Fermi and non-fermi liquid behavior in quantum impurity systems: Conserving slave boson theory

Abstract

The question of Fermi liquid vs. non-Fermi liquid behavior induced by strong correlations is one of the prominent problems in metallic local moment systems. As standard models for such systems, the SU(N)×SU(M) Anderson impurity models exhibit both Fermi liquid and non-Fermi liquid behavior, depending on their symmetry. Taking the Anderson model as an example, these lectures first give an introduction to the auxiliary boson method to describe correlated systems governed by a strong, short-range electronic repulsion. It is then shown how to include the relevant low-lying excitations (coherent spin flip and charge fluctuation processes), while preserving the local gauge symmetry of the model. This amounts to a conserving T-matrix approximation (CTMA). We prove a cancellation theorem showing that the CTMA incorporates all leading and subleading infrared singularities at any given order in a self-consistent loop expansion of the free energy. As a result, the CTMA recovers the correct infrared behavior of the auxiliary particle propagators, indicating that it correctly describes both the Fermi and the non-Fermi regimes of the Anderson model.

Time-resolved collapse and revival of the Kondo state near a quantum phase transition

“…An infinite onsite repulsion within the Ce 4f orbitals was assumed, enforcing the overall single-electron occupancy of the Ce 4f shell. As the impurity solver of the DMFT, an auxiliary-particle representation of the Ce 4f electron fields was employed within the non-crossing approximation [20,21,32] (NCA), reaching down to base temperatures (before terahertz excitation) of T ≈ 0.1 T * K . The DMFT and NCA were generalized to the nonequilibrium case using the Keldysh technique [33].…”

“…The efficient implementation of the NCA algorithm in Ref. [32] was adapted for solving the DMFT with the multi-orbital NCA out of equilibrium. Data availablity: The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.…”

Kondo Destruction in RKKY-Coupled Kondo Lattice and Multi-Impurity Systems

“…Higher order terms, as for instance generated by the RG [see below, Fig. 1 (b)], lead to nonlocality of the incoming and outgoing coordinates of the scattering c electrons, x j , x j ′ , but the f -spin coordinate x i remains strictly local, since the pseudofermion propagator G f (iν) = 1/iν is local [26]. For this reason, speaking of Kondo singlet formation on a single Kondo site is well defined even in a Kondo lattice, and so is the local susceptibility χ f of a single f spin.…”

Ultrafast molecular dynamics in terahertz-STM experiments: Theoretical analysis using the Anderson-Holstein model

“…The small α ∼ 0.02 shows that the electron excitation in HOMO is weakly dressed by the phonon, and the spectral function is dominated by the pure electron excitation with the phonon in the vacuum state, i.e., n = 0 in Eq. (45). For the larger g = 0.4,ε d is shifted to −0.06 and the onsite interaction is reduced toŨ ∼ 0.71.…”

“…It provides the foundation for our understanding of a broad range of physical phenomena, including the Kondo effect in metals [32,33], the electron transport in mesoscopic structures [34][35][36][37], the formation of heavy-fermion electron systems [38][39][40][41]. A broad range of analytical tools have been developed to study equilibrium properties of this model including a Bethe ansatz solution [42,43], the renormalization group approach [26], the slave-particle method [44,45], and dynamical mean-field theory (DMFT) [46][47][48][49][50]. However, the nonequilibrium dynamics of the model remains poorly understood.…”