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arXiv:cond-mat/0306147 · Physical Review B

Quasiparticle vanishing driven by geometrical frustration

A. E. Trumper, C. J. Gazza, L. O. Manuel

Published May 14, 2004• 26 citations
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Abstract

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.

DOI
10.1103/physrevb.69.184407

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We investigate the single hole dynamics in the triangular t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model. We study the structure of the hole spectral function, assuming the existence of a 120\ifmmode∘\else\textdegree\fi120\ifmmode^\circ\else\textdegree\fi{}120\ifmmode∘\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{(J/t)}^{2/3}(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.
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 UUU, and analyzed in terms of a competition between the frustration-induced direct hopping and the virtual hopping. Finite UUU-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.
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{\mathit{N}}_{\mathit{c}}Nc​(Jz{\mathit{J}}_{\mathit{z}}Jz​). Typically, 16- and 26-site clusters give reliable results for Jz{\mathit{J}}_{\mathit{z}}Jz​>0.75 and Jz{\mathit{J}}_{\mathit{z}}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{\mathit{J}}_{\mathit{z}}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.
We present quantum Monte Carlo (QMC) simulations for a single hole in a $t\ensuremath{-}J$ model from J=0.4tJ=0.4tJ=0.4t to J=4tJ=4tJ=4t on square lattices with up to $24\ifmmode\times\else\texttimes\fi{}24$ sites. The lower edge of the spectrum is directly extracted from the imaginary time Green's function. In agreement with earlier calculations, we find flat bands around $(0,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}),$ $(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi},0)$ and the minimum of the dispersion at $(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2).$ For small J, both self-consistent Born approximation and series expansions give a bandwidth for the lower edge of the spectrum in agreement with the simulations, whereas for J/t>1,J/t>1,J/t>1, only series expansions agree quantitatively with our QMC results. This band corresponds to a coherent quasiparticle. This is shown by a finite-size scaling of the quasiparticle weight $Z(\stackrel{\ensuremath{\rightarrow}}{k})$ that leads to a finite result in the thermodynamic limit for the considered values of J/t.J/t.J/t. The spectral function $A(\stackrel{\ensuremath{\rightarrow}}{k},\ensuremath{\omega})$ is obtained from the imaginary time Green's function via the maximum entropy method. Resonances above the lowest edge of the spectrum are identified, whose J dependence is quantitatively described by string excitations up to J/t=2.J/t=2.J/t=2.
We explore with exact diagonalization the propagation of a single hole in four magnetic phases of the $t\text{\ensuremath{-}}J$-like Kitaev-Heisenberg model on a honeycomb lattice: the N\'eel antiferromagnetic, stripe, zigzag, and Kitaev spin-liquid phases. We find coherent propagation of spin-polaron quasiparticles in the antiferromagnetic phase by a mechanism similar to that in the $t\text{\ensuremath{-}}J$ model for high-Tc{T}_{c}Tc​ cuprates. In the stripe and zigzag phases clear quasiparticles features appear in spectral functions of those propagators where holes are created and annihilated on one sublattice, while they remain largely hidden in those spectral functions that correspond to photoemission experiments. As the most surprising result, we find a totally incoherent spectral weight distribution for the spectral function of a hole moving in the Kitaev spin-liquid phase in the strong-coupling regime $t\ensuremath{\gg}J$ relevant for iridates. At intermediate coupling the finite systems calculation reveals a well-defined quasiparticle at the $\ensuremath{\Gamma}$ point; however, we find that the gapless spin excitations wipe out quasiparticles at finite momenta. Also for this more subtle case we conclude that in the thermodynamic limit the lightly doped Kitaev liquid phase does not support quasiparticle states in the neighborhood of $\ensuremath{\Gamma}$, and therefore yields a non-Fermi liquid, contrary to earlier suggestions based on slave-boson studies. These observations are supported by the presented study of the dynamic spin-structure factor in the Kitaev spin liquid regime.
We investigate the dynamics of a single hole coupled to the spiral fluctuations related to the magnetic ground states of the antiferromagnetic J1−−J2−−J3{J}_{1}--{J}_{2}--{J}_{3}J1​−−J2​−−J3​ Heisenberg model on a square lattice. Using exact diagonalization on finite size clusters and the self-consistent Born approximation in the thermodynamic limit, we find, as a general feature, a strong reduction of the quasiparticle weight along the spiral phases of the magnetic phase diagram. For an important region of the Brillouin zone the hole spectral functions are completely incoherent, whereas at low energies the spectral weight is redistributed on several irregular peaks. We find a characteristic value of the spiral pitch $\mathbf{Q}=(0.7,0.7)\ensuremath{\pi}$, for which the available phase space for hole scattering is maximum. We argue that this behavior is due to the nontrivial interference of the magnon-assisted and the free-hopping mechanism for hole motion, characteristic of a hole coupled to semiclassical spiral fluctuations.
The motion of a single hole in a two-dimensional Heisenberg antiferromagnet (hAF) is studied in a representation where holes are described as spinless fermions (holons) and spins as normal bosons. Assuming long-range AF order the spin dynamics is treated in linear spin-wave theory. The formulation highlights the close relation with the conventional polaron problem. The holon Green's function is calculated self-consistently within the Born approximation using finite-cluster geometries for the numerical solution. As a remarkable result we find close agreement with the spectral function A(k,\ensuremath{\omega}) of a hole calculated by exact diagonalization methods. A(k,\ensuremath{\omega}) is characterized by a narrow quasiparticle (QP) peak at the low-energy side of the spectrum, which is well separated from the incoherent part for large enough J values. A complete characterization of our solution is given, including the spectral weight, the dispersion relation, and effective masses of the QP state. A finite-size-scaling study gives a nonvanishing spectral weight of the QP in the thermodynamic limit for values J/t typical for copper oxide superconductors. Our calculations indicate that the self-consistent Born approximation is a valuable scheme for characterizing the dynamics of a hole in the t-J model, even in the strong-coupling regime.