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 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.
Abstract Using quantum Monte Carlo, exact diagonalization, and perturbation theory, we study the spectrum of the S = 1/2 antiferromagnetic Heisenberg trimer chain by varying the ratio g = J2/J1 of the intertrimer and intratrimer coupling strengths. The doublet ground states of trimers form effective interacting S = 1/2 degrees of freedom described by a Heisenberg chain. Therefore, the conventional two-spinon continuum of width ∝ J1 when g = 1 evolves into to a similar continuum of width ∝ J2 when g → 0. The intermediate-energy and high-energy modes are termed doublons and quartons which fractionalize with increasing g to form the conventional spinon continuum. In particular, at g ≈ 0.716, the gap between the low-energy spinon branch and the high-energy band with mixed doublons, quartons, and spinons closes. These features should be observable in inelastic neutron scattering experiments if a quasi-one-dimensional quantum magnet with the linear trimer structure and J2 < J1 can be identified. Our results may open a window for exploring the high-energy fractional excitations.
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.
Abstract Motivated by recent advancements in theoretical and experimental studies of the high-energy excitations on an antiferromagnetic trimer chain, we numerically investigate the quantum phase transition and composite dynamics in this system by applying a magnetic field. The numerical methods we used include the exact diagonalization, density matrix renormalization group, time-dependent variational principle, and cluster perturbation theory. From calculating the entanglement entropy, we have revealed the phase diagram which includes the XY-I, 1/3 magnetization plateau, XY-II, and ferromagnetic phases. Both the critical XY-I and XY-II phases are characterized by the conformal field theory with a central charge c ≃ 1. By analyzing the dynamic spin structure factor, we elucidate the distinct features of spin dynamics across different phases. In the regime with weak intertrimer interaction, we identify the intermediate-energy and high-energy modes in the XY-I and 1/3 magnetization plateau phases as internal trimer excitations, corresponding to the propagating of doublons and quartons, respectively. Notably, applying a magnetic field splits the high-energy spectrum into two branches, labeled as the upper quarton and lower quarton. Furthermore, we explore the spin dynamics of a frustrated trimerized model closely related to the quantum magnet Na 2 Cu 3 Ge 4 O 12 . In the end, we extend our discuss on the possibility of the quarton Bose-Einstein condensation in the trimer systems. Our results are expected to be further verified through the inelastic neutron scattering and resonant inelastic X-ray scattering, and also provide valuable insights for exploring high-energy exotic excitations.
We investigate the excitation spectra of a spin-1/2 antiferromagnetic Heisenberg trimer spin chain by employing a combination of numerical and theoretical techniques. Utilizing the Krylov-space correction-vector method in density matrix renormalization group (DMRG), we calculate both the direct and indirect resonant inelastic x-ray scattering (RIXS) spectra for the trimer spin chain. To interpret the observed features in the RIXS spectra, we perform a theoretical perturbative analysis to compute the energy dispersions, which are then utilized to determine the density of states (DOS) for both the single-particle and the two-particle excitation spectra. Our results show that the single-particle continua of the direct RIXS spectrum align with the energy levels observed in the DOS spectra of spinon, doublon, and quarton excitations. Furthermore, the two-particle continua are revealed in the indirect RIXS process, where all possible single-particle excitations combine to form the various two-particle excitations of the trimer spin chain. Based on our calculations, we propose the RIXS mechanism of generating the fractionalized (spinon) and collective (doublon and quarton) excitations in the trimer spin chain at both the L edge and the K edge, including discussing the interplay of these excitations in the RIXS spectrum for various trimer coupling strength. The computed energy range of the excitations suggest the possibility of experimental detection at both the L edge and the K edge within the current capabilities of RIXS instrumentation resolution.
The recent experimental realization of emergent quasi-particles, such as spinons, doublons, and quartons, in a spin-1/2 trimer chain has spurred new interest in low dimensional magnetic systems. In this study, we investigate the dynamical properties of the isotropic spin-1 trimer chain with intra and inter-trimer antiferromagnetic exchange couplings, (J>0 and J′>0), respectively, unveiling various quasi-particles: magnons, singletons, triplons, pentons, and heptons. For weak inter-trimer exchange coupling J′/J≪1, it behaves as an effective spin-1 chain with valence bond solid (VBS) ground state. Employing density matrix renormalization group (DMRG) techniques, we compute the dynamic structure factor (DSF) which reveals a gapped magnon band alongside weakly dispersive singleton, excited triplon, and penton excitations. The evolution of these excitations with inter-trimer coupling J′ is also examined, providing insight into the underlying excitation mechanisms. For spin-1 chain, these exotic quasi-particles eventually reduce to conventional magnon excitations as J′/J→1. Our results shed light on the rich and complex excitation spectrum of spin-1 trimer chains and offer unique perspectives on the dynamics in quantum spin systems.
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.