Motivated by the unexpected Monte Carlo results as well as the theoretical proposal of a large correction to scaling for the critical theory of the 2-d staggered-dimer spin-1/2 Heisenberg model on the square lattice, we study the phase transitions induced by dimerization of several dimerized quantum Heisenberg models with spatial anisotropy using first principles Monte Carlo method. Remarkably, while our Monte Carlo data for all the models considered here, including the herringbone- and ladder-dimer models on the square lattice, are compatible with the recently proposed scenario of an enhanced correction to scaling, we find it is likely that the enhanced correction to scaling manifests itself as amplification of the nonuniversal prefactors appeared in the scaling forms. In other words, our data are in consistence with the established numerical values for the critical exponents, including the confluent exponent, in the O(3) universality class. Convincing numerical evidence is provided to support this proposed scenario.
Motivated by the unexpected Monte Carlo results as well as the theoretical proposal of a large correction to scaling for the critical theory of the 2-d staggered-dimer spin-1/2 Heisenberg model on the square lattice, we study the phase transitions induced by dimerization of several dimerized quantum Heisenberg models with spatial anisotropy using first principles Monte Carlo method. Remarkably, while our Monte Carlo data for all the models considered here, including the herringbone- and ladder-dimer models on the square lattice, are compatible with the recently proposed scenario of an enhanced correction to scaling, we find it is likely that the enhanced correction to scaling manifests itself as amplification of the nonuniversal prefactors appeared in the scaling forms. In other words, our data are in consistence with the established numerical values for the critical exponents, including the confluent exponent, in the O(3) universality class. Convincing numerical evidence is provided to support this proposed scenario.
Motivated by the indication of a new critical theory for the spin-1/2 Heisenberg model with a spatially staggered anisotropy on the square lattice, we reinvestigate the phase transition of this model induced by dimerization using first-principle Monte Carlo simulations. We focus on studying the finite-size scaling of ${\ensuremath{\rho}}_{s1}2L$ and ${\ensuremath{\rho}}_{s2}2L$, where L stands for the spatial box size used in the simulations and ${\ensuremath{\rho}}_{si}$, with $i\ensuremath{\in}{1,2}$, is the spin-stiffness in the i-direction. Remarkably, while we observe a large correction to scaling for the observable ${\ensuremath{\rho}}_{s1}2L$, the data for ${\ensuremath{\rho}}_{s2}2L$ exhibit a good scaling behavior without any indication of a large correction. As a consequence, we are able to obtain a numerical value for the critical exponent $\ensuremath{\nu}$, which is consistent with the known O(3) result with moderate computational effort. Further, we additionally carry out an unconventional finite-size scaling analysis with which we assume that the ratio of the spatial winding numbers squared is fixed through all simulations. The theoretical correctness of our idea is argued and its validity is confirmed. Using this unconventional finite-size scaling method, even from ${\ensuremath{\rho}}_{s1}L$, which receives the most serious correction among the observables considered in this study, we are able to arrive at a value for $\ensuremath{\nu}$ consistent with the expected O(3) value. A detailed investigation to compare these two finite-size scaling methods should be performed.
Puzzled by the indication of a new critical theory for the spin-1/2 Heisenberg model with a spatially staggered anisotropy on the square lattice as suggested in \cite{Wenzel08}, we re-investigate the phase transition of this model induced by dimerization using first principle Monte Carlo simulations. We focus on studying the finite-size scaling of ρs1L and ρs2L, where L stands for the spatial box size used in the simulations and ρsi with i∈{1,2} is the spin-stiffness in i-direction. From our Monte Carlo data, we find that ρs2L suffers a much less severe correction compared to that of ρs1L. Therefore ρs2L is a better quantity than ρs1L for finite-size scaling analysis concerning the limitation of the availability of large volumes data in our study. Further, motivated by the so-called cubical regime in magnon chiral perturbation theory, we additionally perform a finite-size scaling analysis on our Monte Carlo data with the assumption that the ratio of spatial winding numbers squared is fixed through all simulations. As a result, the physical shape of the system remains fixed in our calculations. The validity of this new idea is confirmed by studying the phase transition driven by spatial anisotropy for the ladder anisotropic Heisenberg model. With this new strategy, even from ρs1L which receives the most serious correction among the observables considered in this study, we arrive at a value for the critical exponent ν which is consistent with the expected O(3) value by using only up to L=64 data points.
We simulate the spin-1/2 Heisenberg model with a spatially staggered anisotropy using first principles Monte Carlo method. In particular, the critical exponents β/ν and ω associated with the quantum phase transition induced by dimerization are determined with high precision. Here β and ν are the exponents related to the magnetization and the correlation length, respectively. In addition, ω is the confluent exponent. With very accurate data of the relevant observables, we first obtain a value of ω compatible with the known result in the O(3) universality class. Further, using either the value of ω determined here or the established one in the literature, the exponent β/ν calculated from our data is in quantitative agreement with the known result β/ν=0.519(1) as well. Our investigation suggests that the quantum phase transition studied here is fully consistent with the O(3) universality class.
Puzzled by the indication of a new critical theory for the spin-1/2 Heisenberg model with a spatially staggered anisotropy on the square lattice as suggested in \cite{Wenzel08}, we re-investigate the phase transition of this model induced by dimerization. We focus on studying the finite-size scaling of the observables ρs1L and ρs2L, where L stands for the spatial box sizes used in the simulations and ρsi with i∈{1,2} is the spin-stiffness in i-direction. We find by performing finite-size scaling using the observable ρs2L, which corresponds to the spatial direction with a fixed antiferromagnetic coupling, one would suffer a much less severe correction compared to that of using ρs1L. Therefore ρs2L is a better quantity than ρs1L for finite-size scaling analysis concerning the limitation for the availability of large volumes data in our study. Remarkably, by employing the method of fixing the aspect-ratio of spatial winding numbers squared in the simulations, even from ρs1L which receives the most serious correction among the observables considered in this study, we arrive at a value for the critical exponent ν which is consistent with the expected O(3) value by using only up to L=64 data points.
Puzzled by the indication of a new critical theory for the spin-1/2 Heisenberg model with a spatially staggered anisotropy on the square lattice, as suggested in Wenzel (2008 Phys. Rev. Lett. 101 127202), we study a similar anisotropic spin-1/2 Heisenberg model on the honeycomb lattice. The critical point where the phase transition occurs due to the dimerization as well as the critical exponent ν are analyzed in great detail. Remarkably, using most of the available data points in conjunction with the expected finite-size scaling ansatz with a sub-leading correction indeed leads to a consistent ν = 0.691(2) with that calculated in Wenzel (2008 Phys. Rev. Lett. 101 127202). However, by using the data with a large number of spins N , we obtain ν = 0.707(6) which agrees with the most accurate Monte Carlo O(3) value ν = 0.7112(5) as well.
In order to gain a deeper understanding of the quantum criticality in the explicitly staggered dimerized Heisenberg models, we study a generalized staggered dimer model named the J 0 — J 1 — J 2 model, which corresponds to the staggered J — J ′ model on a square lattice and a honeycomb lattice when J 1 / J 0 equals 1 and 0, respectively. Using the quantum Monte Carlo method, we investigate all the quantum critical points of these models with J 1 / J 0 changing from 0 to 1 as a function of coupling ratio α = J 2 / J 0 . We extract all the critical values of the coupling ratio α c for these models, and we also obtain the critical exponents ν, β/ν, and η using different finite-size scaling ansätz,. All these exponents are not consistent with the three-dimensional Heisenberg universality class, indicating some unconventional quantum critical points in these models.