Unified static renormalization-group treatment of finite-temperature crossovers close to a quantum critical point

TL;DR

This paper presents a unified RG approach to analyze low-temperature properties near quantum critical points, revealing a richer phase diagram and linking static results to dynamical critical behavior.

Contribution

It introduces a nonconventional RG method that systematically studies quantum criticality and uncovers new crossover phenomena beyond traditional approaches.

Findings

Reveals additional crossovers in the phase diagram.

Links static RG results to dynamical critical exponents.

Shows agreement with known quantum critical scenarios.

Abstract

A nonconventional renormalization-group (RG) treatment close to and below four dimensions is used to explore, in a unified and systematic way, the low-temperature properties of a wide class of systems in the influence domain of their quantum critical point. The approach consists in a preliminary averaging over quantum degrees of freedom and a successive employment of the Wilsonian RG transformation to treat the resulting effective classical Ginzburg-Landau free energy functional. This allows us to perform a detailed study of criticality of the quantum systems under study. The emergent physics agrees, in many aspects, with the known quantum critical scenario. However, a richer structure of the phase diagram appears with additional crossovers which are not captured by the traditional RG studies. In addition, in spite of the intrinsically static nature of our theory, predictions about the dynamical critical exponent, which parametrizes the link between statics and dynamics close to a continuous phase transition, are consistently derived from our static results.