Unconventional quantum critical points in the generalized quantum dimer models

T. A. Zaleski, T. K. Kopeć

Rui Zheng, Bang‐Gui Liu

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.

Stefan Weßel, S. C. Wenzel

G. J. Sreejith, Stephen Powell

We study critical behavior in the classical cubic dimer model (CDM) in the presence of a finite density of monomers. With attractive interactions between parallel dimers, the monomer-free CDM exhibits an unconventional transition from a Coulomb phase to a dimer crystal. Monomers act as charges (or monopoles) in the Coulomb phase and, at nonzero density, lead to a standard Landau-type transition. We use large-scale Monte Carlo simulations to study the system in the neighborhood of the critical point, and find results in agreement with detailed predictions of scaling theory. Going beyond previous studies of the transition in the absence of monomers, we explicitly confirm the distinction between conventional and unconventional criticality, and quantitatively demonstrate the crossover between the two. Our results also provide additional evidence for the theoretical claim that the transition in the CDM belongs in the same universality class as the deconfined quantum critical point in the $\mathrm{SU}(2)$ JQ model.

K. S. Raman, Eduardo Fradkin, Roderich Moessner +2 more

S. C. Wenzel, L. Bogacz, Wolfhard Janke E

The two-dimensional $J\mathrm{\text{\ensuremath{-}}}{J}^{\ensuremath{'}}$ dimerized quantum Heisenberg model is studied on the square lattice by means of (stochastic series expansion) quantum Monte Carlo simulations as a function of the coupling ratio $\ensuremath{\alpha}={J}^{\ensuremath{'}}/J$. The critical point of the order-disorder quantum phase transition in the $J\mathrm{\text{\ensuremath{-}}}{J}^{\ensuremath{'}}$ model is determined as ${\ensuremath{\alpha}}_{c}=2.5196(2)$ by finite-size scaling for up to approximately 10 000 quantum spins. By comparing six dimerized models we show, contrary to the current belief, that the critical exponents of the $J\mathrm{\text{\ensuremath{-}}}{J}^{\ensuremath{'}}$ model are not in agreement with the three-dimensional classical Heisenberg universality class. This lends support to the notion of nontrivial critical excitations at the quantum critical point.