Quantum Chemistry, Anomalous Dimensions, and the Breakdown of Fermi Liquid Theory in Strongly Correlated Systems

TL;DR

This paper develops a local quantum chemistry framework to understand strongly correlated systems, revealing different fixed points including Fermi liquids and incoherent metallic states through renormalization group analysis.

Contribution

It introduces a novel local picture using atomic configurations and RG charges to classify fixed points in strongly correlated metals, including incoherent states.

Findings

Identification of three fixed points: Fermi liquid, and two incoherent metallic states.

Use of quantum chemistry estimates to determine the stability of these fixed points.

Description of the transition mechanisms between different metallic phases.

Abstract

We formulate a local picture of strongly correlated systems as a Feynman sum over atomic configurations. The hopping amplitudes between these atomic configurations are identified as the renormalization group charges, which describe the local physics at different energy scales. For a metallic system away from half-filling, the fixed point local Hamiltonian is a generalized Anderson impurity model in the mixed valence regime. There are three types of fixed points: a coherent Fermi liquid (FL) and two classes of self-similar (scale invariant) phases which we denote incoherent metallic states (IMS). When the transitions between the atomic configurations proceed coherently at low energies, the system is a Fermi liquid. Incoherent transitions between the low energy atomic configurations characterize the incoherent metallic states. The initial conditions for the renormalization group flow are determined by the physics at rather high energy scales. This is the domain of local quantum chemistry. We use simple quantum chemistry estimates to specify the basin of attraction of the IMS fixed points.