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.
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.
Antiferromagnetism (AFM) such as Néel ordering is often closely related to Coulomb interactions such as Hubbard repulsion in two-dimensional (2D) systems. Whether Néel AFM ordering in two dimensions can be dominantly induced by electron-phonon couplings (EPC) has not been completely understood. Here, by employing numerically exact sign-problem-free quantum Monte Carlo (QMC) simulations, we show that bond Su-Schrieffer-Heeger (SSH) phonons with frequency ω and EPC constant λ can induce AFM ordering for a wide range of phonon frequency ω>ω_{c}. For ω<ω_{c}, a valence-bond-solid (VBS) order appears and there is a direct quantum phase transition between VBS and AFM phases at ω_{c}. The phonon mechanism of the AFM ordering is related to the fact that SSH phonons directly couple to electron hopping whose second-order process can induce an effective AFM spin exchange. Our results shall shed new light on understanding AFM ordering in correlated quantum materials.
Electron-phonon coupling is typically not associated with magnetic order but with either charge density waves (patterns of high and low electron density) or valence-bond solids (patterns of strong and weak electronic bonds). Using quantum Monte Carlo simulations, the authors demonstrate that, within the paradigmatic two-dimensional Su-Schrieffer-Heeger model, the electron-phonon interaction favors antiferromagnetic order in large regions of the phase diagram. A valence-bond solid is observed in the adiabatic regime, while the two phases are connected by an apparently direct phase transition.
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.