Breakdown of the periodic potential ansatz in correlated electron systems

TL;DR

This paper examines the limitations of the periodic potential assumption in electronic structure theory for correlated systems, highlighting how ion zero-point motion affects quasiparticle descriptions and proposing a unified approach for heavy-fermion quantum criticality.

Contribution

It challenges the traditional periodic potential assumption and introduces a framework that accounts for ion zero-point motion effects in correlated electron systems.

Findings

Periodic potential assumption breaks down in correlated systems.

Ion zero-point motion leads to a broad distribution of local Kondo scales.

A unified description of heavy-fermion systems at quantum critical points is proposed.

Abstract

Our electronic structure theory for crystalline solids is commonly built on the periodic potential assumption $V(\mathbf r)=V(\mathbf r+\mathbf R)$ for every lattice translation $\mathbf R$, enabling Bloch eigenstates, crystal momentum as a good quantum number, and the standard quasiparticle-based description of the behavior of metals. Because the zero-point motion of the ions, however, in correlated electron systems the electronic environment experienced by an itinerant electron is neither static nor self-averaging at the single-particle level, even in perfectly stoichiometric crystals, leading to a distribution of local Kondo scales that spans two orders of magnitude in temperature. We discuss, through a comparison between uniform scenarios and one that breaks with perfect lattice translational symmetry, how incorporating this distribution yields a unified description for all heavy-fermion systems at the quantum critical point.