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.
Abstract Berry phase interference arguments that underlie the theory of deconfined quantum criticality (DQC) for S = 1 / 2 antiferromagnets have also been invoked to allow for continuous transitions in S = 1 magnets including a Néel to (columnar) valence bond solid (cVBS) transition. We provide a microscopic model realization of this transition on the square lattice consisting of Heisenberg exchange ( J H ) and biquadratic exchange ( J B ) that favor a Néel phase, and a designed Q -term ( Q B ) interaction which favors a cVBS through large-scale quantum Monte Carlo (QMC) simulations. For J H = 0 , this model is equivalent to the SU(3) JQ model with a Néel-cVBS transition that has been argued to be DQC through QMC. Upon turning on J H which brings down the symmetry to SU(2), we find multiple signatures—a single critical point, high quality collapse of correlation ratios and order parameters, ‘U(1)-symmetric’ cVBS histograms and lack of double-peak in order parameter histograms for largest sizes studied near the critical point—that are highly suggestive of a continuous transition scenario. However, Binder analysis finds negative dips that grow sub-extensively that we interpret as these transitions rather being pseudocritical. This, along with recent results on spin- 1 2 models, suggests that deconfined pseudocriticality is the more generic scenario.
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 study the N\'eel to four-fold columnar valence bond solid quantum phase transition in a sign free
S=1 square lattice model. From quantum Monte Carlo simulations, we find evidence for a new kind of direct transition between these ordered phases. Even though both competing order parameters are {\em finite} at the transition, it does not fit into the standard first order picture with its concomitant hysteresis and double peaked histograms. Instead the transition features diverging length scales and an emergent O(5) rotational symmetry between N\'eel and VBS order parameters. We argue that this striking behavior results crucially from a topological term that must be included in a field theoretic description of this system and is hence beyond a Landau order parameter analysis.
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 use stochastic series expansion (SSE) quantum Monte Carlo (QMC) methods to study the phases and transitions displayed by a class of sign-free designer Hamiltonians for
SU(N) analogs of spin
S=1 quantum antiferromagnets on the square lattice. The
SU(N) spins are generators of the single-row two-column representation (complex conjugate of single-row two-column representation) on
A (
B) sublattices of the square lattice, and the Hamiltonian is designed to explore the competition between the nearest-neighbor antiferromagnetic exchange couplings
J and four-spin interactions
Q that favor a plaquette-ordered valence bond solid (p-VBS) ground state. We find that this state is indeed established at large
Q/J for all
N>3. For $3<N\ensuremath{\le}9$, the ground state exhibits a direct first-order quantum phase transition from a small-
Q/J N\'eel ordered antiferromagnetic state to this large-
Q/J p-VBS state. The ground state at
Q/J=0 for $N\ensuremath{\ge}10$ has been previously reported to be a valence bond nematic state, dubbed the Haldane nematic in recent literature. For small nonzero
Q/J and $N\ensuremath{\ge}10$, we additionally find an unusual intermediate state in which the four-site plaquette energy has a Bragg peak at wave vector $(\ensuremath{\pi},\ensuremath{\pi})$ with no accompanying Bragg peaks at wave vectors $(\ensuremath{\pi},0)$ and $(0,\ensuremath{\pi})$. This $(\ensuremath{\pi},\ensuremath{\pi})$ state also appears to be metastable at
Q/J=0, as evidenced by low-temperature histograms of the Haldane nematic and $(\ensuremath{\pi},\ensuremath{\pi})$ order parameters. Deep in the p-VBS phase of the ground state phase diagram, we find the temperature-driven melting of the p-VBS order is in the Ashkin-Teller universality class. In this regime, we identify an interesting signature of Ashkin-Teller criticality in four-site plaquette singlet correlations at wave vector $(\ensuremath{\pi},\ensuremath{\pi})$; this is in addition to the expected critical fluctuations of the conventional p-VBS order parameter at wave vectors $(\ensuremath{\pi},0)$ and $(0,\ensuremath{\pi})$.