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arXiv:cond-mat/0502327 · Physical Review B

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

Martin Hasenbusch B, Andrea Pelissetto C, Ettore Vicari

Published Jul 21, 2005• 28 citations
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Abstract

We study the nature of the multicritical point in the three-dimensional $\mathrm{O}(3)\ensuremath{\bigoplus}\mathrm{O}(2)$ 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 SO(5) theory of high-${T}_{c}$ 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 $\mathrm{O}(3)\ensuremath{\bigoplus}\mathrm{O}(2)$ 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 ${\ensuremath{\phi}}_{4,4}=0.180(15)$, in substantial agreement with recent field-theoretical results. This estimate is much larger than the one-loop $ϵ$-expansion estimate ${\ensuremath{\phi}}_{4,4}=1∕26$, which has often been used in the literature to discuss the multicritical behavior within 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-${T}_{c}$ cuprates should belong to this class---the multicritical point corresponds to a first-order transition.

DOI
10.1103/physrevb.72.014532

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We study the nature of the multicritical point in the three-dimensional O(3)\ensuremath⨁O(2)\mathrm{O}(3)\ensuremath{\bigoplus}\mathrm{O}(2)O(3)\ensuremath⨁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 SO(5) theory of high-Tc{T}_{c}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 O(3)\ensuremath⨁O(2)\mathrm{O}(3)\ensuremath{\bigoplus}\mathrm{O}(2)O(3)\ensuremath⨁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 \ensuremathϕ4,4=0.180(15){\ensuremath{\phi}}_{4,4}=0.180(15)\ensuremathϕ4,4​=0.180(15), in substantial agreement with recent field-theoretical results. This estimate is much larger than the one-loop ϵϵϵ-expansion estimate \ensuremathϕ4,4=1∕26{\ensuremath{\phi}}_{4,4}=1∕26\ensuremathϕ4,4​=1∕26, which has often been used in the literature to discuss the multicritical behavior within 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{T}_{c}Tc​ cuprates should belong to this class---the multicritical point corresponds to a first-order transition.
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The multicritical point at which both a 3-component and a 2-component order parameters order simultaneously in 3 dimensions is shown to have the critical behavior of the decoupled fixed point, with separate n=3 and n=2 behavior. This contradicts both the extrapolation of the epsilon-expansion at leading order, which yields the biconical point, and recent Monte Carlo simulations, which gave isotropic SO(5) behavior. Thus, this tetracritical point carries no information on the relevance of the so-called SO(5) theory of high-T superconductivity.
We discuss several examples of three-dimensional critical phenomena that can be described by Landau–Ginzburg–Wilson ϕ4 theories. We present an overview of field-theoretical results obtained from the analysis of high-order perturbative series in the frameworks of the ∊ and of the fixed-dimension d=3 expansions. In particular, we discuss the stability of the O (N)-symmetric fixed point in a generic N-component theory, the critical behaviors of randomly dilute Ising-like systems and frustrated spin systems with noncollinear order, and the multicritical behavior arising from the competition of two distinct types of ordering with symmetry O (n1) and O (n2) respectively.
We resolve the nature of the quantum phase transition between antiferromagnetic and valence-bond solid ground states in square-lattice spin-1/2 magnets - the putative deconfined quantum-critical point. Using quantum Monte Carlo simulations of J-Q models, in which Heisenberg exchange J competes with multi-spin interactions Qn formed by n singlet projectors, we demonstrate first-order discontinuities increasing with n. For n=2 and n=3, the first-order signatures are very weak and we extract universal scaling dimensions of a proximate multicritical point. Their values coincide closely with known bounds for an SO(5) symmetric conformal field theory (CFT) containing a relevant SO(5) singlet operator that destabilizes the generic deconfined critical point. We characterize the emergent SO(5) symmetry by its scaling dimensions of the leading irrelevant perturbations. Using the J-Q2-Q6 model, we tune the transition from weak to stronger first-order and find scaling of the coexisting order parameters with a large exponent beta ~ 0.85, in agreement with the relevant scaling dimensions of the multicritical point. The exponent that had previously been identified with the correlation length does not have a corresponding CFT level, and we explain it as pseudo-critical length scale of bubbles of one phase inside the other that are compressed in size by an SO(5)-violating irrelevant repulsive interaction between the two order parameters. The bubble scale reflects a hierarchy of excitation gaps generated by the SO(5) perturbation in the neighborhood of the first-order transition, akin to a Higgs mechanism. We argue that the multicritical point is the tip of a gapless spin liquid phase in frustrated Heisenberg models into which the J-Q models can be deformed, but the spin liquid, and perhaps the multicritical point itself, exist outside the regime amenable to sign-free simulations.
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