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Yao-Zhong Zhang

Publications and source records attributed to Yao-Zhong Zhang.

At least 109 records · Page 6Linked to original sources
arXiv2011

Exact solutions for a family of spin-boson systems

We obtain the exact solutions for a family of spin-boson systems. This is achieved through application of the representation theory for polynomial deformations of the $su(2)$ Lie algebra. We demonstrate that the family of Hamiltonians includes, as special cases, known physical models which are the two-site Bose-Hubbard model, the Lipkin-Meshkov-Glick model, the molecular asymmetric rigid rotor, the Tavis-Cummings model, and a two-mode generalisation of the Tavis-Cummings model.

math-ph↗
arXiv2011

Scalar products of the open XYZ chain with non-diagonal boundary terms

With the help of the F-basis provided by the Drinfeld twist or factorizing F-matrix of the eight-vertex solid-on-solid (SOS) model, we obtain the determinant representations of the scalar products of Bethe states for the open XYZ chain with non-diagonal boundary terms. By taking the on shell limit, we obtain the determinant representations (or Gaudin formula) of the norms of the Bethe states.

math-ph↗
arXiv2011

Drinfeld twist and symmetric Bethe vectors of the open XYZ chain with non-diagonal boundary terms

With the help of the Drinfeld twist or factorizing F-matrix for the eight-vertex solid-on-solid (SOS) model, we find that in the F-basis provided by the twist the two sets of pseudo-particle creation operators simultaneously take completely symmetric and polarization free form. This allows us to obtain the explicit and completely symmetric expressions of the two sets of Bethe states of the model.

hep-th↗
arXiv2010

Drinfeld twists of the open XXZ chain with non-diagonal boundary terms

The Drinfeld twists or factorizing F-matrices for the open XXZ spin chain with non-diagonal boundary terms are constructed. It is shown that in the F-basis the two sets of pseudo-particle creation operators simultaneously take completely symmetric and polarization free form. The explicit and completely symmetric expressions of the two sets of Bethe states of the model are obtained.

hep-th↗
arXiv2010

Polynomial algebras and exact solutions of general quantum non-linear optical models II: Multi-mode boson systems

We present higher order polynomial algebras which are the dynamical symmetry algebras of a wide class of multi-mode boson systems in non-linear optics. We construct their unitary representations and the corresponding single-variable differential operator realizations. We then use the results to obtain exact (Bethe ansatz) solutions to the multi-mode boson systems, including the BEC models as special cases.

math-ph↗
arXiv2010

Polynomial algebras and exact solutions of general quantum non-linear optical models I: Two-mode boson systems

We introduce higher order polynomial deformations of $A_1$ Lie algebra. We construct their unitary representations and the corresponding single-variable differential operator realizations. We then use the results to obtain exact (Bethe ansatz) solutions to a class of 2-mode boson systems, including the Boson-Einstein Condensate models as special cases. Up to an overall factor, the eigenfunctions of the 2-mode boson systems are given by polynomials whose roots are solutions of the associated Bethe ansatz equations. The corresponding eigenvalues are expressed in terms of these roots. We also establish the spectral equivalence between the BEC models and certain quasi-exactly solvable Schördinger potentials.

math-ph↗
arXiv2009

Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations

Bethe ansatz formulation is presented for several explicit examples of quasi exactly solvable difference equations of one degree of freedom which are introduced recently by one of the present authors. These equations are deformation of the well-known exactly solvable difference equations of the Meixner-Pollaczek, continuous Hahn, continuous dual Hahn, Wilson and Askey-Wilson polynomials. Up to an overall factor of the so-called pseudo ground state wavefunction, the eigenfunctions within the exactly solvable subspace are given by polynomials whose roots are solutions of the associated Bethe ansatz equations. The corresponding eigenvalues are expressed in terms of these roots.

