Numerical renormalization-group approach to fluctuation exchange in the presence of electron-phonon coupling: Pairing in the Holstein-Hubbard model

Article

关键词: HIGH-TEMPERATURE SUPERCONDUCTIVITY;    ANTIFERROMAGNETIC FERMI-LIQUID;    SELF-CONSISTENT-FIELD;    3-BAND CUO2 MODEL;    CONSERVING APPROXIMATIONS;    COULOMB REPULSION;    ELIASHBERG THEORY;    OPTICAL-SPECTRUM;    QUASI-PARTICLE;    COPPER OXIDES;   

DOI  :  10.1103/PhysRevB.60.1283

来源: SCIE

【 摘 要 】

The fluctuation exchange (FLEX) approximation is applied to study the Holstein-Hubbard model. Due to the retarded nature of the phonon-mediated electron-electron interaction, neither fast Fourier transform nor previously developed numerical renormalization-group (NRG) methods for Hubbard-type purely electronic models are applicable, while brute force solutions are limited by the demands on computational time and storage which increase rapidly at low temperature T. Here, we describe a NRG technique to solve the FLEX equations efficiently. Several orders of magnitude of CPU time and storage can be saved at low T (similar to 80 K). To test our approach, we compare our NRG results to brute force calculations-on small lattices at elevated temperatures. Both s-wave and d-wave superconducting phase diagrams are then obtained by applying the NRG approach at low T. The isotope effect for s-wave pairing is BCS-like in a realistic phonon frequency range, but vanishes at unphysically large phonon frequency (similar to bandwidth). For d-wave pairing, the isotope exponent is negative and small compared to the typical observed values in nonoptimally doped cuprates. [S0163-1829(99)11325-0].

【 授权许可】

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