Charge fluctuations and electron-phonon interaction in the finite-UHubbard model

Abstract

In this paper we employ a gaussian expansion within the finite-U slave-bosons formalism to investigate the momentum structure of the electron-phonon vertex function in the Hubbard model as function of U and n. The suppression of large momentum scattering and the onset a small-q peak structure, parametrized by a cut-off qc, are shown to be essentially ruled by the band narrowing factor ZMF due to the electronic correlation. A phase diagram of ZMF and qc in the whole U -n space is presented. Our results are in more than qualitative agreement with a recent numerical analysis and permit to understand some anomalous features of the Quantum Monte Carlo data.PACS numbers: 71.10. Fd,71.27.+a,71.45.Lr In the past months a variety of experiments have pointed out an important role of the electron-phonon (el-ph) interaction in many physical properties of the cuprates. 1,2,3 These recent findings have triggered a renewed interest for a theoretical understanding of the elph properties in strongly correlated systems.One of the most remarkable effects of the strong electronic correlation on the el-ph properties is a to favor forward (small q) scattering in the electron-phonon vertex, q being the exchanged phonon momentum. This feature was investigated in the past by means of analytical techniques based on slave-bosons or X-operators. 4,5,6,7 The assumption of forward scattering predominance within an el-ph framework was shown to explain in a natural way several anomalous properties of cuprates as the difference between transport and superconducting el-ph coupling constants, 6 the linear temperature behaviour of the resistivity, 8 the d-wave symmetry of the superconducting gap. 7,9 Small q scattering selection was shown moreover to be responsible in a natural way for high-T c superconductivity within the context of the nonadiabatic superconductivity. 10 So far, this important feature was analyzed only by means of analytical approaches in the U = ∞ limit and a definitive confirm of it based on numerical methods was lacking. The charge response at finite U was addressed in Refs. 11,12, which however focused only on q = 0 susceptibilities. With these motivations in a recent paper Huang et al have addressed this issue in the twodimensional Hubbard model with generic U by using Quantum Monte Carlo (QMC) techniques on a 8×8 cluster. 13 Their results provide a good agreement with the previous analytical studies and represent an important contribution to assess the relevance of el-ph interaction in correlated system.In this paper we employ the slave-boson techniques to investigate the evaluation of the momentum structure of the el-ph vertex interaction as function of the Hubbard repulsion U . While the previous analytical studies were limited to the U = ∞ limit, 4,5,6,7 we were able in this way to evaluate the small momenta selection in the whole phase diagram of parameters U -n, where n is the electron filling. In particular we show that the predominance of small q scattering is strongly dependent on the closeness of the system to t...

Renormalization of the electron-phonon coupling in the one-band Hubbard model

“…For high temperatures the boundaries of the phase-separated state were determined in the T-U plane for different dopings and the increase of the static vertex ⌫ near the boundaries was studied, confirming and extending recent results of Ref. 17. At low temperatures and moderate or small dopings we found that ⌫ does not exhibit pronounced forward scattering behavior and that ⌫ reduces dramatically the electron-phonon coupling.…”

“…This has also been pointed out in Ref. 17. Calculating the phase diagram, we find a very peculiar reentrant behavior around the phase separated region for finite U as shown in Fig.…”

Forward scattering peak in the electron–phonon interaction and impurity scattering of cuprate superconductors

“…The latter effect is more pronounced at lower doping. The similar (to Monte Carlo) results were obtained quite recently in [15] in the framework of the Rückenstein-Kotliar (four slave-boson) model. These numerical results prove the correctness of the FSP theory of the EPI, which are based on the X-method.…”

“…This fundamental result allows us to resolve a number of experimental puzzles, which can not be explained by the old Migdal-Eliashberg theory based on the momentum independent (isotropic) EPI. The most important predictions of the FSP theory which includes the EPI and other charge We stress the following two facts coming from the theoretical analysis: (i) the forward scattering peak in the EPI of strongly correlated systems is a general phenomenon by affecting electronic coupling to all phonons; (ii) the existence of the forward scattering peak in the EPI is confirmed numerically by the Monte Carlo calculations for the Hubbard-Holstein model with finite U [14], by exact diagonalization [65], as well as by some approximative theoretical methods [15].…”

Electron-Phonon Interaction and Strong Correlations in High-Temperature Superconductors: One can not avoid the unavoidable

“…We stress the following two facts coming from the theoretical analysis: (i) the forward scattering peak in the EPI of strongly correlated systems is a general phenomenon by affecting electronic coupling to all phonons; (ii) the existence of the forward scattering peak in the EPI is confirmed numerically by the Monte Carlo calculations for the Hubbard-Holstein model with finite U [21], by exact diagonalization [124], as well as by some other methods [22].…”