Abstract Prototypical models and their material incarnations are cornerstones to the understanding of quantum magnetism. Here we show theoretically that the recently synthesized magnetic compound Na 2 BaCo(PO 4 ) 2 (NBCP) is a rare, nearly ideal material realization of the S = 1/2 triangular-lattice antiferromagnet with significant easy-axis spin exchange anisotropy. By combining the automatic parameter searching and tensor-network simulations, we establish a microscopic model description of this material with realistic model parameters, which can not only fit well the experimental thermodynamic data but also reproduce the measured magnetization curves without further adjustment of parameters. According to the established model, the NBCP hosts a spin supersolid state that breaks both the lattice translation symmetry and the spin rotational symmetry. Such a state is a spin analog of the long-sought supersolid state, thought to exist in solid Helium and optical lattice systems, and share similar traits. The NBCP therefore represents an ideal material-based platform to explore the physics of supersolidity as well as its quantum and thermal melting.
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
Using thermal tensor-network approach, we investigate the spin Seebeck effect (SSE) of the triangular lattice quantum antiferromagnet hosting spin supersolid phase. We focus on the low-temperature scaling behaviors of the normalized spin current across the interface. For the 1D Heisenberg chain, we find a negative spinon spin current in the bulk with algebraic temperature scaling; at low fields, boundary effects induce a second sign reversal at lower temperatures. These benchmark results are consistent with field-theoretical analysis. On the triangular lattice, spin frustration dramatically enhances the low-temperature SSE, with distinct spin-current signatures-particularly the sign reversal and characteristic temperature dependence-distinguishing different spin states. Remarkably, we discover a persistent, negative spin current in the spin supersolid phase, which saturates to a nonzero value in the low-temperature limit and can be ascribed to the Goldstone-mode-mediated spin supercurrent. Moreover, a universal scaling T^{d/z} is found at the U(1)-symmetric polarization quantum critical points. These distinct quantum spin transport traits provide sensitive spin current probes for spin supersolid states in quantum magnets such as Na_{2}BaCo(PO_{4})_{2}. Furthermore, our results also establish spin supersolids as a promising quantum platform for spin caloritronics in the ultralow-temperature regime.
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 Na
2BaNi(PO
4)
2 and K
2Ni(SeO
3)
2.
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.
Abstract Quantum spin liquids (QSL) are prototypical examples of ground states with massive many-body entanglement. While an unambiguous realization of this long-sought-after state remains elusive, a growing number of materials candidates keep emerging with varieties of novel and exotic properties. Here, we report a combined experimental and theoretical study of a new antiferromagnet Ba 3 CuNb 2 O 9 which has an in-plane anisotropic exchange interaction arising from distorted triangular arrangements of magnetic Cu 2 + (spin-1/2) ions. We show an unconventional gapless QSL like ground state in this material which does not exhibit any signature of magnetic ordering down to 0.3 K, while a finite Curie–Weiss temperature ∼ − 41 K is evident. The gapless QSL state is supported by a high spin fluctuation, a power-law dependence of magnetic specific heat ( C m ∝ T γ ) and a unique scaling of magnetic susceptibility and specific heat with temperature and magnetic field respectively. Our ab-initio simulation also confirms the anisotropic exchange interaction which can only be explained via superexchange mechanism. While the combined results strongly suggest a random singlet state driven QSL behavior in present material, we strongly believe that the anisotropic exchange interaction has a possible role for this exotic ground state behavior.