Phase diagram, energy scales and nonlocal correlations in the Anderson lattice model

TL;DR

This paper investigates the Anderson lattice model using DMFT and CDMFT to understand heavy fermion materials, revealing a single energy scale and the significance of inter-site correlations near quantum critical points.

Contribution

It compares single-site and cluster DMFT approaches, highlighting the role of nonlocal correlations in the phase diagram and magnetic properties of heavy fermion systems.

Findings

Existence of a single energy scale $T^*$ similar to Kondo temperature

Narrower antiferromagnetic region in CDMFT compared to DMFT

Nonlocal correlations are small above $T_N$ but significant below it

Abstract

We study the Anderson lattice model with one f-orbital per lattice site as the simplest model which describes generic features of heavy fermion materials. The resistivity and magnetic susceptibility results obtained within dynamical mean field theory (DMFT) for a nearly half-filled conduction band show the existence of a single energy scale $T^*$ which is similar to the single ion Kondo temperature $T_K^o$. To determine the importance of inter-site correlations, we have also solved the model within cellular DMFT (CDMFT) with two sites in a unit cell. The antiferromagnetic region on the phase diagram is much narrower than in the single-site solution, having a smaller critical hybridization $V_c$ and N\'eel temperature $T_N$. At temperatures above $T_N$ the nonlocal correlations are small, and the DMFT paramagnetic solution is in this case practically exact, which justifies the ab initio LDA+DMFT approach in theoretical studies of heavy fermions. Strong inter-site correlations in the CDMFT solution for $T<T_N$, however, indicate that they have to be properly treated in order to unravel the physical properties near the quantum critical point.