We introduce an exactly solvable SU(2)-invariant spin-1/2 model with exotic spin excitations. With time reversal symmetry (TRS), the ground state is a spin liquid with gapless or gapped spin-1 but fermionic excitations. When TRS is broken, the resulting spin liquid exhibits deconfined vortex excitations which carry spin-1/2 and obey non-Abelian statistics. We show that this SU(2) invariant non-Abelian spin liquid exhibits the spin quantum Hall effect with quantized spin Hall conductivity σ(xy)(s)=ℏ/2π, and that the spin response is effectively described by the SO(3) level-1 Chern-Simons theory at low energy. We further propose that a SU(2) level-2 Chern-Simons theory is the effective field theory describing the topological structure of the non-Abelian SU(2) invariant spin liquid.We introduce an exactly solvable SU(2)-invariant spin-1/2 model with exotic spin excitations. With time reversal symmetry (TRS), the ground state is a spin liquid with gapless or gapped spin-1 but fermionic excitations. When TRS is broken, the resulting spin liquid exhibits deconfined vortex excitations which carry spin-1/2 and obey non-Abelian statistics. We show that this SU(2) invariant non-Abelian spin liquid exhibits the spin quantum Hall effect with quantized spin Hall conductivity σ(xy)(s)=ℏ/2π, and that the spin response is effectively described by the SO(3) level-1 Chern-Simons theory at low energy. We further propose that a SU(2) level-2 Chern-Simons theory is the effective field theory describing the topological structure of the non-Abelian SU(2) invariant spin liquid.

arXiv:1010.3724Physical Review LettersAug 17, 201199 citations

Entangled, coherent, and squeezed states of a single SU(2) qutrit

Sinem Binicioǧlu, M. Ali Can, Alexander A. Klyachko +1 more

Using the single SU(2) qutrit (spin-1 like system), we show that entanglement may take place for a single particle with respect to its internal degrees of freedom, in other words, beyond the conventional requirements of nonlocality and nonseparability. We show that the SU(2) or spin coherent states do not manifest entanglement, while the so-called squeezed spin states are entangled. We reveal the principle difference between the spin coherent and spin squeezed states in terms of quantum correlations. A number of physical realizations of the SU(2) qutrit is discussed.Using the single SU(2) qutrit (spin-1 like system), we show that entanglement may take place for a single particle with respect to its internal degrees of freedom, in other words, beyond the conventional requirements of nonlocality and nonseparability. We show that the SU(2) or spin coherent states do not manifest entanglement, while the so-called squeezed spin states are entangled. We reveal the principle difference between the spin coherent and spin squeezed states in terms of quantum correlations. A number of physical realizations of the SU(2) qutrit is discussed.

Physical Review AApr 25, 20061 citation

Application of su(2) algebra

Guozhen Wu

Elsevier eBooksJan 1, 20050 citations

Nonsymmorphic spin-space cubic groups and SU(2) $_1$ conformal invariance in one-dimensional spin-1/2 modelsNonsymmorphic spin-space cubic groups and SU(2)$_1$ conformal invariance in one-dimensional spin-1/2 models

Wang Yang, Alberto Nocera, Chao Xu +1 more

Recently, extended gapless phases with emergent SU(2) _1 1 conformal invariance occupying finite regions in the phase diagrams have been found in one-dimensional spin-1/2 models with nonsymmorphic O_h O h symmetry groups. In this work, we investigate the question of whether the conditions for emergent SU(2) _1 1 invariance can be loosened. We find that besides the nonsymmorphic O_h O h group, the other four smaller nonsymmorphic cubic groups including O O , T_h T h , T_d T d and T T can also give rise to emergent SU(2) _1 1 invariance. Minimal spin-1/2 models having these nonsymmorphic cubic groups as symmetry groups are constructed, and numerical evidences for the emergent SU(2) _1 1 invariance are provided. Our work is useful for understanding gapless phases in one-dimensional spin systems with nonsymmorphic symmetries.Recently, extended gapless phases with emergent SU(2) _1 1 conformal invariance occupying finite regions in the phase diagrams have been found in one-dimensional spin-1/2 models with nonsymmorphic O_h O h symmetry groups. In this work, we investigate the question of whether the conditions for emergent SU(2) _1 1 invariance can be loosened. We find that besides the nonsymmorphic O_h O h group, the other four smaller nonsymmorphic cubic groups including O O , T_h T h , T_d T d and T T can also give rise to emergent SU(2) _1 1 invariance. Minimal spin-1/2 models having these nonsymmorphic cubic groups as symmetry groups are constructed, and numerical evidences for the emergent SU(2) _1 1 invariance are provided. Our work is useful for understanding gapless phases in one-dimensional spin systems with nonsymmorphic symmetries.

arXiv:2208.10754SciPost PhysicsOct 1, 20243 citations

SU(K) spin chain

Yoshio Kuramoto, Yusuke S. Kato

Cambridge University Press eBooksAug 6, 20092 citations

Nonsymmorphic spin-space cubic groups and SU(2)

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conformal invariance in one-dimensional spin-1/2 models