math-ph↗
arXiv2009

Partition function of the eight-vertex model with domain wall boundary condition

We derive the recursive relations of the partition function for the eight-vertex model on an $N\times N$ square lattice with domain wall boundary condition. Solving the recursive relations, we obtain the explicit expression of the domain wall partition function of the model. In the trigonometric/rational limit, our results recover the corresponding ones for the six-vertex model.

cond-mat.stat-mech↗
arXiv2009

On Pointed Hopf Algebras with Weyl Groups of exceptional type

All -1-type pointed Hopf algebras and central quantum linear spaces with Weyl groups of exceptional type are found. It is proved that every non -1-type pointed Hopf algebra with real $G(H)$ is infinite dimensional and every central quantum linear space over finite group is finite dimensional. It is proved that except a few cases Nichols algebras of reducible Yetter-Drinfeld modules over Weyl groups of exceptional type are infinite dimensional.

math.QA↗
arXiv2009

Differential operator realizations of superalgebras and free field representations of corresponding current algebras

Based on the particular orderings introduced for the positive roots of finite dimensional basic Lie superalgebras, we construct the explicit differential operator representations of the $osp(2r|2n)$ and $osp(2r+1|2n)$ superalgebras and the explicit free field realizations of the corresponding current superalgebras $osp(2r|2n)_k$ and $osp(2r+1|2n)_k$ at an arbitrary level $k$. The free field representations of the corresponding energy-momentum tensors and screening currents of the first kind are also presented.

hep-th↗
arXiv2008

Free field realization of the $osp(2n|2n)$ current algebra

The $osp(2n|2n)$ current algebra for a {\it generic} positive integer $n$ at general level $k$ is investigated. Its free field representation and corresponding energy-momentum tensor are constructed. The associated screening currents of the first kind are also presented.

hep-th↗
arXiv2008

On explicit free field realizations of current algebras

We construct the explicit free field representations of the current algebras $so(2n)_k$, $so(2n+1)_k$ and $sp(2n)_k$ for a generic positive integer $n$ and an arbitrary level $k$. The corresponding energy-momentum tensors and screening currents of the first kind are also given in terms of free fields.

hep-th↗
arXiv2008

Free field realization of current superalgebra $gl(m|n)_k$

We construct the free field representation of the affine currents, energy-momentum tensor and screening currents of the first kind of the current superalgebra $gl(m|n)_k$ uniformly for $m=n$ and $m\neq n$. The energy-momentum tensor is given by a linear combination of two Sugawara tensors associated with the two independent quadratic Casimir elements of $gl(m|n)$.

hep-th↗
arXiv2008

Local Quasitriangular Hopf Algebras

We find a new class of Hopf algebras, local quasitriangular Hopf algebras, which generalize quasitriangular Hopf algebras. Using these Hopf algebras, we obtain solutions of the Yang-Baxter equation in a systematic way. The category of modules with finite cycles over a local quasitriangular Hopf algebra is a braided tensor category.

math.QA↗
arXiv2007

Classification of PM Quiver Hopf Algebras

We describe certain quiver Hopf algebras by parameters. This leads to the classification of multiple Taft algebras as well as pointed Yetter-Drinfeld modules and their corresponding Nichols algebras. In particular, when the ground-field $k$ is the complex field and $G$ is a finite abelian group, we classify quiver Hopf algebras over $G$, multiple Taft algebras over $G$ and Nichols algebras in $^{kG}_{kG} {\cal YD}$. We show that the quantum enveloping algebra of a complex semisimple Lie algebra is a quotient of a semi-path Hopf algebra.

math.QA↗
arXiv2007

Multiple reference states and complete spectrum of the $Z_n$ Belavin model with open boundaries

The multiple reference state structure of the $\Z_n$ Belavin model with non-diagonal boundary terms is discovered. It is found that there exist $n$ reference states, each of them yields a set of eigenvalues and Bethe Ansatz equations of the transfer matrix. These $n$ sets of eigenvalues together constitute the complete spectrum of the model. In the quasi-classic limit, they give the complete spectrum of the corresponding Gaudin model.

hep-th↗