Quantum Algebra as Deformation Symmetry

The deformation maps as well as the general algebraic maps among algebras with three generators are systematically investigated in terms of symplectic geometry and geometric quantization on 2-D manifolds, from which the explicit Hamiltonian of Heisenberg model with SU_q(2) symmetry and arbitrary spin values are given. The deformation symmetries in differential dynamical systems and the q-deformed transformations of SO(3) group in usual R³ are also discussed.     

q-Deformed SU(1,1) ⊗ SO(6) Spectra of Interacting s,d Bosons in Nuclei

The quantum groups SU_q(1,1) and SU_q(2) are used to describe the interacting s, d bosons system which hae the q-deformed SU(1,1) ⊗ SO(6) dynamic symmetry and a Hamiltonian similar to that of O(6)-limit in the interacting boson model is constructed. Three regions of q-number are taken to analyze the influences of deformation on the deformed SU(1,1) ⊗ SO(6) spectra. It is found that the deformation parameter has important influences on the higher excited states within a quasi- rotational band. Yt isotopes with O(6) characteristics are investigated.     

The Temperley-Lieb-Jones Algebra and Symmetry Group in Heisenberg Spin Models in One and Two Dimensions

We present a systematic method to construct the spin models of Heisenberg type in higher dimensions with nearesband non-nearest neighbour interactions. These models constructed in this way are of Temperley-Lieb-Jones (TLJ) algebraic structures and SU(2)-invariances. The TLJ algebra is generalized to adjusting the lattice spin models. The Hamiltonians of Heisenberg spin models in one dimension (including second nearest neighbour interactions) and in two-dimensional triangular lattice (with nearest interaction) are constructed explicitly. The hidden symmetries are shown to be the SU(2) group, and the terms in Ilamiltonian for different lattice cells are explicitly shown to be the representations of elements of (TLJ) algebra.     

Relationship Between Negative Binomial State and SU(1, l) Coherent State and Its q-Deformed Generalization

By choosing a suitable single-mode boson realization of SU(1,1) algebra we show that the associated SU(1,1) cohkrent state can be directly reformed as a negative binomial state. The q-deformed negative binomial state is introduced, and the relationship between this state and the SU_q(1,1) coherent state is also demonstrated.     

Irreducible Representations and Reduced Coefficients of Quantum Algebra SUq(4) in the SUq(4)⊃ SUq(2)⊕SUq(2) Basis

In this paper, the tensor-like method is presented, and the applications to quantum algebra SU_q(4) are given. The irreducible representation of SU_q(4) and a recurrent formula to calculate reduced coefficients of SU_q(4)⊃ SU_q(2)⊕SU_q(2) is obtained. Some of reduced matrix elements and q-reduced scalar factors (qRF) are tabulated.     

Symmetries and exact solutions of some integrable Haldane-Shastry-like spin chains

Here we construct some integrable Haldane-Shastry (HS) like spin chains, which exhibit multi-parameter deformed or non-standard variants of Y(gl_m) Yangian symmetry. By projecting the eigenstates of Dunkl operators in a suitable way, we also derive a class of exact eigenfunctions for such spin chains and subsequently conjecture that these exact eigenfunctions would lead to the highest weight states (HWS) associated with multi-parameter deformed or non-standard variants of Y(gl_M) Yangian algebra. By using this conjecture, and acting descendent operator on the HWS associated with a non-standard Y(gl₂) Yangian algebra, we are able to find out the complete set of eigenvalues and eigenfunctions for the related HS-like chain. It turns out that some additional energy levels, which are forbidden due to a selection rule in the case of SU(2) HS model, interestingly appear in the spectrum of the above mentioned HS-like spin chain with non-standard Y(gl²) symmetry.     

Realization of a SU(2)×SU(6) system of fermions in a cold atomic gas

We report the realization of a novel degenerate Fermi mixture with an SU(2)×SU(6) symmetry in a cold atomic gas. We successfully cool the mixture of the two fermionic isotopes of ytterbium 171Yb with the nuclear spin I=1/2 and 173Yb with I=5/2 below the Fermi temperature T_{F} as 0.46TF for 171Yb and 0.54TF for 173Yb. The same scattering lengths for different spin components make this mixture featured with the novel SU(2)×SU(6) symmetry. The nuclear spin components are separately imaged by exploiting an optical Stern-Gerlach effect. In addition, the mixture is loaded into a 3D optical lattice to implement the SU(2)×SU(6) Hubbard model. This mixture will open the door to the study of novel quantum phases such as a spinor Bardeen-Cooper-Schrieffer-like fermionic superfluid.     

Square-lattice algebraic spin liquid with SO(5) symmetry

We propose a critical spin liquid ground state for S=1/2 antiferromagnets on the square lattice. In a renormalization group analysis of the "staggered flux" algebraic spin liquid, we examine perturbations, present in the antiferromagnet, which break its global SU(4) symmetry to SO(5). At physical parameter values, we find an instability towards a fixed point with SO(5) symmetry. We discuss the possibility that this fixed point describes a transition between the Néel and valence bond solid states, and the relationship to the SO(5) nonlinear sigma model of Tanaka and Hu.     

q-Deformed U(5) Limit in s,d IBM for Nuclei

The q-deformed Hamiltonian with U(5) symmetry in s , d interacting boson model can be constructed by using quantum algebra SU_P (2), SU_q(1,1) and q-deformed boson operator. The energy spectra and E2 transition rates of ^110~114Cd iso topes are calculated. The calculated results agree with the experimental data rather well. Analyses on the calculated results show that the q-deformed U(5) limit is deviated from the symmetry in the original model and the degree of deviation is dependent on the deformation parameter.     

