We investigate the $S=1/2$ antiferromagnetic Heisenberg model with a $3\ifmmode\times\else\texttimes\fi{}3$ checkerboard lattice structure in a longitudinal magnetic field. By using the stochastic series expansion quantum Monte Carlo method, we obtain the properties of the nonplateau XY phase; 1/9, 3/9, 5/9, and 7/9 magnetization plateau phases; and fully polarized phase. Then, we determine the precise phase transition critical points belonging to the three-dimensional XY universality class through finite-size scaling. Moreover, we study the longitudinal and transverse dynamic spin structure factors of this model in different phases. For the nonplateau XY phase, the energy spectra present a gap between the low-energy gapless branch and the high-energy part due to the competition of magnetic field and interaction. The gapless branch can be described by the spin wave theory of the effective ``block spin'' model in the canted antiferromagnetic phase. In the magnetization plateau phase, we identify that the low-energy excitations arise from the localized disturbances within the sublattice and are capable of spreading in momentum space. The high-energy quasiparticles could be the multiplet excitations similar to the ``triplon'' in the dimerized system and ``doublon'' and ``quarton'' in the trimerized system. This paper offers theoretical insights and interpretations for the characteristics of the ground state and the inelastic neutron scattering spectra in two-dimensional quantum magnetic materials. Specifically, it focuses on materials with odd-spin configurations in the checkerboard unit cells under the influence of a longitudinal magnetic field.
We investigate the S=1/2 antiferromagnetic Heisenberg model with a 3\ifmmode×\else\texttimes\fi3 checkerboard lattice structure in a longitudinal magnetic field. By using the stochastic series expansion quantum Monte Carlo method, we obtain the properties of the nonplateau XY phase; 1/9, 3/9, 5/9, and 7/9 magnetization plateau phases; and fully polarized phase. Then, we determine the precise phase transition critical points belonging to the three-dimensional XY universality class through finite-size scaling. Moreover, we study the longitudinal and transverse dynamic spin structure factors of this model in different phases. For the nonplateau XY phase, the energy spectra present a gap between the low-energy gapless branch and the high-energy part due to the competition of magnetic field and interaction. The gapless branch can be described by the spin wave theory of the effective block spin'' model in the canted antiferromagnetic phase. In the magnetization plateau phase, we identify that the low-energy excitations arise from the localized disturbances within the sublattice and are capable of spreading in momentum space. The high-energy quasiparticles could be the multiplet excitations similar to the triplon'' in the dimerized system and doublon'' and quarton'' in the trimerized system. This paper offers theoretical insights and interpretations for the characteristics of the ground state and the inelastic neutron scattering spectra in two-dimensional quantum magnetic materials. Specifically, it focuses on materials with odd-spin configurations in the checkerboard unit cells under the influence of a longitudinal magnetic field.
We investigate the S=1/2 antiferromagnetic Heisenberg model with a 3$\times$3 checkerboard lattice structure in a longitudinal magnetic field. By using the stochastic series expansion quantum Monte Carlo (SSE-QMC) method, we obtain the properties of the non-plateau XY phase, 1/9, 3/9, 5/9, 7/9 magnetization plateau phases, and fully polarized phase. Then, we determine the precise phase transition critical points belonging to the 3D XY universality class through finite-size scaling. Moreover, we study the longitudinal and transverse dynamic spin structure factors of this model in different phases. For the non-plateau XY phase, the energy spectra present a gap between the low-energy gapless branch and the high-energy part under the competition of magnetic field and interaction. The gapless branch can be described by the spin wave theory in the canted antiferromagnetic phase of the effective "block spin" model. In the magnetization plateau phase, we identify that the excitation arises from localized disturbances within the sublattice, which are capable of spreading in momentum space. This study offers theoretical insights and interpretations for the characteristics of the ground state and the inelastic neutron scattering spectrum in two-dimensional quantum magnetic materials. Specifically, it focuses on materials with a checkerboard unit cell structure and odd-spin configurations under the influence of a longitudinal magnetic field.
Spin excitation spectra of two dimensional S=1/2 Heisenberg model with checkerboard structures.
We study the excitation spectra of two-dimensional spin-1/2 Heisenberg model with checkerboard structures using stochastic analytic continuation of imaginary-time correlation function obtained from quantum Monte Carlo simulation. The checkerboard models have two different antiferromagnetic nearest-neighbor interactions J1 and J2, and the tuning parameter g is defined as J2/J1. The dynamic structure factors are systematically calculated in all phases of the models as well as at the critical points. To give a full understanding of the dynamic spectra, wave theory is employed to explain some features of numerical results, especially for the low-energy part. When g is close to 1, the features of the excitation spectra of each checkerboard model are roughly the same as those of the original square lattice antiferromagnetic Heisenberg model, and the high-energy continuum among them are discussed. In contrast to the other checkerboard structures investigated in this paper, the 3×3 checkerboard model has distinctive excitation features, like a gap between a low-energy gapless branch and a gapped high-energy part exists when g is small. The gapless branch in this case can be regarded as wave in Neˊel order formed by block spin in each 3×3 plaquette with effective exchange interaction originated from renormalization. One finding is that the continuum also appears in this low-energy branch, which may originated from nearly deconfined process in block spin.
