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Acta Physica Sinica

Flow equations for solving elementary excitation energy spectrum of the t-J model

Hong Wang, Ping Lou, Zhuang Yong-He, (1)安徽大学物理系,合肥 230039; (2)中国电子科技集团公司第43研究所,合肥 230022

Published Jan 1, 2004• 1 citation
Publisher

Abstract

The t-J model is one of the most important models that is often used to study the theory of the effect of strong electron correlations and high-Tc superconductivity. In this article, the method of renormalization group is used to investigate the t-J model and the elementary excitation energy spectrum of the t-J model is obtained by using the flow equations. Using the symmetry of functions, we can solve the specific expression of the energy spectrum. The result is compared with the result of Green's function method.

DOI
10.7498/aps.53.577

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The t-J model is one of the most important models that is often used to study the theory of the effect of strong electron correlations and high-Tc superconductivity. In this article, the method of renormalization group is used to investigate the t-J model and the elementary excitation energy spectrum of the t-J model is obtained by using the flow equations. Using the symmetry of functions, we can solve the specific expression of the energy spectrum. The result is compared with the result of Green's function method.
The t_J model is one of the most important models that is often used to stud y the theory of the effect of strong electron correlations and high_Tc superconductivity. In this article, the method of renormalization group is use d to investigate the t_J model， and the elementary excitation energy spectra of t_J model (Ｔ≠０) are obtained by the flow equations. The result is compared with that of Green's function method and agrees with its result. At th e same time, the result of renormalization group method is the analytical soluti on while that of Green’s function method is the numerical solution.
A microscopic theory of electronic spectrum and superconducting pairing within the Hubbard model is formulated.The Dyson equation for the normal and anomalous Green functions in terms of the Hubbard operators is derived by applying the Mori-type projection technique.The self-energy is evaluated in the noncrossing approximation for electron scattering on spin and charge fluctuations induced by kinematic interaction for Hubbard operators.Numerical results for electron dispersion in the strong correlation limit are presented.Superconducting pairing mediated by antiferromagnetic exchange and spin fluctuations is discussed.
Superconductivity in the t-J model is studied by extending the recently introduced extremely correlated fermi liquid theory. Exact equations for the Greens functions are obtained by generalizing Gor’kov’s equations to include extremely strong local repulsion between electrons of opposite spin. These equations are expanded in a parameter λ representing the fraction of double occupancy, and the lowest order equations are further simplified near Tc, resulting in an approximate integral equation for the superconducting gap. The condition for Tc is studied using a model spectral function embodying a reduced quasiparticle weight Z near half-filling, yielding an approximate analytical formula for Tc. This formula is evaluated using parameters representative of single layer High-Tc systems. In a narrow range of electron densities that is necessarily separated from the Mott–Hubbard insulator at half filling, we find a typical Tc ∼ 102 K.
A general theory of superconductivity is formulated within the thermodynamic Green function method for vari-ous types of pairing mediated by phonons, spin fluctuations, and strong Coulomb correlations in the Hubbard and t-J models. A rigorous Dyson equation for matrix Green functions is derived in terms of a self-energy as a many-particle Green function. By applying the noncrossing approximation for the self-energy, a closed self-consistent system of equations is obtained, similar to the conventional Eliashberg equations. A brief discus-sion of superconductivity mediated by kinematic interaction with an estimation of a superconducting transition temperature in the Hubbard model is given. Key words: Green functions, theory of superconductivity, strong electron correlations PACS: 74.20.-z, 74.20.Mn, 74.72.-h
The feasibility of a perturbation expansion for Green's functions of the t-J model directly in terms of X-operators is demonstrated using the Baym-Kadanoff functional method. As an application we derive explicit expressions for the kernel of the linearized equation for the superconducting order parameter in leading order of a 1/N expansion. The linearized equation is solved numerically on a square lattice taking instantaneous and retarded contributions into account. Classifying the order parameter according to irreducible representations of the point group C4v of the square lattice and according to even or odd parity in frequency we find that a reasonably strong instability occurs only for even frequency pairing with d-wavelike symmetry. The corresponding transition temperature Tc is where t is the nearest-neighbor hopping integral. The underlying effective interaction consists of an attractive, instantaneous term and a retarded term due to charge and spin fluctuations. The latter is weakly attractive at low frequencies below ,strongly repulsive up to and attractive towards even higher energies. Tc increases with decreasing doping until a d-wavelike bond-order wave instability is encountered near optimal doping at for J=0.3. Tc is essentially linear in J and rather insensitive to an additional second-nearest neighbor hopping integral t'. A rather striking property of Tc is that it is hardly affected by the soft mode associated with the bond-order wave instability or by the Van Hove singularity in the case with second-nearest neighbor hopping. This unique feature reflects the fact that the solution of the gap equation involves momenta far away from the Fermi surface (due to the instantaneous term) and many frequencies (due to the retarded term) so that singular properties in momentum or frequency are averaged out very effectively.