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.
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.
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 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 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.
Abstract Understanding exotic forms of magnetism in quantum spin systems is an emergent topic of modern condensed matter physics. Quantum dynamics can be described by particle-like carriers of information, known-as quasiparticles that appear from the collective behaviour of the underlying system. Spinon excitations, governing the excitations of quantum spin-systems, have been accurately calculated and precisely verified experimentally for the antiferromagnetic chain model. However, identification and characterization of novel quasiparticles emerging from the topological excitations of the spin system having periodic exchange interactions are yet to be obtained. Here, we report the identification of emergent composite excitations of the novel quasiparticles doublons and quartons in spin-1/2 trimer-chain antiferromagnet Na2Cu3Ge4O12 (having periodic intrachain exchange interactions J1-J1-J2) and its topologically protected quantum 1/3 magnetization-plateau state. The characteristic energies, dispersion relations, and dynamical structure factor of neutron scattering as well as macroscopic quantum 1/3 magnetization-plateau state are in good agreement with the state-of-the-art dynamical density matrix renormalization group calculations.
Trimerized Spin-1/2 Chain: Emergent Low-Energy Hamiltonian, Higher-Energy Excitations, and Magnetic and Thermodynamic Responses
We investigate a spin-1/2 antiferromagnetic chain with trimerized exchange couplings relevant to Na2Cu3Ge4O12. We show that the low-energy Hilbert space maps onto an effective Heisenberg chain of composite spin-1/2 trimer degrees of freedom with positive coupling, enabling an exact spinon excitations via the Bethe ansatz. To access higher-energy dynamics, we develop a self-consistent Jordan-Wigner mean-field theory that yields three fermionic bands reflecting the underlying trimer structure. Remarkably, this approach reproduces the exact low-energy spinon continuum while predicting two additional higher-energy excitation bands consistent with the experimental observations and previous numerical simulations. The theory further captures the 1/3 magnetization plateau under an applied magnetic field, and provides testable predictions in magnetic susceptibility and specific heat. Our results establish a unified framework connecting low- and high-energy excitations in trimerized quantum spin chains.
We study the elementary excitations and magnetization of a one-dimensional spin-1/2 XX chain comprising trimer-dimer units (the J1-J1-J2-J3-J2 topology) under a transverse magnetic field h. Using Green's function theory and the Jordan-Wigner transformation, we map the system onto spinless fermions and focus on antiferromagnetic (AFM) interactions. At zero temperature, distinct 1/5 and 3/5 magnetization plateaus emerge, determined by the global periodicity Q=5, with the number of plateaus matching the number of excitation gaps above the Fermi level of the spinless fermions. The magnetic phase diagram in the (h-Js) plane features a Luttinger liquid (LL) state, a gapless AFM state, two magnetization plateau states, and a fully polarized gapped magnetic state. The widths of the LL and gapless AFM phases are found to be proportional to the bandwidths gamma = |E(k=0)-E(k=pi)| of the corresponding elementary excitations, whereas the widths of the magnetization plateau states are governed by the excitation gaps. Our study opens new directions for exploring interacting trimer-dimer spin chains in quantum magnetism using experimental techniques such as neutron scattering, as well as theoretical and numerical approaches including quantum Monte Carlo (QMC) and density-matrix renormalization group (DMRG) methods. Furthermore, we extend the Oshikawa-Yamanaka-Affleck (OYA) condition to generalized cluster chains, demonstrating that the allowed magnetization plateaus are governed by the global periodicity of the chain (e.g., Q=5 for a trimer-dimer chain), rather than by the local periodicity of individual units (Q=3 for a trimer or Q=2 for a dimer).