Interplay of single-particle and collective degrees of freedom near the quantum critical point

TL;DR

This paper compares two theories for quantum critical points in strongly interacting Fermi systems, favoring a topological Fermi surface change over critical fluctuations to explain experimental non-Fermi-liquid behavior.

Contribution

It demonstrates that the conventional fluctuation-based scenario conflicts with conservation laws, proposing a topological Fermi surface change as a better explanation for QCP phenomena.

Findings

Conventional fluctuation scenario is incompatible with conservation laws.

Topological Fermi surface change explains experimental non-Fermi-liquid behavior.

Combining topology with quantum phase transition theory offers a comprehensive framework.

Abstract

Competing scenarios for quantum critical points (QCPs) of strongly interacting Fermi systems signaled by a divergent density of states at zero temperature are contrasted. The conventional scenario, which enlists critical fluctuations of a collective mode and attributes the divergence to a coincident vanishing of the quasiparticle strength $z$, is shown to be incompatible with identities arising from conservation laws prevailing in the fermionic medium. An alternative scenario, in which the topology of the Fermi surface is altered at the QCP, is found to explain the non-Fermi-liquid thermodynamic behavior observed experimentally in Yb-based compounds close to the QCP. It is suggested that combination of the topological scenario with the theory of quantum phase transitions will provide a proper foundation for analysis of the extended QCP region.