Motivated by a recent experimental study on the quantum Ising magnet ${\text{K}}_{2}\text{Co}{({\text{SeO}}_{3})}_{2}$ that presented spectroscopic evidence of zero-field supersolidity (Chen et al., arXiv:2402.15869), we simulate the excitation spectrum of the corresponding microscopic $XXZ$ model for the compound using the recently developed excitation ansatz for infinite projected entangled-pair states. We map out the ground state phase diagram and compute the dynamical spin structure factors across a range of magnetic field strengths, focusing especially on the two supersolid phases found near zero and saturation fields. Our simulated excitation spectra for the zero-field supersolid ``Y'' phase are in excellent agreement with the experimental data, recovering the low-energy branches and integer quantized excited energy levels ${\ensuremath{\omega}}_{n}=n{J}_{zz}$. Furthermore, we demonstrate the nonlocal multi-spin-flip features for modes at ${\ensuremath{\omega}}_{2}$, indicative of their multimagnon nature. Additionally, we identify characteristics of the high-field supersolid ``$\mathrm{\ensuremath{\Psi}}$'' phase in the simulated spectra, which should be compared with future experimental results.
Motivated by a recent experimental study on the quantum Ising magnet K2Co(SeO3)2 that presented spectroscopic evidence of zero-field supersolidity (Chen et al., arXiv:2402.15869), we simulate the excitation spectrum of the corresponding microscopic XXZ model for the compound using the recently developed excitation ansatz for infinite projected entangled-pair states. We map out the ground state phase diagram and compute the dynamical spin structure factors across a range of magnetic field strengths, focusing especially on the two supersolid phases found near zero and saturation fields. Our simulated excitation spectra for the zero-field supersolid Y'' phase are in excellent agreement with the experimental data, recovering the low-energy branches and integer quantized excited energy levels ${\ensuremath{\omega}}_{n}=n{J}_{zz}$. Furthermore, we demonstrate the nonlocal multi-spin-flip features for modes at ${\ensuremath{\omega}}_{2}$, indicative of their multimagnon nature. Additionally, we identify characteristics of the high-field supersolid \ensuremathΨ'' phase in the simulated spectra, which should be compared with future experimental results.
Motivated by recent experiments, we investigate the spin- 1 2 XXZ model on the triangular lattice with strong Ising anisotropy, combining large-scale numerical simulations and analytical methods to uncover unconventional spin dynamics at T = 0 . First, we compute the dynamical spin structure factor using density matrix renormalization group (DMRG) simulations and find excellent agreement with inelastic neutron scattering data on the layered compound K 2 Co ( SeO 3 ) 2 . The low-energy spectrum reveals a rotonlike minimum at the M point, absent in linear spin-wave theory, accompanied by peak intensity and a broad continuum above it. Near the Γ point, we observe an approximately linear dispersion with vanishing spectral weight. Second, we compare two analytical frameworks that reproduce the observed features. The first is a hard-core boson approach, which includes (i) an effective staggered boson model at zero magnetic field, (ii) perturbation theory applied to the one-third magnetization plateau, and (iii) a self-consistent mean-field Schwinger boson theory (SBT). The second framework is based on a variational supersolid quantum dimer model (QDM) ansatz, combined with a single-mode approximation. The SBT captures the broad continuum, the M -point minimum, and linear dispersion at Γ , whereas the QDM reproduces the roton minimum and linear dispersion at finite momentum near Γ . Remarkably, both the QDM wave function and the DMRG ground state exhibit nearly identical structure factors with pronounced transverse photonlike excitations. Together, our comprehensive theoretical and numerical analysis elucidates the microscopic origin of supersolid excitations in the XXZ triangular-lattice model and their proximity to a spin-liquid phase observed experimentally.
