Two Scenarios of the Quantum Critical Point

TL;DR

This paper compares two scenarios of quantum critical points, highlighting flaws in the standard view and exploring a topological alternative involving bifurcation points in Fermi liquids.

Contribution

It introduces and analyzes a topological scenario of the QCP, contrasting it with the standard phase transition approach, and applies it to 3D Fermi liquids.

Findings

Standard QCP scenario has conceptual flaws.

Topological scenario involves bifurcation points in the Fermi surface.

Application to 3D Fermi liquids with attractive interactions.

Abstract

Two different scenarios of the quantum critical point (QCP), a zero-temperature instability of the Landau state, related to the divergence of the effective mass, are investigated. Flaws of the standard scenario of the QCP, where this divergence is attributed to the occurrence of some second-order phase transition, are demonstrated. Salient features of a different {\it topological} scenario of the QCP, associated with the emergence of bifurcation points in equation $\epsilon(p)=\mu$ that ordinarily determines the Fermi momentum, are analyzed. The topological scenario of the QCP is applied to three-dimensional (3D) Fermi liquids with an attractive current-current interaction.