Coupling Between the Group—Related Coherent States

When two representations of the Lie algebra are coupled,the coupling integral kernels are presented to relate the coupled to uncoupled group-related coherent states,These kernels have a connection with usual coupling coefficients.The explicit expressions of these kernels for SU(2),SO(4) and SUq(2) are given.When the direct product of three representations is formed in two ways,the recoupling integral kernels relating to the coupled group-related coherent states corresponding to two different schemes are introduced,and the relations between these kernels and the general recoupling coefficients are obtained.The properties of these kerels are discussed.     

Fermionic Magnons, non-Abelian spinons, and the spin quantum Hall effect from an exactly solvable spin-1/2 Kitaev model with SU(2) symmetry

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)=?/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.     

Algebraic vortex liquid in spin-1/2 triangular antiferromagnets: scenario for Cs2CuCl4

Motivated by inelastic neutron scattering data on Cs2CuCl4, we explore spin-1/2 triangular lattice antiferromagnets with both spatial and easy-plane exchange anisotropies, the latter due to an observed Dzyaloshinskii-Moriya interaction. Exploiting a duality mapping followed by a fermionization of the dual vortex degrees of freedom, we find a novel critical spin-liquid phase described in terms of Dirac fermions with an emergent global SU(4) symmetry minimally coupled to a noncompact U(1) gauge field. This "algebraic vortex liquid" supports gapless spin excitations and universal power-law correlations in the dynamical spin structure factor which are consistent with those observed in Cs2CuCl4. We suggest future neutron scattering experiments that should help distinguish between the algebraic vortex liquid and other spin liquids and quantum critical points previously proposed in the context of Cs2CuCl4.     

A SUPERSYMMETRICAL PREON MODEL WITH SU(2)L × SU(2)R ×U(1)B-L SYMMETRY BROKEN BY COUPLING TO SUPERGRAVITY

A supersymmetrical preon model is proposed. In this model there are Higgs particles which are massless at the scale of confinement of hypercolor due to the supersymmetry and a discrete R symmetry. We show that in this model the low energy gauge symmetry SU(2)_L×SU(2)_R×U(1)_B-L can be broken to U(1)_Q at the scale of supersymmetry breaking by coupling to supergravity.     

Z2 × Z2 Discrete Symmetry in the Left-Right Symmetric Model SU(2)L × SU(2)R × U(l)B-L

From the point that the Higgs fields can be regarded as the gauge fields on a discrete group, we construct a gauge theory of the leftright symmetric model SU(2)_L × SU(2)_R × U(1)_B-L (LRSM) over Z₂ ⊙ Z₂ discrete symmetry.     

The SU(8) GUT for chiral families

We argue that there is a natural inclusion of the standard model with the family-unified chiral local symmetry SU(3)_H in a new SU(8) GUT inspired by Georgi's SU(11) model. The SU(8) symmetry breaking along the chain with the intermediate electro-weak-horizontal unification SU(8)→SU(5)_EWH×SU(3)_c×U(1) is proved d to be the distinguished pattern. The model predicts a long-lived proton (10³³–10³⁵yr) and practically the observed value of the Weinberg angle, in sharp contrast to the ordinary GUTs. The observation of the specific flavour-changing baryon decays (p→π,μ,Ke,…) could unambiguously single out the flavour unified GUTs as well as confirm the existence of the elementary horizontal forces at small distances.     

New gravitational instantons and universal spin structures

An infinite class of new gravitational instantons for the axial anomaly is found. It consists entirely of algebraic spin- manifolds. In theories that allow manifolds without ordinary spin structure we find the presence of spinorial matter fields to require the existence of a “universal” gauged SU(2) or higher internal symmetry (e.g., SU(2) × SU(2) × G) and of an “internal-spin” -statistics connection. The possible relation of this to the gauge theory of weak and electromagnetic interactions is explored.     

STRING THEORY WITH THREE FAMILIES OF CHIRAL FERMIONS

A heterotic string theory is constructed by compactifying directly from 26 to 4 dimensions via a smooth manifold T²²/G. In the low energy limit, there are three families of chiral fermions with exactly the same quantum numbers as thatin the standard supersymmetric SU(3)×SU(2)×XU(1) model. They couple to supergravity and supergauge fields with the gauge symmetry SU(3)_F×SU(3)_c×SU(3)_L×U(1)_YR×U(1)_I3R.     

The sixth quark mass

In six quark models with the gauge group SU (2)_L × SU (2)_R × U (1), and left-right symmetry, we investigate how weak mixing angles can be predicted in a natural way as functions of the quark masses, and find that the mass of the sixth quark can be naturally determined by the five others.     

Nuclear Matter in a Chiral SU(3) Quark Mean-Field Model

A quark meson coupling model based on SU(3)_L×SU(3)_R symmetry and scale invariance is proposed. The quarks and mesons get masses through symmetry broken. We apply this SU(3) chiral constituent quark model to investigating the nuclear matter at finite temperature and density. The effective baryon masses, compression modulus and hyperon potentials are all reasonable. The critical temperature of liquid-gas phase transition is also calculated in this model.     

Flux Period, Spin Gap, and Pairing in the One-Dimensional t-J-J' Model

Using the factorization of the wave function in the t-J-J' model at small exchange couplings, we demonstrate the connection between the existence of a spin gap and an hc/2e flux periodicity of the ground state energy. We conjecture that all spin-gapped SU(2)-invariant Luttinger liquids have hc/2e flux periodicity, and that this is connected to the fact that a gapped spin-1/2 chain always breaks translational symmetry by doubling the unit cell.