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arXiv:cond-mat/9408057

Spin dynamics of the doped t-J model

R. Eder, Y. Ohta

Published Aug 19, 1994• 0 citations
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Abstract

We present a new method for studying the low energy excitations in finite cluster systems and apply it to clarify the nature of the low energy spin excitations in the moderately doped t-J model. We find that the character of the low energy spin excitations changes within the Brillouin zone, with the dominant excitation for momentum transfer (pi,pi) being a spin wave-like collective mode. Spin excitations with momentum transfer different from (pi,pi) have particle-hole character. We give an explicit construction of a low energy collective spin mode in a system with `almost broken symmetry' and demonstrate its validity by explicit numerical check.

DOI
10.48550/arxiv.cond-mat/9408057

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We present a new method for studying the low energy excitations in finite cluster systems and apply it to clarify the nature of the low energy spin excitations in the moderately doped t-J model. We find that the character of the low energy spin excitations changes within the Brillouin zone, with the dominant excitation for momentum transfer (pi,pi) being a spin wave-like collective mode. Spin excitations with momentum transfer different from (pi,pi) have particle-hole character. We give an explicit construction of a low energy collective spin mode in a system with `almost broken symmetry' and demonstrate its validity by explicit numerical check.
Based on a variational approach, we propose that there are two kinds of low-energy states in the t-J-type models at low doping. In a quasiparticle state an unpaired spin bound to a hole with a well-defined momentum can be excited with spin waves. The resulting state shows a suppression of antiferromagnetic order around the hole with the profile of a spin bag. These spin-bag states with spin and charge or hole separated form a continuum of low-energy excitations. Very different properties predicted by these two kinds of states explain a number of anomalous results observed in the exact diagonalization studies on small clusters up to 32 sites.
The numerically exact diagonalization study on small clusters of the t-J model with the second- and third- neighbor hopping terms shows that a novel spin liquid state is realized around a doped hole with momentum k=(pi,0) and energy \sim 2J compared with that with (pi/2,pi/2) in insulating cuprates, where the spin and charge degrees of freedom are approximately decoupled. Our finding implies that the excitations in the insulating cuprates are mapped onto the the d-wave resonating valence bond state.
Spin-fermion model on a square lattice is investigated in the perturbation expansion in terms of the spin-fermion Kondo coupling. The fermion self-energy is calculated in a self-consistent treatment by a dominant pole approximation. The quasi-particle excitation of a doped fermion turns out to be totally incoherent. It suggests that the low energy excitations should be described by the bound state of a fermion and spins as a collective mode and imply that the fixed point of the spin-fermion model with a single fermion is the t - J model. It also suggests the spin-charge separation of the low energy excitations in the light doping region of these two models.
In this paper, we present analytical and numerical calculations of the \ensuremath{\pi} resonance in the $t\ensuremath{-}J$ model. We show in detail how the $\ensuremath{\pi}$ resonance in the particle-particle channel couples to the dynamical spin correlation function in a superconducting state. The contribution of the \ensuremath{\pi} resonance to the spin excitation spectrum can be estimated from general model-independent sum rules, and it agrees with our detailed calculations. The results are in overall agreement with the exact diagonalization studies of the $t\ensuremath{-}J$ model. Earlier calculations predicted the correct doping dependence of the neutron resonance peak in the YBa2Cu3O6+x{\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6+x}YBa2​Cu3​O6+x​ superconductor, and in this paper detailed energy and momentum dependence of the spin correlation function is presented. The microscopic equations of motion obtained within current formalism agree with that of the SO(5) nonlinear \ensuremath{\sigma} model, where the \ensuremath{\pi} resonance is interpreted as a pseudo-Goldstone mode of the spontaneous SO(5) symmetry breaking.
We study the doping evolution of spin excitations in a one-dimensional (1D) Hubbard model and its downfolded spin Hamiltonians, by using exact diagonalization combined with cluster perturbation theory. In all models we observe hardening (softening) of spin excitations upon electron (hole) doping, which are reminiscent of recent experiments on two-dimensional (2D) cuprate materials. We also find that the three-site and even higher-order terms are crucial for the low-energy effective spin models to reproduce the magnetic spectra of doped Hubbard systems at a quantitative level. To interpret the numerical results, we further employ a strong coupling slave-boson mean-field theory. The mean-field theory provides an intuitive understanding of the overall compact support of dynamic spin structure factors, including the shift of zero-energy modes and change of spin excitation bandwidth with doping. Our results can serve as predictive benchmarks for future inelastic x-ray or neutron scattering experiments on doped 1D antiferromagnetic Mott insulators.
We have studied hole states on square lattices with 8, 10, 16, 18, and 20 sites by exactly diagonalizing the single-hole t-J model with twisted boundary conditions in the whole Brillouin zone. The bottom of the hole band is found to be extremely flat and anisotropic. The hole effective mass is highly anisotropic and enhanced in a quantum antiferromagnet. The momentum of a hole in the ground state is not located at high-symmetry points such as (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2), (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi},0), or (0,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}). They are strongly lattice-size dependent and weakly parameter J/t (t is the hopping constant and J is the exchange constant) dependent. As the lattice size increases, the momentum of the ground state approaches the zone face center (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2).