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We consider models of heavy fermions in the strong coupling or local moment limit and include phonon degrees of freedom on the conduction electrons. Due to the large mass or low coherence temperature of the heavy fermion state, it is shown that such a regime is dominated by vertex corrections which leads to the complete failure of the Migdal theorem. Even at weak electron-phonon couplings, binding of the conduction electrons competes with the Kondo effect and substantially reduces the coherence temperature, ultimately leading to the Kondo breakdown. Those results are obtained using a combination of the slave boson method and Migdal-Eliashberg approximation as well as the dynamical mean-field theory approximation.
Resolving the heavy fermion band in the conduction electron momentum resolved spectral function of the Kondo lattice model is challenging since, in the weak coupling limit, its spectral weight is exponentially small. In this article we consider a com
The spontaneous generation of charge-density-wave order in a Dirac fermion system via the natural mechanism of electron-phonon coupling is studied in the framework of the Holstein model on the honeycomb lattice. Using two independent and unbiased qua
We report the novel pressure(P)-temperature(T) phase diagrams of antiferromagnetism (AF) and superconductivity (SC) in CeRhIn$_5$, CeIn$_3$ and CeCu$_2$Si$_2$ revealed by the NQR measurement. In the itinerant helical magnet CeRhIn$_5$, we found that
One of the challenges in strongly correlated electron systems, is to understand the anomalous electronic behavior that develops at an antiferromagnetic quantum critical point (QCP), a phenomenon that has been extensively studied in heavy fermion mate
We develop a theory for the electronic excitations in UPt$_3$ which is based on the localization of two of the $5f$ electrons. The remaining $f$ electron is delocalized and acquires a large effective mass by inducing intra-atomic excitations of the l