Magnetic field induced quantum criticality and the Luttinger sum rule

TL;DR

This paper investigates how a field-induced quantum critical point involving a Fermi surface change affects the Luttinger sum rule, introducing a topological index to distinguish phases.

Contribution

It introduces a generalized Luttinger-Friedel sum rule accounting for Fermi surface transitions at quantum critical points in heavy-fermion systems.

Findings

Additional term in the sum rule changes abruptly at the transition

The sum rule characterizes phases as a topological index

The model explains Fermi surface changes at QCPs

Abstract

We show that when there is a sudden transition from a small to a large Fermi surface at a field-induced quantum critical point, similar to what may have been observed in some heavy-fermion compounds, an additional term has to be taken into account in the Luttinger-Friedel sum rule.We calculate this additional term for a local model which has a field-induced quantum critical point (QCP) and show that it changes abruptly at the transition, such that it satisfies a generalized Luttinger-Friedel sum rule on each side of the transition, and characterizes the two Fermi-liquid phases separated by the QCP as a discrete (topological) index.