Common non-Fermi liquid phases in quantum impurity physics

TL;DR

This paper investigates local quantum phase transitions in impurity models, revealing exact properties of non-Fermi liquid phases, including self-energy structures, sum rules, and critical behaviors, with applications to pseudogap and two-level impurity models.

Contribution

It provides a detailed theoretical analysis of local moment phases and quantum critical points in quantum impurity models, including new sum rules and the role of multiple self-energies.

Findings

Distinct self-energies characterize local moment phases.

Universal magnitude of the Luttinger integral in the LM phase.

Divergence of local susceptibility as the QPT is approached.

Abstract

We study correlated quantum impurity models which undergo a local quantum phase transition (QPT) from a strong coupling, Fermi liquid phase to a non-Fermi liquid phase with a globally doubly degenerate ground state. Our aim is to establish what can be shown exactly about such `local moment' (LM) phases; of which the permanent (zero-field) local magnetization is a hallmark, and an order parameter for the QPT. A description of the zero-field LM phase is shown to require two distinct self-energies, which reflect the broken symmetry nature of the phase and together determine the single self-energy of standard field theory. Distinct Friedel sum rules for each phase are obtained, via a Luttinger theorem embodied in the vanishing of appropriate Luttinger integrals. By contrast, the standard Luttinger integral is non-zero in the LM phase, but found to have universal magnitude. A range of spin susceptibilites are also considered; including that corresponding to the local order parameter, whose exact form is shown to be RPA-like, and to diverge as the QPT is approached. Particular attention is given to the pseudogap Anderson model, including the basic physical picture of the transition, the low-energy behavior of single-particle dynamics, the quantum critical point itself, and the rather subtle effect of an applied local field. A two-level impurity model which undergoes a QPT (`singlet-triplet') to an underscreened LM phase is also considered, for which we derive on general grounds some key results for the zero-bias conductance in both phases.