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

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.

Effect of biquadratic exchange on the phase diagram of a spin-1 transverse XY model with single-ion anisotropy

“…) where H 0 = J(0) + 17 18 I(0) − 2 3 D. Then, to order of interest for H → 0 we have the required critical line equation…”

“…In particular, it has received recently a great attention for understanding the thermodynamic properties of advanced magnetic materials with general non-collinear magnetic structures as the helimagnetic thin films [7][8][9]. From these investigations, a very rich structure of the phase diagram emerges providing a remarkable tool for understanding the complex magnetic properties of several innovative materials [10][11][12][13][14][15], also involving quantum phase transitions (QPTs) [16][17][18]. The effect of the BQE interactions on the finite temperature phase transitions in systems with XY symmetry, also in presence of a SIA, has received less attention.…”

Devlin-like approach to a spin-1 transverse XY model with biquadratic exchange and single-ion anisotropy

“…In the last decade there has been a renewed interest in investigating the role played by the interplay between quantum fluctuations, bilinear and biquadratic exchange interactions and crystal lattice geometry which is expected to result in a rich variety of quantum phases and exotic phenomena [1][2][3][4][5][6][7] especially when magnetic field induced quantum phase transitions (QPTs) [8][9][10][11] are present. In this context, the effect of competition between biquadratic exchange (BQE) and single-ion anisotropy (SIA) has been explored for quantum anisotropic magnetic models by using different approximate schemes (see, for instance, [12][13][14][15][16]).…”