We show numerically that the "deconfined" quantum critical point between the Néel antiferromagnet and the columnar valence-bond solid, for a square lattice of spin 1/2, has an emergent SO(5) symmetry. This symmetry allows the Néel vector and the valence-bond solid order parameter to be rotated into each other. It is a remarkable (2+1)-dimensional analogue of the SO(4)=[SU(2)×SU(2)]/Z(2) symmetry that appears in the scaling limit for the spin-1/2 Heisenberg chain. The emergent SO(5) symmetry is strong evidence that the phase transition in the (2+1)-dimensional system is truly continuous, despite the violations of finite-size scaling observed previously in this problem. It also implies surprising relations between correlation functions at the transition. The symmetry enhancement is expected to apply generally to the critical two-component Abelian Higgs model (noncompact CP(1) model). The result indicates that in three dimensions there is an SO(5)-symmetric conformal field theory that has no relevant singlet operators, so is radically different from conventional Wilson-Fisher-type conformal field theories.
We show numerically that the "deconfined" quantum critical point between the Néel antiferromagnet and the columnar valence-bond solid, for a square lattice of spin 1/2, has an emergent SO(5) symmetry. This symmetry allows the Néel vector and the valence-bond solid order parameter to be rotated into each other. It is a remarkable (2+1)-dimensional analogue of the SO(4)=[SU(2)×SU(2)]/Z(2) symmetry that appears in the scaling limit for the spin-1/2 Heisenberg chain. The emergent SO(5) symmetry is strong evidence that the phase transition in the (2+1)-dimensional system is truly continuous, despite the violations of finite-size scaling observed previously in this problem. It also implies surprising relations between correlation functions at the transition. The symmetry enhancement is expected to apply generally to the critical two-component Abelian Higgs model (noncompact CP(1) model). The result indicates that in three dimensions there is an SO(5)-symmetric conformal field theory that has no relevant singlet operators, so is radically different from conventional Wilson-Fisher-type conformal field theories.
We introduce a quantum spin-1/2 model with many-body correlated Heisenberg-type interactions on the two-dimensional square lattice, designed so that the system can host a fourfold degenerate plaquette valencebond solid (PVBS) ground state that spontaneously breaks Z 4 symmetry.The system is sign-problem free and amenable to large-scale quantum Monte Carlo simulations, thus allowing us to carry out a detailed study of the quantum phase transition between the standard Néel antiferromagnetic (AFM) and PVBS states.We find a first-order transition, in contrast to previously studied continuous transitions from the AFM phase into a columnar valence-bond solid (CVBS) phase.The theory of deconfined quantum criticality predicts generic continuous AFM-CVBS and AFM-PVBS transitions, and, in one version of the theory, the two critical order parameters transform under SO(5) symmetry.Emergent SO(5) symmetry has indeed been observed in studies of the AFM-CVBS transition, and here we show that the first-order AFM-PVBS transition also exhibits SO(5) symmetry at the transition point.Such unexpected symmetry of the coexistence state, which implies a lack of energy barriers between the coexisting phases, has recently been observed at other first-order transitions, but the case presented here is the first example with SO(5) symmetry.The extended symmetry may indicate that the transition is connected to a deconfined critical point.We also discuss the first-order transition in the context of a recent proposal of spinons with fracton properties in the PVBS state, concluding that the fracton scenario is unlikely.Furthermore, we discover a novel type of eightfold degenerate VBS phase, arising when the PVBS state breaks a remaining Z 2 symmetry.This second phase transition, which is continuous, implies that the PVBS phase can be regarded as an intermediate "vestigial" phase, a concept recently introduced to describe multistage phase transitions involving a continuous symmetry.Here we construct a six-dimensional order parameter and also introduce a general graph-theoretic approach to describe the two-stage discrete symmetry breaking.We discuss different ways of breaking the symmetries in one or two stages at zero and finite temperatures.In the latter case, we observe fluctuation-induced first-order transitions, which are hallmarks of vestigial phase transitions.We also mention possible connections of the AFM-PVBS transition to the SO(5) theory of high-T c superconductivity.
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.
The classical cubic-lattice dimer model undergoes an unconventional transition between a columnar crystal and a dimer liquid, in the same universality class as the deconfined quantum critical point in spin-1/2 antiferromagnets but with very different microscopic physics and microscopic symmetries. Using Monte Carlo simulations, we show that this transition has emergent SO(5) symmetry relating quantities characterizing the two phases. While the low-temperature phase has a conventional order parameter, the defining property of the Coulomb liquid on the high-temperature side is deconfinement of monomers, and so SO(5) relates fundamentally different types of objects. Studying linear system sizes up to L=96, we find that this symmetry applies with an excellent precision, consistently improving with system size over this range. It is remarkable that SO(5) emerges in a system as basic as the cubic dimer model, with only simple discrete degrees of freedom. Our results are important evidence for the generality of the SO(5) symmetry that has been proposed for the noncompact CP^{1} field theory. We describe an interpretation for these results in terms of a consistent hypothesis for the renormalization-group flow structure, allowing for the possibility that SO(5) may ultimately be a near-symmetry rather than exact.
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 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.
Spectroscopic evidences for the spontaneous symmetry breaking at the SO(5) deconfined critical point of J-Q3 model
Recent numerical and theoretical studies on the two-dimensional J-Q3 model suggests that the deconfined quantum critical point is actually a SO(5)-symmetry-enhanced first-order phase transition that is spontaneously broken to O(4). However, this conclusion has mainly relied on finite-size scaling of the entanglement entropy, lacking direct evidence from physical observables.} Here, we investigate the dynamical spectra of spin and bond operators at the deconfined critical point of the J-Q3 model using large-scale quantum Monte Carlo simulations, and contrasting them with the well-established O(3) Wilson-Fisher criticality in the J1-J2 Heisenberg model. Although both models exhibit two gapless magnon modes in the Néel phase, their critical behaviors diverge strikingly. At the J1-J2 critical point, the Higgs mode becomes gapless, yielding three gapless modes that reflect the full restoration of the O(3) symmetry. {In the J-Q3 model, we instead observe four gapless transverse modes at the either side of the transition. This spectral feature, together with the entanglement entropy results, provides direct evidence for the weakly first-order scenario that the deconfined quantum critical point exhibits an emergent SO(5) symmetry that spontaneously breaks to O(4).