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arXiv:cond-mat/9909019

Dynamic spin susceptibility in the t-J model

George Jackeli, Nikolay M. Plakida

Published Sep 1, 1999• 1 citation
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Abstract

Dynamic spin susceptibility is calculated for the t-J model in the paramagnetic phase by applying the memory function method in terms of the Hubbard operators. A self-consistent system of equations for the memory function is obtained within the mode coupling approximation. Both itinerant hole excitations and localized spin fluctuations give contributions to the memory function. Spin dynamics have a diffusive character in the hydrodynamic limit; spin-wave-like excitations are regained in the high-frequency region.

DOI
10.48550/arxiv.cond-mat/9909019

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Dynamic spin susceptibility is calculated for the t-J model in the paramagnetic phase by applying the memory function method in terms of the Hubbard operators. A self-consistent system of equations for the memory function is obtained within the mode coupling approximation. Both itinerant hole excitations and localized spin fluctuations give contributions to the memory function. Spin dynamics have a diffusive character in the hydrodynamic limit; spin-wave-like excitations are regained in the high-frequency region.
The dynamic charge susceptibility and the optical conductivity are calculated in the planar $t\ensuremath{-}J$ model within the memory function method, working directly in terms of Hubbard operators. The density fluctuation spectrum consists of a damped soundlike mode for small wave vectors and a broad high energy peak $(\ensuremath{\sim}t)$ for large momenta. The study of the optical conductivity shows that electron scattering from spin fluctuations leads to the Drude-frequency dependent relaxation rate which exhibits a crossover from ${\ensuremath{\omega}}^{3/2}$ behavior at low frequencies $(\ensuremath{\omega}<2|\ensuremath{\mu}|),$ to a linear $\ensuremath{\omega}$ dependence for frequencies larger than $2|\ensuremath{\mu}|.$ Due to the spin-polaron nature of charge carriers, extra absorptions arise starting at a frequency $\ensuremath{\omega}\ensuremath{\gtrsim}J.$ The obtained results are in a good agreement with exact diagonalization studies.
A relaxation-function theory for the dynamic spin susceptibility in the $t\text{\ensuremath{-}}J$ model is presented. By a sum-rule-conserving generalized mean-field approximation (GMFA), the two-spin correlation functions of arbitrary range, the staggered magnetization, the uniform static susceptibility, and the antiferromagnetic correlation length are calculated in a wide region of hole doping and temperatures. A good agreement with available exact diagonalization (ED) data is found. The correlation length is in reasonable agreement with neutron-scattering experiments on ${\text{La}}_{2\ensuremath{-}\ensuremath{\delta}}{\text{Sr}}_{\ensuremath{\delta}}{\text{CuO}}_{4}$. Going beyond the GMFA, the self-energy is calculated in the mode-coupling approximation. The spin dynamics at arbitrary frequencies and wave vectors is studied for various temperatures and hole doping. At low doping a spin-wave-type behavior is found as in the Heisenberg model, while at higher doping a strong damping caused by hole hopping occurs, and a relaxation-type spin dynamics is observed in agreement with the ED results. The local spin susceptibility and its $\ensuremath{\omega}/T$ scaling behavior are calculated in a reasonable agreement with experimental and ED data.
Based on the Hubbard-Hirsch model, we studied the dynamical susceptibility and spin excitation of an itinerant-electron system within the random-phase approximation by using a Green's-function technique. It is shown that the two-center matrix elements in the Hubbard-Hirsch model not only change the dynamic property of the susceptibility, but also widen the gap between two spin subbands, which suppresses the electron-hole single excitations. In contrast, the region of collective excitations of the spin becomes larger. \textcopyright{} 1996 The American Physical Society.
The charge and spin dynamics of the two-dimensional Hubbard model in the paramagnetic phase is first studied by means of the two-pole approximation within the framework of the composite operator method. The fully self-consistent scheme requires: no decoupling, the fulfillment of both Pauli principle and hydrodynamic constraints, the simultaneous solution of fermionic and bosonic sectors, and a very rich momentum dependence of the response functions. The temperature and momentum dependencies, as well as the dependency on the Coulomb repulsion strength and the filling, of the calculated charge and spin susceptibilities and correlation functions are in very good agreement with the numerical calculations present in the literature.
The authors construct a diagram technique for the (t-J) model Hamiltonian expressed in terms of Hubbard operators. This technique combines features of the diagram technique for normal Fermi systems and those for the Heisenberg model with spin operators. The general graphic structure is identified for one-particle Green functions composed of Hubbard operators. The (t-J) model has logical consistency, is reasonably simple and can serve as a working tool in exploring various properties of this model. To an approximation that resides in summing ladder-type diagrams with antiparallel electron lines, the authors calculate the system's magnetic susceptibility. A formula is derived which reflects the dual nature of the magnetic states in the Hubbard model; this duality manifests itself in the presence of a localised and an itinerant contribution in the bare susceptibility. The authors trace how the relative value of the localised contribution varies as the electron concentration is increased from 0 to 1. With n>2/3, the paramagnetic phase of the system becomes unstable with respect to the occurrence of ferromagnetic or antiferromagnetic ordering. A magnetic phase diagram for zero temperature is constructed on the (t/U, n) plane.
Using the description in terms of the Hubbard operators hole and spin Green's functions of the two-dimensional $t\ensuremath{-}J$ model are calculated in an approximation that retains the rotation symmetry of the spin susceptibility in the paramagnetic state and has no predefined magnetic ordering. In this approximation, Green's functions are represented by continued fractions that are interrupted with the help of the decoupling corrected by the constraint of zero site magnetization in the paramagnetic state. Results obtained in this approach for an undoped $32\ifmmode\times\else\texttimes\fi{}32$ lattice (the Heisenberg model) and for one hole in a $4\ifmmode\times\else\texttimes\fi{}4$ lattice are in good agreement with Monte Carlo and exact-diagonalization data, respectively. In the limit of heavy doping the hole spectrum described by the obtained formulas acquires features of the spectrum of weakly correlated excitations.