We study the spin excitation spectra of the two-dimensional spin-21 Heisenberg model with a checkerboard structure using stochastic analytic continuation of the imaginary-time correlation function obtained from a quantum Monte Carlo simulation. The checkerboard models have two different antiferromagnetic nearest-neighbor interactions J1 and J2, and the tuning parameter g is defined as J2/J1. The dynamic spin structure factors are systematically calculated in all phases of the models as well as at the critical points. To give a full understanding of the dynamic spectra, spin wave theory is employed to explain some features of numerical results, especially for the low-energy part. When g is close to 1, the features of the spin excitation spectra of each checkerboard model are roughly the same as those of the original square lattice antiferromagnetic Heisenberg model, and the high-energy continuum among them is discussed. In contrast to the other checkerboard structures investigated in this paper, the $3\ifmmode\times\else\texttimes\fi{}3$ checkerboard model has distinctive excitation features, such as a gap between a low-energy gapless branch and a gapped high-energy part that exists when g is small. The gapless branch in this case can be regarded as a spin wave in N\'eel order formed by a ``block spin'' in each $3\ifmmode\times\else\texttimes\fi{}3$ plaquette with an effective exchange interaction originating from renormalization. One unexpected finding is that the continuum also appears in this low-energy branch.
We investigate the magnetic excitations of the two-dimensional (2D) S = 1/2 trimerized Heisenberg models with intratrimer interaction J 1 and intertrimer interaction J 2 on four different lattices using a combination of stochastic series expansion quantum Monte Carlo (SSE QMC) and stochastic analytic continuation methods (SAC), complemented by cluster perturbation theory (CPT). These models exhibit quasi-particle-like excitations when g = J 2 / J 1 is weak, characterized by low-energy magnons, intermediate-energy doublons, and high-energy quartons. The low-energy magnons are associated with the magnetic ground states. They can be described by the linear spin wave theory (LSWT) of the effective block spin model and the original spin model. Doublons and quartons emerge from the corresponding internal excitations of the trimers with distinct energy levels, which can be effectively analyzed using perturbative calculation when the ratio of exchange interactions g is weak. In this weak g regime, we observe a clear separation between the magnon and higher-energy spectra. As g increases, doublon and quarton gradually merge into the magnon modes or some continua. Notably, in the Collinear II and trimerized Hexagon lattice, a broad continuum emerges above the single-magnon spectrum, originating from the quasi-1D physics due to the dilute connections between chains. In addition, we also compare our numerical results to the experimental RIXS spectrum and analyze the difference. Our numerical analysis of these 2D trimers yields valuable theoretical predictions and explanations for the inelastic neutron scattering (INS) spectra of 2D magnetic materials featuring trimerized lattices.
We study the S>1/2 antiferromagnetic Heisenberg model on the 1/5-depleted square lattice as a function of the ratio of the intraplaquette coupling to the interplaquette coupling. Using stochastic series expansion quantum Monte Carlo simulations, we numerically identify three quantum phases, including the dimer phase, N\'eel phase, and plaquette valence-bond-solid phase. We also obtain the accurate quantum critical points that belong to the O(3) universality class using the large-scale finite-size scaling. Most importantly, we study the dynamic spin structure factors of different phases, which can be measured by inelastic neutron scattering experiments. The low-energy excitations can be explained as triplons in the dimer phase and plaquette valence-bond-solid phase, while in the N\'eel phase, the more prominent magnon mode can be found as the spin magnitude increases. Furthermore, we find a broader continuum at smaller S, which may be the dynamical signature of nearly deconfined spinon excitations.
We investigate the quantum dynamics of the spins on different Heisenberg antiferromagnetic spin lattice systems. Firstly, we applied the coupled-cluster method to the spin-1/2 antiferromagnetic \emph{XXZ} model on a square lattice by employing an approximation which contains two-body long-range correlations and high-order four-body local correlations. Improvement is found for the ground-state energy, sublattice magnetization, and the critical anisotropy when comparing with the approximation including the two-body correlations alone. We also obtain the full excitation spectrum which is in good agreement with the quantum Monte Carlo results and the high-order spin-wave theory.Secondly, we study the longitudinal excitations of quantum antiferromagnets on a triangular lattice by a recently proposed microscopic many-body approach based on magnon-density waves. We calculate the full longitudinal excitation spectra of the antiferromagnetic Heisenberg model for a general spin quantum number in the isotropic limit. Similar to the square lattice model, we find that, at the center of the first hexagonal Brillouin zone Γ(q=0) and at the magnetic ordering wavevectors ±[Q=(4π/3,0)], the excitation spectra become gapless in the thermodynamic limit, due to the slow, logarithmic divergence of the structure factor. However, these longitudinal modes on two-dimensional models may be considered as quasi-gapped, as any finite-size effect or small anisotropy will induce a large energy gap, when compared with the counterpart of the transverse spin-wave excitations. We have also investigated the excited states of the quasi-one-dimensional quantum antiferromagnets on hexagonal lattices, including the longitudinal modes based on the magnon-density waves. A model Hamiltonian with a uniaxial single-ion anisotropy is first studied by a spin-wave theory based on the one-boson method; the ground state thus obtained is employed for the study of the longitudinal modes. The full energy spectra of both the transverse modes (i.e., magnons) and the longitudinal modes are obtained as functions of the nearest-neighbor coupling and the anisotropy constants. We have found two longitudinal modes due to the non-collinear nature of the triangular antiferromagnetic order, similar to that of the phenomenological field theory approach by Affleck. The excitation energy gaps due to the anisotropy and the energy gaps of the longitudinal modes without anisotropy are then investigated. We then compares our results for the longitudinal energy gaps at the magnetic wavevectors with the experimental results for several antiferromagnetic compounds with both integer and non-integer spin quantum numbers, and we find good agreements after the higher-order contributions are included in our calculations.