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Acta Physica Sinica

Flow equations for solving energy spectrum （T≠0）of the t-J model

Wang Hong, Ping Lou, Zhuang Yong-He, 安徽大学物理与材料科学学院，安徽省信息材料与器件重点实验室合肥; (2)中国电子科技集团公司第43研究所,合肥

Published Jan 1, 2005• 0 citations
Publisher

Abstract

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.

DOI
10.7498/aps.54.3764

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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.
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.
We present the numerical solution of the renormalization group (RG) equations derived in Tsai, Castro Neto, Shankar, et al. [Phys. Rev. B to appear], for the problem of superconductivity in the presence of both electron–electron and electron–phonon coupling at zero temperature. We study the instability of a Fermi liquid to a superconductor and the RG flow of the couplings in the presence of retardation effects and the crossover from weak to strong coupling. We show that our numerical results provide an ansatz for the analytic solution to the problem in the asymptotic limits of weak and strong coupling.
We apply the functional renormalization group method to the calculation of dynamical properties of zero-dimensional interacting quantum systems. As case studies we discuss the anharmonic oscillator and the single impurity Anderson model. We truncate the hierarchy of flow equations such that the results are at least correct up to second order perturbation theory in the coupling. For the anharmonic oscillator energies and spectra obtained within two different functional renormalization group schemes are compared to numerically exact results, perturbation theory, and the mean field approximation. Even at large coupling the results obtained using the functional renormalization group agree quite well with the numerical exact solution. The better of the two schemes is used to calculate spectra of the single impurity Anderson model, which then are compared to the results of perturbation theory and the numerical renormalization group. For small to intermediate couplings the functional renormalization group gives results which are close to the ones obtained using the very accurate numerical renormalization group method. In particulare the low-energy scale (Kondo temperature) extracted from the functional renormalization group results shows the expected behavior.
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.
We give a self-contained derivation of the differential equations for Wilson's renormalization group for the one-particle irreducible Green functions in fermionic systems. The application of this equation to the (t,t′)-Hubbard model appears in Ref. [HSFR]. Here we focus on theoretical aspects. After deriving the equations, we discuss the restrictions imposed by symmetries on the effective action. We discuss scaling properties due to the geometry of the Fermi surface and give precise criteria to determine when they justify the use of one-loop flows. We also discuss the relationship of this approach to other RG treatments, as well as aspects of the practical treatment of truncated equations, such as the projection to the Fermi surface and the calculation of susceptibilities.
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