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.
We study the transition between N\'eel and columnar valence-bond solid ordering in two-dimensional
S=3/2 square lattice quantum antiferromagnets with SO(3) symmetry. According to the deconfined criticality scenario, this transition can be direct and continuous like the well-studied
S=1/2 case. To study the global phase diagram, we work with four multi-spin couplings with full rotational symmetry, that are free of the sign-problem of quantum Monte Carlo. Exploring the phase diagram with quantum Monte Carlo simulations, we find that the phase transition between N\'eel and valence-bond solid is strongly first-order in the parts of the phase diagram that we have accessed.
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.
We use quantum Monte Carlo simulations to study an S = 1/2 spin model with competing multi-spin interactions. We find a quantum phase transition between a columnar valence-bond solid (cVBS) and a Néel antiferromagnet (AFM), as in the scenario of deconfined quantum-critical points, as well as a transition between the AFM and a staggered valence-bond solid (sVBS). By continuously varying a parameter, the sVBS–AFM and AFM–cVBS boundaries merge into a direct sVBS–cVBS transition. Unlike previous models with putative deconfined AFM–cVBS transitions, e.g., the standard J–Q model, in our extended J–Q model with competing cVBS and sVBS inducing terms the transition can be tuned from continuous to first-order. We find the expected emergent U(1) symmetry of the microscopically Z 4 symmetric cVBS order parameter when the transition is continuous. In contrast, when the transition changes to first-order, the clock-like Z 4 fluctuations are absent and there is no emergent higher symmetry. We argue that the confined spinons in the sVBS phase are fracton-like. We also present results for an SU(3) symmetric model with a similar phase diagram. The new family of models can serve as a useful tool for further investigating open questions related to deconfined quantum criticality and its associated emergent symmetries.
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).
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.