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arXiv:0805.4334

Search for Deconfined Criticality: SU(2) Déjà Vu

Anatoly B. Kuklov, Munehisa Matsumoto, Nikolay V. Prokof'ev, Boris V. Svistunov, Matthias Troyer

Published May 28, 2008• 0 citations
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Abstract

Monte Carlo simulations of the SU(2)-symmetric deconfined critical point action reveal strong violations of scale invariance for the deconfinement transition. We find compelling evidence that the generic runaway renormalization flow of the gauge coupling is to a weak first order transition, similar to the case of U(1)$\times$U(1) symmetry. Our results imply that recent numeric studies of the Nèel antiferromagnet to valence bond solid quantum phase transition in SU(2)-symmetric models were not accurate enough in determining the nature of the transition.

DOI
10.48550/arxiv.0805.4334

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Monte Carlo simulations of the SU(2)-symmetric deconfined critical point action reveal strong violations of scale invariance for the deconfinement transition. We find compelling evidence that the generic runaway renormalization flow of the gauge coupling is to a weak first order transition, similar to the case of U(1)×\times×U(1) symmetry. Our results imply that recent numeric studies of the Nèel antiferromagnet to valence bond solid quantum phase transition in SU(2)-symmetric models were not accurate enough in determining the nature of the transition.
Monte Carlo simulations of the SU(2)-symmetric deconfined critical point action reveal strong violations of scale invariance for the deconfinement transition. We find compelling evidence that the generic runaway renormalization flow of the gauge coupling is to a weak first-order transition, similar to the case of U(1) x U(1) symmetry. Our results imply that recent numeric studies of the Nèel antiferromagnet to valence bond solid quantum phase transition in SU(2)-symmetric models were not accurate enough in determining the nature of the transition.
The theory for the vanishing of N\'eel order in the spin S=1/2S=1/2S=1/2 square lattice antiferromagnet has been the focus of attention for many decades. A consensus appears to have emerged in recent numerical studies on the antiferromagnet with first and second neighbor exchange interactions (the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model): A gapless spin liquid is present for a narrow window of parameters between the vanishing of the N\'eel order and the onset of a gapped valence bond solid state. We propose a deconfined critical SU(2) gauge theory for a transition into a stable Z2{\mathbb{Z}}_{2}Z2​ spin liquid with massless Dirac spinon excitations; on the other side of the critical point, the SU(2) spin liquid (the `$\ensuremath{\pi}$-flux' phase) is presumed to be unstable to confinement to the N\'eel phase. We identify a dangerously irrelevant coupling in the critical SU(2) gauge theory, which contributes a logarithm-squared renormalization. This critical theory is also not Lorentz invariant and weakly breaks the SO(5) symmetry which rotates between the N\'eel and valence bond solid order parameters. We also propose a distinct deconfined critical U(1) gauge theory for a transition into the same gapless Z2{\mathbb{Z}}_{2}Z2​ spin liquid; on the other side of the critical point, the U(1) spin liquid (the `staggered flux' phase) is presumed to be unstable to confinement to the valence bond solid. This critical theory has no dangerously irrelevant coupling, dynamic critical exponent $z\ensuremath{\ne}1$, and no SO(5) symmetry. All of these phases and critical points are unified in a SU(2) gauge theory with Higgs fields and fermionic spinons which can naturally realize the observed sequence of phases with increasing J2/J1{J}_{2}/{J}_{1}J2​/J1​: N\'eel, gapless Z2{\mathbb{Z}}_{2}Z2​ spin liquid, and valence bond solid.
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.
We introduce an SU(N) symmetric two-dimensional quantum spin model, the X-Q model, which hosts a ground state transition between Néel antiferromagnetic and spontaneously dimerized states. The Q terms are products of two adjacent singlet projectors on nearest-neighbor sites, as in the often studied J-Q model (where J is the Heisenberg exchange), while the X terms are products of two permutation operators on second-neighbor sites. Quantum Monte Carlo simulations reveal close proximity to a deconfined quantum critical point for N=2, as in the J-Q model. However, for N>2 the transition becomes strongly first order, contrary to conventional expectations that increasing N should weaken discontinuities. We attribute this behavior to the inability of the X term to induce U(1) fluctuations of the dimer pattern, while those from the Q term are suppressed by 1/N. These results provide insights into the interactions that support deconfined criticality.
Abstract Berry phase interference arguments that underlie the theory of deconfined quantum criticality (DQC) for S = 1 / 2 antiferromagnets have also been invoked to allow for continuous transitions in S = 1 magnets including a Néel to (columnar) valence bond solid (cVBS) transition. We provide a microscopic model realization of this transition on the square lattice consisting of Heisenberg exchange ( J H ) and biquadratic exchange ( J B ) that favor a Néel phase, and a designed Q -term ( Q B ) interaction which favors a cVBS through large-scale quantum Monte Carlo (QMC) simulations. For J H = 0 , this model is equivalent to the SU(3) JQ model with a Néel-cVBS transition that has been argued to be DQC through QMC. Upon turning on J H which brings down the symmetry to SU(2), we find multiple signatures—a single critical point, high quality collapse of correlation ratios and order parameters, ‘U(1)-symmetric’ cVBS histograms and lack of double-peak in order parameter histograms for largest sizes studied near the critical point—that are highly suggestive of a continuous transition scenario. However, Binder analysis finds negative dips that grow sub-extensively that we interpret as these transitions rather being pseudocritical. This, along with recent results on spin- 1 2 models, suggests that deconfined pseudocriticality is the more generic scenario.
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.