arXiv:1011.0874v2 [cond-mat.str-el] 10 Nov 2010 A test of the bosonic spinon hypothesis for the triangular antiferromagnet spectrum A. Mezio, C. N. Sposetti, L. O. Manuel, and A. E. Trumper Instituto de F´ ısica Rosario (CONICET) and Universidad Nacional de Rosario, Boulevard 27 de Febrero 210 bis, (2000) Rosario, Argentina (Dated: November 11, 2010) We compute the dynamical structure factor of the spin-1/2 triangular Heisenberg model using a Schwinger boson mean field theory. We find that the reconstructed dispersion, resulting from a non trivial redistribution of the spectral weight, agrees quite well with the spectrum recently found with series expansion. We show that the agreement is strongly dependent on the mean field decoupling. In particular, the two singlet bond operator scheme seems to be more effective to recover the physical spectrum than the one singlet bond operator scheme. The appearance of the roton minima at high energy can be identified with the quantum mechanical tendency of the ground state to fluctuate collinearly even in the 120 ◦ N´ eel order. Furthermore, near the roton minima the contribution of the two spinon continuum to the static structure factor is about 40% of the total weight. The origin of a remnant weak signal in the spectrum related to the local constraint violation is also discussed. During a long time the magnetic ground state of the spin 1/2 triangular Heisenberg model has attracted the attention of many researchers, due to the possible real- ization of a resonating valence bond (RVB) ground state proposed by P. W. Anderson in 1973 1 . The revival of the RVB theory for the cuprates 2 prompted the inves- tigations of quantum disordered ground states within large N theories where the Heisenberg interaction is nat- urally written in terms of singlet bond operators and fractional spin 1 2 excitations with bosonic or fermionic character 3 . The fermionic version leads to exotic dis- ordered ground states 4 while the bosonic one allows to describe disordered and ordered ground states 5 by relat- ing the magnetization with the condensation of bosons 6 . For this case, using gauge field theoretical arguments, it has been conjectured that when short range spiral corre- lations are present in the disordered phases the bosonic spinons would be in a deconfined regime 5 . Therefore, a broad two spinon continuum would be expected in the spin excitation spectrum. From the numerical side, instead, thanks to the enormous effort of the community to develop unbiased techniques 7 , it has been firmly established that the ground state of the spin 1/2 triangular Heisenberg model (THM) is a robust 120 ◦ N´ eel order. These numerical results precluded the fermionic version of the RVB the- ory giving support to both the linear spin wave theory (LSWT) and the bosonic version of the RVB theory, namely the Schwinger boson theory. In fact, both theo- ries agree quite well with numerical results on finite size systems 8,9 although for spiral phases the singlet struc- ture of the mean field Schwinger bosons does not recover the spin wave relation dispersion in the large s limit 10 . So, linear spin wave theory seemed to capture the quan- tum and semiclassical features expected for a 120 ◦ N´ eel ground state of the THM. However, recent series expansions studies 11 challenged LSWT showing that for s =1/2 the functional form of the dispersion relation differs considerably (blue points of Fig. 1) from that of LSWT (green solid line of Fig. 1). In particular, a strong downward renormalization of A B C O A Q D 0 0.5 1 1.5 2 ω FIG. 1: Intensity curves for the dynamical structure factor, Eq. (4) along the path shown in the inset of Fig. 3. Solid green line: LSWT results. Blue dots: series expansion results. the high energy part of the spectrum along with the ap- pearance of roton like minima at the midpoints of faces of the hexagonal Brillouin zone (BZ) (B and D points of the inset of Fig. 3) was observed. The authors argued that the differences could be attributed to the presence of fermionic spinon excitations. Nevertheless, further spin wave studies 12 to first order in 1/s showed that due to the non collinearity of the ground state there appear non trivial corrections to the spin wave dispersion giving a fairly accurate description of the series expansion results, although magnons may not necessarily be well defined for all wave vectors of the BZ 13 . On the other hand, since the singlet structure of the Schwinger boson theory pre- dicts quite accurate results for the static ground state properties of the THM, such as energy, structure factor, local magnetization, and spin stiffness 8 , it is important to investigate whether the anomalous features of the spec- trum found with series expansions can be captured, or not, by a theory that naturally incorporates fractional