We present a systematic numerical study of the spin-1 antiferromagnetic Heisenberg model on the triangular lattice in an out-of-plane magnetic field, using Density Matrix Renormalization Group (DMRG) methods. By mapping out the quantum phase diagram as a function of the single-ion anisotropy Dz and magnetic field, we identify distinct dipolar and quadrupolar spin supersolid states, characterized by spontaneous U(1) symmetry breaking with finite spin superfluid stiffness coexisting with longitudinal translational symmetry breaking. At zero field, the dipolar spin supersolid with a 'Y'-type spin configuration persists down to Dz=0, whereas the quadrupolar spin supersolid prevails at large Dz. At intermediate fields, the phase diagram is dominated by an up-up-down phase. At high fields below saturation, a quadrupolar spin superfluid emerges in the large-Dz regime, whereas a dipolar spin supersolid with a 'V'-type spin configuration dominates at small Dz. These phases are characterized through their order parameters and spin superfluid stiffness using calculations on various system sizes. Furthermore, the dynamical spin structure factor is obtained across the phase diagram, where characteristic spectral signatures of different phases are observed, including the gapless Goldstone mode and the roton-like minima. These features are directly accessible to inelastic neutron scattering experiments. Our results provide a theoretical understanding of the interplay between frustrations, anisotropy, and Zeeman interactions in driving distinct spin supersolid phases in the spin-1 system, which are relevant to various triangular-lattice antiferromagnets such as Na2BaNi(PO4)2 and K2Ni(SeO3)2.
Motivated by recent experimental evidence for spin supersolid states in triangular-lattice compounds, we numerically investigate the dynamical properties of magnetic field-induced phases in the spin-1/2 easy-axis triangular antiferromagnetic Heisenberg model in the presence of magnetic impurities. In both weak- and strong-field spin supersolid states, the gapless Goldstone mode at the K points remains robust against impurities, which is a direct manifestation of spin superfluidity. By contrast, at the same impurity density, impurities induce a splitting of the magnon bands in the conventional magnetic state, the so-called up-up-down state. In addition, the finite superfluid stiffness probed by the twisted phase in the spin supersolid states is consistent with the excitation spectrum. We argue that the excitation spectrum with impurities provides direct spectroscopic evidence for dissipationless spin dynamics in the spin supersolid states, which is experimentally accessible via inelastic neutron scattering.
We study the spin-1/2 XXZ model on the triangular lattice with a nearest neighbor antiferromagnetic Ising coupling J(z) > 0 and unfrustrated (J(perpendicular) < 0) or frustrated (J(perpendicular) >0) kinetic terms in a zero magnetic field. Incorporating long-range Jastrow correlations over a mean-field spin state, we obtain the variational phase diagram of this model on large lattices for arbitrary J(z) and either sign of J(perpendicular). For J(perpendicular) < 0, we find a square root(3) x square root(3) supersolid for J(z)/J(perpendicular)| approximately > 4.7, in excellent agreement with quantum Monte Carlo data. For J(perpendicular) > 0, a distinct square root(3) x square root(3) supersolid is found to emerge for J(z)/J(perpendicular) > or = 1. Both supersolids exhibit a spontaneous density deviation from half-filling. At J(z)/J(perpendicular) = infinity, the crystalline order parameters of these two supersolids are nearly identical, consistent with exact results.
Based on the recent experiments on the triangular lattice antiferromagnet Na 2 BaCo ( PO 4 ) 2 , we propose the easy-axis XXZ spin-1/2 model on the triangular lattice, that exhibits a quantum spin supersolid, to be a precursory Dirac spin liquid. Despite the presence of a three-sublattice magnetic order as a spin supersolid, we suggest that this system is close to a Dirac spin liquid by exploring its spectroscopic response. The physical consequence is examined from the spectroscopic response, and we establish the continuous spectra near the M point in addition to the K point excitation from the spinon continuum on top of the three-sublattice order. Moreover, the satellite peaks were predicted at the mid-points connecting the Γ and K points. This proposal offers a plausible understanding of the recent inelastic neutron scattering measurement in Na 2 BaCo ( PO 4 ) 2 and could inspire further research in relevant models and materials, such as K 2 Co ( SeO 3 ) 2 and Rb 2 Co ( SeO 3 ) 2 , and even more anisotropic magnets like PrMgAl 11 O 19 . Published by the American Physical Society 2024
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.