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.
We discuss zero‐temperature phase transititions from an antiferromagnetic ground state into a valence‐bond‐solid (VBS) in two different square‐lattice quantum spin models. In one limit these models reduce to the standard S = 1/2 XY and Heisenberg models, respectively, which have long‐range antiferromagnetic order at T = 0. Introducing particular types of four‐spin interactions, amenable to quantum Monte Carlo (QMC) simulation without negative‐sign problems, drives phase transitions into VBS states with broken Z4 symmetry. It has recently been argued that continuous quantum phase transitions of this nature represent a new class of deconfined quantum‐critical points [Senthil et al., Science 303, 1490 (2004)], which are not captured within the standard Ginzburg‐Landau framework of phase transitions. Here we discuss a QMC study aimed at accurately characterizing the transition in the XY model. We find some evidence that the transition is actually weakly first‐order, but other scenarios, such as a continuous transition violating hyperscaling, also cannot be completely ruled out. For the Heisenberg model with four‐spin interactions we have confirmed that a VBS state exists. Preliminary finite‐size scaling results show consistency with a continuous transition into the Néel state, with dynamic exponent z = 1. This model is thus a candidate for deconfined quantum criticality.
Using ground-state projector quantum Monte Carlo simulations in the valence-bond basis, it is demonstrated that nonfrustrating four-spin interactions can destroy the Néel order of the two-dimensional S=1/2 Heisenberg antiferromagnet and drive it into a valence-bond solid (VBS) phase. Results for spin and dimer correlations are consistent with a single continuous transition, and all data exhibit finite-size scaling with a single set of exponents, z=1, nu=0.78+/-0.03, and eta=0.26+/-0.03. The unusually large eta and an emergent U(1) symmetry, detected using VBS order parameter histograms, provide strong evidence for a deconfined quantum critical point.
We investigate thermal phase transitions to a valence-bond solid phase in
SU(N) Heisenberg models with four- or six-body interactions on a square or honeycomb lattice, respectively. In both cases, a thermal phase transition occurs that is accompanied by rotational symmetry breaking of the lattice. We perform quantum Monte Carlo calculations in order to clarify the critical properties of the models. The estimated critical exponents indicate that the universality classes of the square- and honeycomb-lattice cases are identical to those of the classical
XY model with a
Z4 symmetry-breaking field and the three-state Potts model, respectively. In the square-lattice case, the thermal exponent, $\ensuremath{\nu}$, monotonically increases as the system approaches the quantum critical point, while the values of the critical exponents, $\ensuremath{\eta}$ and $\ensuremath{\gamma}/\ensuremath{\nu}$, remain constant. From a finite-size scaling analysis, we find that the system exhibits weak universality, because the
Z4 symmetry-breaking field is always marginal. In contrast, $\ensuremath{\nu}$ in the honeycomb-lattice case exhibits a constant value, even in the vicinity of the quantum critical point, because the
Z3 field remains relevant in the SU(3) and SU(4) cases.
We study the
S=1/2 Heisenberg (
J) model on the two-dimensional (2D) square lattice in the presence of additional higher-order spin interactions (
Q) which lead to a valence-bond-solid (VBS) ground state. Using quantum Monte Carlo simulations, we analyze the thermal VBS transition. We find continuously varying exponents, with the correlation-length exponent $\ensuremath{\nu}$ close to the Ising value for large
Q/J and diverging when
Q/J approaches the quantum-critical point (the critical temperature ${T}_{c}\ensuremath{\rightarrow}0$). We identify the transition with a class of conformal field theories with charge
c=1 and critical exponents varying between those of the 2D Ising model and the Kosterlitz-Thouless (KT) fixed point. We find explicit evidence for KT physics by studying the emergence of
U(1) symmetry of the order parameter at
T=Tc when ${T}_{c}\ensuremath{\rightarrow}0$.
A new efficient scheme for the finite-size-scaling study of ground-state phase transitions in quantum spin systems is proposed on the basis of the quantum Monte Carlo method. That is, Trotter numbers and simulated temperatures are scaled in accordance with system sizes, and only one simulation is required for each system size. The transition point is estimated independently of the critical exponents using the non-equilibrium relaxation of the order parameter in a very large system. This scheme is confirmed by the estimation of the critical phenomenon of the one-dimensional S =1/2 asymmetric XY model.