We report a quantum Monte Carlo study of the phase transition between antiferromagnetic and valence-bond solid ground states in the square-lattice S = 1/2 J – Q model. The critical correlation function of the Q terms gives a scaling dimension corresponding to the value ν = 0.455 ± 0.002 of the correlation-length exponent. This value agrees with previous (less precise) results from conventional methods, e.g., finite-size scaling of the near-critical order parameters. We also study the Q -derivatives of the Binder cumulants of the order parameters for L 2 lattices with L up to 448. The slope grows as L 1/ ν with a value of ν consistent with the scaling dimension of the Q term. There are no indications of runaway flow to a first-order phase transition. The mutually consistent estimates of ν provide compelling support for a continuous deconfined quantum-critical point.
We report a quantum Monte Carlo study of the phase transition between antiferromagnetic and valence-bond solid ground states in the square-lattice S = 1/2 J – Q model. The critical correlation function of the Q terms gives a scaling dimension corresponding to the value ν = 0.455 ± 0.002 of the correlation-length exponent. This value agrees with previous (less precise) results from conventional methods, e.g., finite-size scaling of the near-critical order parameters. We also study the Q -derivatives of the Binder cumulants of the order parameters for L 2 lattices with L up to 448. The slope grows as L 1/ ν with a value of ν consistent with the scaling dimension of the Q term. There are no indications of runaway flow to a first-order phase transition. The mutually consistent estimates of ν provide compelling support for a continuous deconfined quantum-critical point.
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 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 S=1/2 square-lattice J-Q model hosts a deconfined quantum phase transition between antiferromagnetic and dimerized (valence-bond solid) ground states. We here study two deformations of this model-a term projecting staggered singlets, as well as a modulation of the J terms forming alternating "staircases" of strong and weak couplings. The first deformation preserves all lattice symmetries. Using quantum Monte Carlo simulations, we show that it nevertheless introduces a second relevant field, likely by producing topological defects. The second deformation induces helical valence-bond order. Thus, we identify the deconfined quantum critical point as a multicritical Lifshitz point-the end point of the helical phase and also the end point of a line of first-order transitions. The helical-antiferromagnetic transitions form a line of generic deconfined quantum-critical points. These findings extend the scope of deconfined quantum criticality and resolve a previously inconsistent critical-exponent bound from the conformal-bootstrap method.
We investigate the boundary phases of a (2+1)-dimensional quantum critical Heisenberg model with a dangling spin chain. By introducing a multispin Q-term along the boundary, we drive a continuous boundary transition from an antiferromagnetic (AF) order to a valence-bond solid (VBS) order. Using large-scale quantum Monte Carlo simulations, we locate the critical point at Qc=0.310(11), and obtain the critical exponents at Qc, including ys=0.81(4) and the scaling dimensions of AF and VBS order parameters Δs=0.660(15) and Δv=0.204(14). The weak long-range AF order for $Q
Abstract Motivated by recent progress on the experimental realization of proximate deconfined quantum critical point in a frustrated quantum magnet, we study the low-energy spin dynamics of a related checkerboard J-Q model by using quantum Monte Carlo simulations. The ground state of this model undergoes a weakly first-order quantum phase transition with an emergent O(4) symmetry between an antiferromagnetic state and a plaquette valence bond solid. The calculated spin lattice relaxation rate of nuclear magnetic resonance, 1 / T 1 , exhibits distinct low-temperature behaviors depending on the ground states. With decreasing the temperature, 1 / T 1 rises up on the antiferromagnetic side, characterizing a crossover to the renormalized classical regime, whereas 1 / T 1 drops exponentially on the side of valence bond solid, reflecting the gap opening in the plaquette ordered phase. The extracted spin gap scales with the distance to the transition point as a power-law with an exponent φ ≈ 0.3, consistent with the scaling ansatz ϕ = ν z with ν ≈ 0.3 and z = 1. Near the quantum phase transition, the temperature dependent 1 / T 1 shows a broad crossover regime where a universal scaling 1 / T 1 ∼ T η with η ≈ 0.6 is found. Our results suggest a quantum scaling regime associated with the emergent enhanced symmetry near this first-order quantum phase transition.
We study the N\'eel to fourfold columnar valence bond solid (cVBS) quantum phase transition in a sign-free S=1 square-lattice model. This is the same kind of transition that for S=1/2 has been argued to realize the prototypical deconfined critical point. Extensive numerical simulations of the square-lattice S=1/2 N\'eel-VBS transition have found consistency with the deconfined critical point scenario with no direct evidence for first-order behavior. In contrast to the S=1/2 case, in our quantum Monte Carlo simulations for the S=1 model, we present unambiguous evidence for a direct conventional first-order quantum phase transition. Classic signs of a first-order transition demonstrating coexistence including double-peaked histograms and switching behavior are observed. The sharp contrast from the S=1/2 case is remarkable; we hypothesize that this is a striking demonstration of the role of the size of the quantum spin in the phase diagram of two-dimensional lattice models.