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arXiv:cond-mat/0105063

Spin waves in the spiral phase of a doped antiferromagnet: a strong-coupling approach

N. Dupuis

Published May 3, 2001• 0 citations
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Abstract

We study spin fluctuations in the spiral phase of the two-dimensional Hubbard model at low doping on the basis of the spin-particle-hole coherent-state path integral. In the strong correlation limit, we obtain an analytical expression of the spin-wave excitations over the entire Brillouin zone except in the vicinity of ${\bf q}=0$. We discuss the validity of the Hartree-Fock and random-phase approximations in the strong-coupling limit, and compare our results with previous numerical and analytical calculations. Although the spiral phase is unstable, as shown by a negative mean-field compressibility and the presence of imaginary spin-fluctuation modes, we expect the short-wavelength fluctuation modes (with real energies) to survive in the actual ground-state of the system.

DOI
10.48550/arxiv.cond-mat/0105063

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Journal of Physics Condensed Matter•Feb 14, 2019•1 citation
We study spin fluctuations in the spiral phase of the two-dimensional Hubbard model at low doping on the basis of the spin-particle-hole coherent-state path integral. In the strong correlation limit, we obtain an analytical expression of the spin-wave excitations over the entire Brillouin zone except in the vicinity of q=0{\bf q}=0q=0. We discuss the validity of the Hartree-Fock and random-phase approximations in the strong-coupling limit, and compare our results with previous numerical and analytical calculations. Although the spiral phase is unstable, as shown by a negative mean-field compressibility and the presence of imaginary spin-fluctuation modes, we expect the short-wavelength fluctuation modes (with real energies) to survive in the actual ground-state of the system.
The homogeneous Hartree-Fock antiferromagnetic (AF) state of the doped Hubbard model is shown to be unstable for infinitesimal doping concentration. Driven by long-wavelength intraband fluctuations, this instability with respect to infinitesimal fluctuations around the mean-field state is inferred from the nature of the static spin response, which increases away from the AF wave vector (\ensuremath{\pi},\ensuremath{\pi}). The effective interaction between antiparallel-spin holes in the lower band is found to contain a short-range attractive component, with an energy scale Jx. We discuss the crossover of the characteristic length scale for intraband fluctuations from the antiferromagnetic state to the spiral state, also unstable for infinitesimal doping concentration.
We reconsider some of the previous studies of the interactions between the holes and the spin background in the Hubbard model in the small-doping limit. We show that the hole-hole interaction due to the transverse magnetization fluctuations (i.e., spin waves) is finite at arbitrarily small hole density. It may be comparable to the coupling due to the longitudinal magnetization fluctuations (which are the essence of the ``spin-bag'' mechanism of Schrieffer, Wen, and Zhang). This suggests that the two couplings should be considered simultaneously when studying the phase diagram of the lightly doped quantum antiferromagnets at the values of U/t relevant to the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ superconducting materials. We also show that in the large-(U/t) limit the Hubbard-model expressions for the coupling of holes reduce to those given by Shraiman and Siggia for the t-J model. This provides a link between the weak- and the strong-coupling theories of the doped quantum antiferromagnets, in the small-doping limit.
All the linear excitations are calculated in the random-phase approximation around a doped inhomogeneous Hartree-Fock state as well as the undoped uniform antiferromagnetic state in the one-dimensional Hubbard model. Upon doping, shape modes appear, localized around an introduced hole, as well as some ``shake-off'' branches related to combinations of local and extended Hartree-Fock orbitals. These modes are in addition to spin wave and ultragap branches in the pure antiferromagnetic state. Some characteristics of the shape modes are similar to bare processes in the t-t'-J model derived from the Hubbard model at strong coupling. Spectral weights in different susceptibility channels are calculated and shown to have peaks in low-energy regions, arising from specific shape modes.
The properties of spin excitations superposed on a uniform ground state with antiferromagnetic (or spiral) spin structure are studied in a 2 D Hubbard model. Expressions are derived for the spin susceptibility in the random phase approximation (RPA) using split Hubbard bands as a zeroth approximation. The calculated collective modes with dispersion ω ( Q )= c | Q −(π, π)| near Q ∼(π, π) reproduce well the characteristics of the spin excitations observed in undoped cuprates. For doped systems with an antiferromagnetic structure of the ground state, calculating X ″( Q,ω →0) gives the same mode with a peak at Q ∼(π, π), regardless of the type of Fermi surface. It is shown that in doped systems with a spiral ground state spin structure, X ″( Q,ω →0) peaks occur with incommensurate quasimomenta Q that are coupled to the spirality vector.
Lieb and hole-doped ferrimagnetism, spiral, resonating valence-bond states, and phase separation in large-U AB2AB_{2}AB2​ Hubbard chains
The ground state (GS) properties of the quasi-one-dimensional AB2AB_2AB2​ Hubbard model are investigated taking the effects of charge and spin quantum fluctuations on equal footing. In the strong-coupling regime, we derive a low-energy Lagrangian suitable to describe the ferrimagnetic phase at half filling and the phases in the hole-doped regime. At half filling, a perturbative spin-wave analysis allows us to find the GS energy, sublattice magnetizations, and Lieb total spin per unit cell of the effective quantum Heisenberg model, in very good agreement with previous results. In the challenging hole doping regime away from half filling, we derive the corresponding t-Jt\textrm{-}Jt-J Hamiltonian. Under the assumption that charge and spin quantum correlations are decoupled, the evolution of the second-order spin-wave modes in the doped regime unveils the occurrence of spatially modulated spin structures and the emergence of phase separation in the presence of resonating-valence-bond states. We also calculate the doping-dependent GS energy and total spin per unit cell, in which case it is shown that the spiral ferrimagnetic order collapses at a critical hole concentration. Notably, our analytical results in the doped regime are in very good agreement with density matrix renormalization group studies, where our assumption of spin-charge decoupling is numerically supported by the formation of charge-density waves in anti-phase with the modulation of the magnetic structure.
Hubbard model are investigated taking the effects of charge and spin quantum fluctuations on equal footing. In the strong-coupling regime, a functional integral representation allows us to derive a low-energy Lagrangian suitable to describe the ferrimagnetic phase at half filling and the phases in the hole-doped regime. At half filling, a perturbative spin-wave analysis allows us to find the GS energy, sublattice magnetizations, and total spin per unit cell in the Lieb ferrimagnetic GS of the effective quantum Heisenberg model, in very good agreement with previous results. In the challenging hole doping regime away from half filling, we derive the corresponding [Formula: see text] Hamiltonian. Under the assumption that charge and spin quantum correlations are decoupled, the evolution of the second-order spin-wave modes in the doped regime unveils the occurrence of spatially modulated spin structures and the emergence of phase separation in the presence of resonating-valence-bond states. We also calculate the doping-dependent GS energy and total spin per unit cell, including both Zeeman and orbital contributions, in which case it is shown that the spiral ferrimagnetic order collapses at a critical hole concentration. Notably, our analytical results in the doped regime are in very good agreement with density matrix renormalization group studies, where our assumption of spin-charge decoupling is numerically supported by the formation of charge-density waves in anti-phase with the modulation of the magnetic structure.