Quasiparticle vanishing driven by geometrical frustration

We investigate the single hole dynamics in the triangular $t\ensuremath{-}J$ model. We study the structure of the hole spectral function, assuming the existence of a $120\ifmmode^\circ\else\textdegree\fi{}$ magnetic N\'eel order. Within the self-consistent Born approximation (SCBA) there is a strong momentum and t sign dependence of the spectra, related to the underlying magnetic structure and the particle-hole asymmetry of the model. For positive t, and in the strong coupling regime, we find that the low-energy quasiparticle excitations vanish outside the neighborhood of the magnetic Goldstone modes; while for negative t the quasiparticle excitations are always well defined. In the latter, we also find resonances of magnetic origin whose energies scale as ${(J/t)}^{2/3}$ and can be identified with string excitations. We argue that this complex structure of the spectra is due to the subtle interplay between magnon-assisted and free-hopping mechanisms. Our predictions are supported by an excellent agreement between the SCBA and the exact results on finite-size clusters. We conclude that the conventional quasiparticle picture can be broken by the effect of geometrical magnetic frustration.

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