Strong coupling theory of heavy fermion criticality II

TL;DR

This paper develops a theoretical framework for understanding the critical behavior of three-dimensional heavy fermion metals at quantum critical points, highlighting the role of strong coupling and fixed points in their thermodynamic and dynamical properties.

Contribution

It introduces a strong-coupling fixed point theory for heavy fermion quantum criticality, extending previous weak-coupling approaches and incorporating hyperscaling with fractional exponents.

Findings

Identification of two stable fixed points governing the system

Derivation of hyperscaling behavior with fractional exponents

Application to antiferromagnetic heavy fermion compounds

Abstract

We present a theory of the scaling behavior of the thermodynamic, transport and dynamical properties of a three-dimensional metal governed by $d$-dimensional fluctuations at a quantum critical point, where the electron quasiparticle effective mass diverges. We determine how the critical bosonic order parameter fluctuations are affected by the effective mass divergence. The coupled system of fermions and bosons is found to be governed by two stable fixed points: the conventional weak-coupling fixed point and a new strong-coupling fixed point, provided the boson-boson interaction is irrelevant. The latter fixed point supports hyperscaling, characterized by fractional exponents. The theory is applied to the antiferromagnetic critical point in certain heavy fermion compounds, in which the strong-coupling regime is reached.