Quantum tricriticality in transverse Ising-like systems

TL;DR

This paper investigates the quantum tricritical behavior of transverse Ising-like systems using renormalization group methods, revealing phase diagrams, shift exponents, and crossover phenomena near quantum tricritical points.

Contribution

It provides a detailed phase diagram and critical exponents for quantum tricriticality in d-dimensional transverse Ising-like systems, highlighting new crossover behavior.

Findings

Phase diagram with critical lines and tricritical points for 3<d<4

Identified a new quantum tricritical shift exponent =1/2(d-1)

Quantum tricritical region dominated by mean-field critical exponents

Abstract

The quantum tricriticality of d-dimensional transverse Ising-like systems is studied by means of a perturbative renormalization group approach focusing on static susceptibility. This allows us to obtain the phase diagram for 3<d<4, with a clear location of the critical lines ending in the conventional quantum critical points and in the quantum tricritical one, and of the tricritical line for temperature T \geq 0. We determine also the critical and the tricritical shift exponents close to the corresponding ground state instabilities. Remarkably, we find a tricritical shift exponent identical to that found in the conventional quantum criticality and, by approaching the quantum tricritical point increasing the non-thermal control parameter r, a crossover of the quantum critical shift exponents from the conventional value \phi = 1/(d-1) to the new one \phi = 1/2(d-1). Besides, the projection in the (r,T)-plane of the phase boundary ending in the quantum tricritical point and crossovers in the quantum tricritical region appear quite similar to those found close to an usual quantum critical point. Another feature of experimental interest is that the amplitude of the Wilsonian classical critical region around this peculiar critical line is sensibly smaller than that expected in the quantum critical scenario. This suggests that the quantum tricriticality is essentially governed by mean-field critical exponents, renormalized by the shift exponent \phi = 1/2(d-1) in the quantum tricritical region.