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arXiv:cond-mat/0506488 · Physical Review B

Hole and electron dynamics in a triangular-lattice antiferromagnet: Interplay of frustration and spin fluctuations

Pooja Srivastava, Avinash Singh

Published Dec 7, 2005• 6 citations
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Abstract

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.

DOI
10.1103/physrevb.72.224409

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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.
Self-energy corrections due to to fermion-magnon interaction are studied in the antiferromagnetic state of the $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{''}}$ Hubbard model within the noncrossing approximation in the full UUU range from weak to strong coupling. The role of classical (mean-field) features of fermion and magnon dispersion, associated with finite $U,{t}^{\ensuremath{'}},{t}^{\ensuremath{''}}$, are examined on quantum corrections to quasiparticle energy, weight, one-particle density of states, etc. A finite-UUU induced classical dispersion term, absent in the $t\ensuremath{-}J$ model, is found to play an important role in suppressing the quasiparticle weight for states near k=(0,0)\mathbf{k}=(0,0)k=(0,0), as seen in cuprates. For intermediate UUU, the renormalized antiferromagnetic (AF) band gap is found to be nearly half of the classical value, and the weak-coupling limit is quite nontrivial due to strongly suppressed magnon amplitude. For finite ${t}^{\ensuremath{'}}$, the renormalized AF band gap is shown to vanish at a critical interaction strength Uc{U}_{c}Uc​, yielding a spin fluctuation driven first-order AF insulator--paramagnetic metal transition. Quasiparticle dispersion evaluated with the same set of Hubbard model cuprate parameters, as obtained from a recent magnon spectrum fit, provides excellent agreement with angle-resolved photoemission spectroscopy data for Sr2CuO2Cl2{\mathrm{Sr}}_{2}\mathrm{Cu}{\mathrm{O}}_{2}{\mathrm{Cl}}_{2}Sr2​CuO2​Cl2​.
Ferromagnetism in the Hubbard model is investigated on sc, bcc, and fcc lattices using a systematic inverse-degeneracy (1∕N)(1∕\mathcal{N})(1∕N) expansion which incorporates self-energy and vertex corrections such that spin-rotation symmetry and the Goldstone mode are explicitly preserved. First-order quantum corrections to magnon energies are evaluated for several cases, providing a comprehensive picture of the interplay of lattice, band dispersion, and interaction effects on the stability of the ferromagnetic state with respect to both long- and short-wavelength fluctuations. Our results support the belief that ferromagnetism is a generic feature of the Hubbard model at intermediate and strong coupling provided the density of states (DOS) is sufficiently asymmetric and strongly peaked near the band edge, as for the fcc lattice with finite ${t}^{\ensuremath{'}}$. For short-wavelength modes, the behavior of a characteristic energy scale ${\ensuremath{\omega}}^{*}\ensuremath{\sim}{T}_{c}$ (magnon DOS peak energy) is in excellent agreement with the Tc{T}_{c}Tc​ vs nnn behavior within dynamical mean field theory, with respect to both the stable range of densities (0.20<n<0.85)(0.20<n<0.85)(0.20<n<0.85) as well as the optimal density n=0.65n=0.65n=0.65. However, our finding of vanishing spin stiffness near optimal density highlights the role of long-wavelength fluctuations in further reducing the stable range of densities.
We introduce a slave-fermion formulation in which to study the charge dynamics of the half-filled Hubbard model on the square lattice. In this description, the charge degrees of freedom are represented by fermionic holons and doublons and the Mott-insulating characteristics of the ground state are the consequence of holon–doublon bound-state formation. The bosonic spin degrees of freedom are described by the antiferromagnetic Heisenberg model, yielding long-ranged (Néel) magnetic order at zero temperature. Within this framework and in the self-consistent Born approximation, we perform systematic calculations of the average double occupancy, the electronic density of states, the spectral function and the optical conductivity. Qualitatively, our method reproduces the lower and upper Hubbard bands, the spectral-weight transfer into a coherent quasiparticle band at their lower edges and the renormalisation of the Mott gap, which is associated with holon–doublon binding, due to the interactions of both quasiparticle species with the magnons. The zeros of the Green function at the chemical potential give the Luttinger volume, the poles of the self-energy reflect the underlying quasiparticle dispersion with a spin-renormalised hopping parameter and the optical gap is directly related to the Mott gap. Quantitatively, the square-lattice Hubbard model is one of the best-characterised problems in correlated condensed matter and many numerical calculations, all with different strengths and weaknesses, exist with which to benchmark our approach. From the semi-quantitative accuracy of our results for all but the weakest interaction strengths, we conclude that a self-consistent treatment of the spin-fluctuation effects on the charge degrees of freedom captures all the essential physics of the antiferromagnetic Mott–Hubbard insulator. We remark in addition that an analytical approximation with these properties serves a vital function in developing a full understanding of the fundamental physics of the Mott state, both in the antiferromagnetic insulator and at finite temperatures and dopings.
We investigate the metal-insulator transition in the half-filled Hubbard model on the two-dimensional triangular lattice using both the Kotliar-Ruckenstein slave-boson technique and an exact numerical diagonalization of finite clusters. Contrary to the case of a square lattice, where a perfect nesting of the Fermi surface leads to a metal-insulator transition at arbitrarily small values of U, always accompanied by antiferromagnetic ordering, on a triangular lattice, due to the lack of perfect nesting, the transition takes place at a finite value of U, and frustration induces a nontrivial competition among different magnetic phases. Indeed, within the mean-field approximation in the slave-boson approach, as the interaction grows the paramagnetic metal turns into a metallic phase with incommensurate spiral ordering. Increasing the interaction further, a linear spin-density wave is stabilized, and finally for strong coupling the latter phase undergoes a first-order transition toward an antiferromagnetic insulator. No trace of the intermediate phases is seen in the exact diagonalization results, indicating a transition between a paramagnetic metal and an antiferromagnetic insulator.
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{(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.
We study kinetic magnetism for the Fermi-Hubbard models in triangular type lattices, including a zigzag ladder, four- and six-legged triangular cylinders and a full two-dimensional triangular lattice. We focus on the regime of strong interactions, U≫tU\gg tU≫t and filling factors around one electron per site. For temperatures well above the hopping strength, the Curie-Weiss form of the magnetic susceptibility suggests effective antiferromagnetic correlations for systems that are hole doped with respect to ν=1ν=1ν=1, and ferromagnetic correlations for systems with electron dopings. We show that these correlations arise from magnetic polaron dressing of charge carrier propagating in a spin incoherent Mott insulator. Effective interactions corresponding to these correlations can strongly exceed the magnetic super-exchange energy. In the case of hole doping, antiferromagnetic polarons originate from kinetic frustration of individual holes in a triangular lattice. In the case of electron doping, Nagaoka type ferromagnetic correlations are induced by propagating doublons. These results provide a theoretical explanation of recent experimental results in moire TMDC materials. To understand many-body states arising from antiferromagentic polarons at low temperatures, we study hole doped systems in finite magnetic fields. At low dopings and intermediate magnetic fields we find a magnetic polaron phase, separated from the fully polarized state by a metamagnetic transition. With decreasing magnetic field the system shows a tendency to phase separate, with hole rich regions forming antiferromagnetic spinbags. We demonstrate that direct observations of magnetic polarons in triangular lattices can be achieved in experiments with ultracold atoms, which allow measurements of three point hole-spin-spin correlations.