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arXiv:1012.3691 · Physical Review B

Impurity spin texture at the critical point between Néel-ordered and valence-bond-solid states in two-dimensional SU(3) quantum antiferromagnets

Argha Banerjee, Kedar Damle, Fabien Alet

Published Jun 7, 2011• 22 citations
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Abstract

We study the impurity physics at a continuous quantum phase transition from an SU(3) symmetric N\'eel-ordered state to a valence-bond-solid state that breaks lattice symmetries, using quantum Monte Carlo techniques. This continuous transition is expected to be an example of ``deconfined criticality'' in an SU(3) symmetric system. We find that the spin-texture induced by a missing-spin defect at the transition takes on a finite-size scaling form consistent with expectations from standard scaling arguments at a scale-invariant quantum critical point, albeit with significant subleading power-law finite size corrections that we analyze in detail. Together with recently found logarithmic violations of scaling at similar continuous transitions in the SU(2) case, our results provide indirect evidence of the existence of operators that become marginal as $N$ is reduced to $2$ in the field theoretical description of these deconfined critical points.

DOI
10.1103/physrevb.83.235111

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We study the impurity physics at a continuous quantum phase transition from an SU(3) symmetric N'eel-ordered state to a valence-bond-solid state that breaks lattice symmetries, using quantum Monte Carlo techniques. This continuous transition is expected to be an example of ``deconfined criticality'' in an SU(3) symmetric system. We find that the spin-texture induced by a missing-spin defect at the transition takes on a finite-size scaling form consistent with expectations from standard scaling arguments at a scale-invariant quantum critical point, albeit with significant subleading power-law finite size corrections that we analyze in detail. Together with recently found logarithmic violations of scaling at similar continuous transitions in the SU(2) case, our results provide indirect evidence of the existence of operators that become marginal as NNN is reduced to 222 in the field theoretical description of these deconfined critical points.
The spin texture surrounding a nonmagnetic impurity in a quantum antiferromagnet is a sensitive probe of the novel physics of a class of quantum phase transitions between a N\'eel ordered phase and a valence-bond solid phase in square lattice S=1/2S=1/2S=1/2 antiferromagnets. Using a newly developed T=0T=0T=0 quantum Monte Carlo technique, we compute this spin texture at these transitions and find that it does not obey the universal scaling form expected at a scale invariant quantum critical point. We also identify the precise logarithmic form of these scaling violations. Our results are expected to yield important clues regarding the probable theory of these unconventional transitions.
We study a spin-1/2 SU(2) model on the honeycomb lattice with nearest-neighbor antiferromagnetic exchange J that favors Néel order and competing six-spin interactions Q that favor a valence-bond-solid (VBS) state in which the bond energies order at the "columnar" wave vector K=(2π/3,-2π/3). We present quantum Monte Carlo evidence for a direct continuous quantum phase transition between Néel and VBS states, with exponents and logarithmic violations of scaling consistent with those at analogous deconfined critical points on the square lattice. Although this strongly suggests a description in terms of deconfined criticality, the measured threefold anisotropy of the phase of the VBS order parameter shows unusual near-marginal behavior at the critical point.
The antiferromagnetic to valence-bond-solid phase transition in the two-dimensional J-Q model (an S=1/2 Heisenberg model with four-spin interactions) is studied using large-scale quantum Monte Carlo simulations. The results support a continuous transition of the ground state, in agreement with the theory of "deconfined" quantum criticality. There are, however, large corrections to scaling, of logarithmic or very slowly decaying power-law form, which had not been anticipated. This suggests that either the SU(N) symmetric noncompact CP;{N-1} field theory for deconfined quantum criticality has to be revised or that the theory for N=2 (as in the system studied here) differs significantly from N-->infinity (where the field theory is analytically tractable).
Using ground-state projector quantum Monte Carlo simulations in the valence-bond basis, it is demonstrated that nonfrustrating four-spin interactions can destroy the Néel order of the two-dimensional S=1/2 Heisenberg antiferromagnet and drive it into a valence-bond solid (VBS) phase. Results for spin and dimer correlations are consistent with a single continuous transition, and all data exhibit finite-size scaling with a single set of exponents, z=1, nu=0.78+/-0.03, and eta=0.26+/-0.03. The unusually large eta and an emergent U(1) symmetry, detected using VBS order parameter histograms, provide strong evidence for a deconfined quantum critical point.
We use quantum Monte Carlo simulations to study an S = 1/2 spin model with competing multi-spin interactions. We find a quantum phase transition between a columnar valence-bond solid (cVBS) and a Néel antiferromagnet (AFM), as in the scenario of deconfined quantum-critical points, as well as a transition between the AFM and a staggered valence-bond solid (sVBS). By continuously varying a parameter, the sVBS–AFM and AFM–cVBS boundaries merge into a direct sVBS–cVBS transition. Unlike previous models with putative deconfined AFM–cVBS transitions, e.g., the standard J–Q model, in our extended J–Q model with competing cVBS and sVBS inducing terms the transition can be tuned from continuous to first-order. We find the expected emergent U(1) symmetry of the microscopically Z 4 symmetric cVBS order parameter when the transition is continuous. In contrast, when the transition changes to first-order, the clock-like Z 4 fluctuations are absent and there is no emergent higher symmetry. We argue that the confined spinons in the sVBS phase are fracton-like. We also present results for an SU(3) symmetric model with a similar phase diagram. The new family of models can serve as a useful tool for further investigating open questions related to deconfined quantum criticality and its associated emergent symmetries.
We describe the spin distribution in the vicinity of a nonmagnetic impurity in a two-dimensional antiferromagnet undergoing a transition from a magnetically ordered N\'eel state to a paramagnet with a spin gap. The quantum critical ground state in a finite system has total spin S=1∕2S=1∕2S=1∕2 (if the system without the impurity had an even number of S=1∕2S=1∕2S=1∕2 spins), and recent numerical studies in a double layer antiferromagnet [K. H. H\"oglund et al., Phys. Rev. Lett. 98, 087203 (2007)] have shown that the spin has a universal spatial form delocalized across the entire sample. We present the field theory describing the uniform and staggered magnetizations in this spin texture for two classes of antiferromagnets: (i) the transition from a N\'eel state to a paramagnet with local spin singlets, in models with an even number of S=1∕2S=1∕2S=1∕2 spins per unit cell, which are described by a O(3) Landau-Ginzburg-Wilson field theory; and (ii) the transition from a N\'eel state to a valence bond solid, in antiferromagnets with a single S=1∕2S=1∕2S=1∕2 spin per unit cell, which are described by a ``deconfined'' field theory of spinons.