Instability of the O(5) multicritical behavior in the SO(5) theory of high-Tc superconductors

TL;DR

This study investigates the stability of the O(5) fixed point in the Landau-Ginzburg-Wilson theory relevant for high-Tc superconductors, concluding that the multicritical point is not characterized by O(5) symmetry and is likely first-order.

Contribution

The paper provides Monte Carlo and field-theoretical evidence that the O(5) fixed point is unstable, challenging the assumption of symmetry enlargement at the multicritical point in high-Tc superconductor models.

Findings

O(5) fixed point is unstable due to spin-4 perturbation

Multicritical point likely corresponds to a first-order transition

Field-theoretical analysis supports Monte Carlo results

Abstract

We study the nature of the multicritical point in the three-dimensional O(3)+O(2) symmetric Landau-Ginzburg-Wilson theory, which describes the competition of two order parameters that are O(3) and O(2) symmetric, respectively. This study is relevant for the SO(5) theory of high-Tc superconductors, which predicts the existence of a multicritical point in the temperature-doping phase diagram, where the antiferromagnetic and superconducting transition lines meet. We investigate whether the O(3)+O(2) symmetry gets effectively enlarged to O(5) approaching the multicritical point. For this purpose, we study the stability of the O(5) fixed point. By means of a Monte Carlo simulation, we show that the O(5) fixed point is unstable with respect to the spin-4 quartic perturbation with the crossover exponent $\phi_{4,4}=0.180(15)$, in substantial agreement with recent field-theoretical results. This estimate is much larger than the one-loop $\epsilon$-expansion estimate $\phi_{4,4}=1/26$, which has often been used in the literature to discuss the multicritical behavior within the SO(5) theory. Therefore, no symmetry enlargement is generically expected at the multicritical transition. We also perform a five-loop field-theoretical analysis of the renormalization-group flow. It shows that bicritical systems are not in the attraction domain of the stable decoupled fixed point. Thus, in these systems--high-Tc cuprates should belong to this class--the multicritical point corresponds to a first-order transition.