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

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.

arXiv comment8 pages of main text, 10 pages of appendices

References in corpus (29)

• Quantum Spin Liquid States
• Entanglement spectrum of a topological phase in one dimension
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Spin Liquid Ground State of the Spin-1/2 Square $J_1$-$J_2$ Heisenberg Model
• The quadrupolar phases of the S=1 bilinear-biquadratic Heisenberg model on the triangular lattice
• Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J1-J2 Square Heisenberg Model
• Spin Nematic Phase in S=1 Triangular Antiferromagnets
• Plaquette valence bond solid in the frustrated Heisenberg quantum antiferromagnet on the square lattice
• Direct evidence for a gapless $Z_2$ spin liquid by frustrating Néel antiferromagnetism
• Spontaneous plaquette dimerization in the $J_1-J_2$ Heisenberg model
• Critical level crossings and gapless spin liquid in the square-lattice spin-$1/2$ $J_1$-$J_2$ Heisenberg antiferromagnet
• Spin nematic correlations in bilinear-biquadratic S=1 spin chains
• Spin nematics in the bilinear-biquadratic S=1 spin chain
• Quantum Spin Liquid in Spin 1/2 J1-J2 Heisenberg Model on Square Lattice: Many-Variable Variational Monte Carlo Study Combined with Quantum-Number Projections
• Three-sublattice ordering of the SU(3) Heisenberg model of three-flavor fermions on the square and cubic lattices
• A tensor product state approach to spin-1/2 square $J_1$-$J_2$ antiferromagnetic Heisenberg model: evidence for deconfined quantum criticality
• Effective field theory for S=1 quantum nematic
• Search for the Nondimerized Quantum Nematic Phase in the Spin-1 Chain
• $U(1)$-symmetric infinite projected entangled-pair state study of the spin-$1/2$ square $J_1-J_2$ Heisenberg model
• Spin-1/2 J1-J2 Heisenberg antiferromagnet on a square lattice: a plaquette renormalized tensor network study
• Competition between two- and three-sublattice ordering for S=1 spins on the square lattice
• Phase diagram and continuous pair-unbinding transition of the bilinear-biquadratic S=1 Heisenberg chain in a magnetic field
• The SU(3) bosons and the spin nematic state on the spin-1 bilinear-biquadratic triangular lattice
• Possibility of S=1 spin liquids with fermionic spinons on triangular lattices
• Gutzwiller Projected wavefunctions in the fermonic theory of S=1 spin chains
• New gapped quantum phases for S=1 spin chain with D2h symmetry
• Simulating a two-dimensional frustrated spin system with fermionic resonating-valence-bond states
• Boundary Critical Phenomena in SU(3) "Spin" Chains