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arXiv:1010.1937 · Physical Review B

Quantum criticality in SU(3) and SU(4) antiferromagnets

Ribhu K. Kaul

Published Aug 2, 2011• 52 citations
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Abstract

We study the quantum phase transition out of the N\'eel state in SU(3) and SU(4) generalizations of the Heisenberg antiferromagnet with a sign-problem-free four-spin coupling (so-called $JQ$ model), by extensive quantum Monte Carlo simulations. We present evidence that the SU(3) and SU(4) order parameters and the SU(3) and SU(4) stiffness go to zero continuously without any evidence of a first-order transition. However, we find considerable deviations from simple scaling laws for the stiffness even in the largest system sizes studied. We interpret these as arising from multiplicative scaling terms in these quantities that affect the leading behavior, i.e., they will persist in the thermodynamic limit, unlike the conventional additive corrections from irrelevant operators. We conjecture that these multiplicative terms arise from dangerously irrelevant operators whose contributions to the quantities of interest are nonanalytic.

DOI
10.1103/physrevb.84.054407

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We study the quantum phase transition out of the N'eel state in SU(3) and SU(4) generalizations of the Heisenberg antiferromagnet with a sign-problem-free four-spin coupling (so-called JQJQJQ model), by extensive quantum Monte Carlo simulations. We present evidence that the SU(3) and SU(4) order parameters and the SU(3) and SU(4) stiffness go to zero continuously without any evidence of a first-order transition. However, we find considerable deviations from simple scaling laws for the stiffness even in the largest system sizes studied. We interpret these as arising from multiplicative scaling terms in these quantities that affect the leading behavior, i.e., they will persist in the thermodynamic limit, unlike the conventional additive corrections from irrelevant operators. We conjecture that these multiplicative terms arise from dangerously irrelevant operators whose contributions to the quantities of interest are nonanalytic.
We present results of extensive quantum Monte Carlo simulations of the three-dimensional S=1/2S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2S=1/2 Heisenberg antiferromagnet. Finite-size scaling of the spin stiffness and the sublattice magnetization gives the critical temperature ${T}_{\mathrm{c}}/J\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.946\ifmmode\pm\else\textpm\fi{}0.001$. The critical behavior is consistent with the classical 3D Heisenberg universality class, as expected. We discuss the general nature of the transition from quantum mechanical to classical (thermal) order parameter fluctuations at a continuous Tc>0{T}_{\mathrm{c}}>0Tc​>0 phase transition.
Square-lattice J-Q models provide a sign-problem-free setting for probing the quantum phase transition between Néel antiferromagnet and columnar valence-bond solid. We analyze this transition through the scaling of Lee--Yang zeros, computed within stochastic series expansion quantum Monte Carlo by reweighting configurations sampled near criticality in the presence of complex source fields. Benchmark studies of the dimerized Heisenberg model and the checkerboard J-Q model validate the method, yielding stable O(3)\mathrm{O}(3)O(3) critical scaling in the former and clear spacetime-volume scaling in the latter, as expected for a first-order transition. Applying the same analysis to the J-Q models, we find a pronounced and systematic drift of the leading-zero scaling with increasing system size, consistent with an extended pseudocritical regime. The Lee--Yang scaling implies an effective scaling dimension ΔϕΔ_ϕΔϕ​ of the SO(5)\mathrm{SO}(5)SO(5) order-parameter field that decreases with size and is consistent with vanishing in the thermodynamic limit. Such behavior lies below the scalar unitarity bound of any unitary relativistic conformal field theory in 2+12{+}12+1 dimensions and enforces inverse spacetime-volume scaling of the zeros, the hallmark of a first-order transition. These results support a weakly first-order interpretation of the Néel--VBS transition and establish the finite-size Lee--Yang zeros as a sensitive, symmetry-resolved diagnostic of pseudocriticality and transition order in the J-Q family.
To examine the validity of the scenario of the deconfined critical phenomena, we carry out a quantum Monte Carlo simulation for the SU(NNN) generalization of the Heisenberg model with four-body and six-body interactions. The quantum phase transition between the SU(NNN) N\'eel and valence-bond solid phases is characterized for N=2N=2N=2, 3, and 4 on the square and honeycomb lattices. While finite-size scaling analysis works well up to the maximum lattice size (L=256L=256L=256) and indicates the continuous nature of the phase transition, a clear systematic change towards the first-order transition is observed in the estimates of the critical exponent $y\ensuremath{\equiv}1/\ensuremath{\nu}$ as the system size increases. We also confirm the relevance of a squared valence-bond solid field ${\ensuremath{\Psi}}^{2}$ for the SU(3) model.
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