Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1811.00474

Hidden $SU(2)$ Symmetries, the Symmetry Hierarchy and the Emergent Eight-Fold Way in Spin-1 Quantum Magnets

Hui-Ke Jin·Jian-Jian Miao·Yi Zhou
View original source ↗Read source document ↗Export metadata ↓

Abstract

The largest allowed symmetry in a spin-1 quantum system is an $SU(3)$ symmetry rather than the $SO(3)$ spin rotation. In this work, we reveal some $SU(2)$ symmetries as subgroups of $SU(3)$ that, to the best of our knowledge, have not previously been recognized. Then, we construct $SU(2)$ symmetric Hamiltonians and explore the ground-state phase diagram in accordance with the $SU(3)\supset SU(2)\times U(1)$ symmetry hierarchy. It is natural to treat the eight generators of the $SU(3)$ symmetry on an equal footing; this approach is called the eight-fold way. We find that the spin spectral functions and spin quadrupole spectral functions share the same structure, provided that the elementary excitations are flavor waves at low energies, which serves as a clue to the eight-fold way. An emergent $S=1/2$ quantum spin liquid is proposed to coexist with gapful spin nematic order in one of the ground states. In analogy to quantum chromodynamics, we find the gap relation for hydrodynamic modes in quantum spin-orbital liquid states, which is nothing but the Gell-Mann-Okubo formula.

Explore related subjects

cond-mat.str-el

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Hui-Ke Jin, Jian-Jian Miao, Yi Zhou. 2019-08-02. Hidden $SU(2)$ Symmetries, the Symmetry Hierarchy and the Emergent Eight-Fold Way in Spin-1 Quantum Magnets. https://doi.org/10.1103/physrevb.100.085101

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Strong Coupling Quantum Impurity Solver on the Real and Imaginary Axes

The diagrammatic Monte Carlo method has so far been used mainly for weak-coupling expansions. Here we show that the strong-coupling expansion offers a key advantage: it can be implemented efficiently on both the real and imaginary frequency axes at finite temperature. Using a quantum-impurity solver for dynamical mean-field theory (DMFT) as an example, we find rapid convergence with expansion order. We derive closed-form real-axis Feynman rules for diagrams of arbitrary order, and implement them in a bold hybridization-expansion quantum Monte Carlo (BHQMC) impurity solver. Benchmarking against state-of-the-art numerical renormalization group (NRG) results for the DMFT Mott transition of the Hubbard model, we obtain a highly accurate frequency-dependent scattering rate at finite temperature. This enables reliable spectroscopy and provides benchmark transport results within DMFT and cluster-DMFT.

cond-mat.str-el↗
arXiv2026

Skyrmions of Frustrated Quantum Dimer Systems

Magnetic skyrmions are topologically protected solitons observed in various classes of real magnets. In two-dimensional systems, where the target space of local magnetization values is the two-sphere $S^2$, skyrmion textures are classified by the homotopy classes of two-loops $S^2$ in $S^2$: $Π_2(S^2) \cong Z$. Here, we demonstrate that more general topological skyrmion textures emerge in the classical limit of quantum dimer systems, where the phase space of the relevant classical theory is $\mathbb{CP}^{N-1}$ (with $N=4$ for the case of interest), because the relevant second homotopy group, $Π_2(\mathbb{CP}^{N-1}) \cong Z$ for $N\geq 2$, remains unchanged. Building on the framework established by Zhang et al. (2023), we consider a classical limit based on SU(4) coherent states, which preserve intra-dimer entanglement. We show that the zero-temperature phase diagram of frustrated spin-dimer systems on a bilayer triangular lattice with weak inter-dimer coupling includes two magnetic-field-induced $\mathbb{CP}^{3}$ skyrmion crystal phases.

cond-mat.str-el↗
arXiv2026

Collective excitations in chiral spin liquid: chiral roton and long-wavelength nematic mode

Chiral spin liquid (CSL) is a magnetic analogue of the fractional quantum Hall (FQH) liquid. Collective excitations play a vital role in shaping our understanding of these exotic quantum phases of matter and their quantum phase transitions. While the magneto-roton and long-wavelength chiral graviton modes in the FQH and fractional Chern insulator (FCI) liquids have been extensively explored, whether CSLs host analogous or qualitatively different modes remains elusive. Here we explore the collective excitations in the SU(2) symmetric CSL phase. Combining exact diagonalization and time-dependent variational principle calculations, we identify two spin-singlet collective modes: a chiral p-wave roton mode at finite momentum, and a elliptically polarized d-wave nematic mode at zero momentum, both of which are prominent across the CSL phase. The chiral p-wave singlet roton has no counterpart in FQH of FCI systems, and the q = 0 d-wave mode also exhibits fingerprint distinct from those of FQH/FCI liquids. We also elucidate that both singlet modes are general for CSLs on various lattice models. By tuning J2, we find the nematic mode to be pronouncedly soft, together with the spin-triplet two-spinon bound states, potentially promoting strong nematic and spin stripe instabilities. Our work paves the way for further understanding CSL from the dynamical perspective and provides new spectroscopic signatures for future experiments of CSL candidates.

cond-mat.str-el↗