangular-lattice model including the ground-state energy and the sublattice magnetization. PACS numbers: 75.10.Jm, 75.30.Ds, 78.70.Nx I. INTRODUCTION Heisenberg antiferromagnet (HAF) on a triangular lat- tice has been a focus of much attention as one of the basic model systems in which geometric frustration and low dimensionality are expected to yield new physical phenomena. Although available experimental realiza- tions of the triangular-lattice antiferromagnet 1–6 are de- scribed by such a model only approximately, either due to anisotropies or because of additional interactions, the ideal nearest-neighbor Heisenberg antiferromagnet on a triangular lattice given by ˆ = J H X S i · S j , hiji remains the principal reference point. The semiclassical S 1 triangular-lattice HAF or- ders in the so-called 120 ◦ structure, see Fig. 1. Histori- cally, it was anticipated that enhanced quantum fluctua- tions destroy the long-range antiferromagnetic order for the spin-1/2 model. 7 However, calculations of quantum corrections within the spin-wave theory have suggested that the 120 ◦ magnetic structure remains stable even for S = 1/2. 8–11 The early numerical results for small clusters were less conclusive, some supporting magnet- ically disordered state 12 and some confirming the spin- wave results. 13 Since the quantum Monte Carlo suffers from the infamous sign problem when applied to frus- trated models, it is not until the Green’s function Monte Carlo work 14 that the magnetically ordered ground state of the spin-1/2 triangular-lattice HAF has been gener- ally agreed upon. More recent series-expansion 15 and density-matrix renormalization group (DMRG) studies 16 have confirmed the stability of the 120 ◦ spin structure for the case of S = 1/2 and yielded the value of ordered mo- ments hSi ≈ 0.20, close to the previous result. 14 Gradually, it has been recognized that the truly dis- tinct physics of the quantum triangular-lattice antiferro- magnet concerns its excitation spectrum and the thermo- dynamic properties. The anomalous behavior of the lat- ter has been discovered earlier by the high-temperature series-expansion study. 17 The temperature dependence of such quantities as entropy or susceptibility, exhibits significant differences between the triangular- and the square-lattice models: upon lowering temperature down to about J/2 the square-lattice antiferromagnet shows strong signs of ordering, while the triangular-lattice one does not. More recently, developments in the series- expansion method have allowed to calculate the excita-