We discuss ground-state projector simulations of a modified two-dimensional
S=1/2 Heisenberg model in the valence bonds basis. Tuning matrix elements corresponding to the diagonal and off-diagonal terms in the quantum dimer model, we show that there is a quantum phase transition from the antiferromagnet into a columnar valence-bond solid (VBS). There are no signs of discontinuities, suggesting a continuous or very weak first-order transition. The
Z4-symmetric VBS order parameter exhibits an emergent U(1) symmetry as the phase transition is approached. We extract the associated length-scale governing the $\text{U}(1)\ensuremath{-}{\text{Z}}_{4}$ cross-over inside the VBS phase.
We consider the
S=1/2 Heisenberg model with nearest-neighbor interaction
J and an additional multispin interaction
Q3 on the square lattice. The
Q3 term consists of three bond-singlet projectors and is chosen to favor the formation of a valence-bond solid (VBS) where the valence bonds (singlet pairs) form a staggered pattern. The model exhibits a quantum phase transition from the N\'eel state to the VBS as a function of
Q3/J. We study the model using quantum Monte Carlo (stochastic series expansion) simulations. The N\'eel-VBS transition in this case is strongly first order in nature, in contrast to similar previously studied models with continuous transitions into columnar VBS states. The qualitatively different transitions illustrate the important role of an emerging
U(1) symmetry in the latter case, which is not possible in the present model due to the staggered VBS pattern (which does not allow local fluctuations necessary to rotate the local VBS order parameter).
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 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 a loop–cluster algorithm we investigate the spin- Heisenberg antiferromagnet on a square lattice with exchange coupling J and an additional four-spin interaction of strength Q . We confirm the existence of a phase transition separating antiferromagnetism at J / Q > J c / Q from a valence bond solid (VBS) state at J / Q < J c / Q . Although our Monte Carlo data are consistent with those of previous studies, we do not confirm the existence of a deconfined quantum critical point. Instead, using a flowgram method on lattices as large as 80 2 , we find evidence for a weak first-order phase transition. We also present a detailed study of the antiferromagnetic phase. For J / Q > J c / Q the staggered magnetization, the spin stiffness and the spinwave velocity of the antiferromagnet are determined by fitting Monte Carlo data to analytic results from the systematic low-energy effective field theory for magnons. Finally, we also investigate the physics of the VBS state at J / Q < J c / Q and we show that long but finite antiferromagnetic correlations are still present.
We use quantum Monte Carlo methods to study the ground-state phase diagram of a
S=1/2 honeycomb lattice magnet in which a nearest-neighbor antiferromagnetic exchange
J (favoring N\'eel order) competes with two different multispin interaction terms: a six-spin interaction
Q3 that favors columnar valence-bond solid (VBS) order, and a four-spin interaction
Q2 that favors staggered VBS order. For ${Q}_{3}\ensuremath{\sim}{Q}_{2}\ensuremath{\gg}J$, we establish that the competition between the two different VBS orders stabilizes N\'eel order in a large swath of the phase diagram even when
J is the smallest energy scale in the Hamiltonian. When ${Q}_{3}\ensuremath{\gg}({Q}_{2},J)$ $\mathrm{[}{Q}_{2}\ensuremath{\gg}({Q}_{3},J)\text{]}$, this model exhibits at zero temperature phase transition from the N\'eel state to a columnar (staggered) VBS state. We establish that the N\'eel-columnar VBS transition is continuous for all values of
Q2, and that critical properties along the entire phase boundary are well characterized by critical exponents and amplitudes of the noncompact
CP1 (NCCP1) theory of deconfined criticality, similar to what is observed on a square lattice. However, a surprising threefold anisotropy of the phase of the VBS order parameter at criticality, whose presence was recently noted at the
Q2=0 deconfined critical point, is seen to persist all along this phase boundary. We use a classical analogy to explore this by studying the critical point of a three-dimensional
XY model with a fourfold anisotropy field which is known to be weakly irrelevant at the three-dimensional
XY critical point. In this case, we again find that the critical anisotropy appears to saturate to a nonzero value over the range of sizes accessible to our simulations.