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.
We revisit the problem of the dispersion of a single hole injected into a quantum antiferromagnet. We applied a spin-density-wave formalism extended to a large number of orbitals and obtained an integral equation for the full quasiparticle Green's function in the self-consistent ``noncrossing'' Born approximation. We found that for $t/J\ensuremath{\gg}1$, the bare fermionic dispersion is completely overshadowed by the self-energy corrections. In this case, the quasiparticle Green's function contains a broad incoherent continuum which extends over a frequency range of $\ensuremath{\sim}6t$. In addition, there exists a narrow region of width
O(JS) below the top of the valence band, where the excitations are mostly coherent, though with a small quasiparticle residue $Z\ensuremath{\sim}J/t$. The top of the valence band is located at $(\ensuremath{\pi}/2,\ensuremath{\pi}/2)$. We found that the form of the fermionic dispersion, and, in particular, the ratio of the effective masses near $(\ensuremath{\pi}/2,\ensuremath{\pi}/2)$ strongly depend on the assumptions one makes for the form of the magnon propagator. We argue in this paper that two-magnon Raman scattering as well as neutron-scattering experiments strongly suggest that the zone-boundary magnons are not free particles since a substantial portion of their spectral weight is transferred into an incoherent background. We modeled this effect by introducing a cutoff
qc in the integration over magnon momenta. We found analytically that for small
qc, the strong-coupling solution for the Green's function is universal, and both effective masses are equal to ${(4JS)}^{\ensuremath{-}1}$. We further computed the full fermionic dispersion for
J/t=0.4 relevant for
Sr2CuO2Cl2, and ${t}^{\ensuremath{'}}=\ensuremath{-}0.4J$ and found not only that the masses are both equal to ${(2J)}^{\ensuremath{-}1}$, but also that the energies at
(0,0) and $(0,\ensuremath{\pi})$ are equal, the energy at $(0,\ensuremath{\pi}/2)$ is about half of that at
(0,0), and the bandwidth for the coherent excitations is around
3J. All of these results are in full agreement with the experimental data. Finally, we found that weakly damped excitations only exist in a narrow range around $(\ensuremath{\pi}/2,\ensuremath{\pi}/2)$. Away from the vicinity of $(\ensuremath{\pi}/2,\ensuremath{\pi}/2)$, the excitations are overdamped, and the spectral function possesses a broad maximum rather than a sharp quasiparticle peak. This last feature was also reported in photoemission experiments.
A finite-size scaling analysis of the spectral function and of the optical conductivity of a single hole moving in an antiferromagnetic background is performed. It is shown that both the low-energy quasiparticle peak and the broad higher-energy structure are robust with increasing cluster size from 4\ifmmode\times\else\texttimes\fi{}4 to \ensuremath{\surd}26 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}26 sites. In the absence of spin fluctuations, for most static or dynamical quantities saturation occurs when the size exceeds a characteristic size
Nc(
Jz). Typically, 16- and 26-site clusters give reliable results for
Jz>0.75 and
Jz>0.3, respectively. The hole optical mass is shown to be very large (>20) in agreement with the small bandwidth. Due to the energy gap to flip a spin in the vicinity of a hole, a small gap \ensuremath{\propto}
Jz separates the low-energy \ensuremath{\delta} function from the rest of the spectrum in the dynamical correlation functions. On the other hand, with ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$ this gap seems to disappear with increasing system size as one would expect since the spin waves are gapless in the thermodynamic limit. The large momentum dependence of the quasiparticle weight in the isotropic case is inconsistent with a string picture but agrees well with the self-consistent Born approximation.An accurate estimation of the higher-energy part of the spectral functions of the t-J model can be made for momenta close to (0,0) or (\ensuremath{\pi},\ensuremath{\pi}); it consists of a broad featureless band. For momenta close to the Fermi surface, no evidence for excited string states is found. This may be either because the string scenario breaks down or because exact calculations at momenta near (\ensuremath{\pi}/2,\ensuremath{\pi}/2) are limited by the differing geometries of the finite clusters. In the Ising limit, the spectral function also depends crucially on the momentum, but a feature resembling a string excitation is seen for momenta close to (0,0). Our data on the finite-frequency optical conductivity of a single hole in the t-J model reveal that the total spectral weight at finite frequency has a strong size dependence and decreases with increasing size (for J not too small). This suggests that the optical mass and the optical absorption of the t-J model may have been overestimated in the past.
Single-particle dynamics in the 120\ifmmode^\circ\else\textdegree\fi{} ordered antiferromagnetic state of the triangular-lattice Hubbard model is studied using a physically transparent fluctuation approach in terms of multiple magnon emission and absorption processes within the noncrossing approximation. Hole and electron spectral features are evaluated at intermediate
U, and analyzed in terms of a competition between the frustration-induced direct hopping and the virtual hopping. Finite
U-induced competing interactions and frustration effects contributing through the magnon dispersion are also discussed. Finite contribution to self-energy correction from long-wavelength (Goldstone) modes, together with the high density of electron scattering states in the narrow, sharp peak in the upper band, result in strong fermion-magnon scattering leading to pronounced incoherent behavior in the electron dynamics. The fluctuation-induced first-order metal-insulator transition due to vanishing band gap is also discussed.
The t-J model in the large-t/J and low-doping limit is approximated by an effective Hamiltonian that treats spin degrees of freedom within the linear-spin-wave approximation and the hole-hopping term with a hole-spin interaction vertex that is linear in the spin-wave operators. The Dyson's equation for the single-hole Green's function is solved numerically on finite- but sufficiently large-size square lattices. Our calculation is based on an approximate equation for the hole motion that has been obtained using a self-consistent perturbation approach where crossing diagrams are neglected. We have studied the contribution of vertex corrections and found that the leading two-loop crossing diagram is exactly zero. Thus, the leading nonzero contribution to the proper self-energy from crossing diagrams is a three-loop correction. In two dimensions, it is possible to solve Dyson's equation numerically including these three-loop corrections. The results demonstrate that the contribution of such vertex corrections is indeed small. Our solution for the hole spectral function, obtained by neglecting such small contributions from vertex corrections, shows that most features describing the hole motion are in close agreement with the results of the exact diagonalization on the
42 lattice in the region of J/t\ensuremath{\le}0.2. The results obtained on sufficiently large-size lattices suggest that certain important features of the spectral function remain while others change due to finite-size effects. In particular, we find well-defined peaks above the lowest-energy peak that survive in the thermodynamic limit. We analyze these higher-energy peaks of the spectral functions and find that they can be understood as ``string'' excitations, which are created by the hole moving in a nearly linear potential.