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Yao-Zhong Zhang

Publications and source records attributed to Yao-Zhong Zhang.

At least 145 records · Page 8Linked to original sources
arXiv2005

Super Coherent States, Boson-Fermion Realizations and Representations of Superalgebras

Super coherent states are useful in the explicit construction of representations of superalgebras and quantum superalgebras. In this contribution, we describe how they are used to construct (quantum) boson-fermion realizations and representations of (quantum) superalgebras. We work through a few examples: $osp(1|2)$ and its quantum version $U_t[osp(1|2)]$, $osp(2|2)$ in the non-standard and standard bases and $gl(2|2)$ in the non-standard basis. We obtain free boson-fermion realizations of these superalgebras. Applying the boson-fermion realizations, we explicitly construct their finite-dimensional representations. Our results are expected to be useful in the study of current superalgebras and their corresponding conformal field theories.

hep-th↗
arXiv2005

Non-diagonal solutions of the reflection equation for the trigonometric $A^{(1)}_{n-1}$ vertex model

We obtain a class of non-diagonal solutions of the reflection equation for the trigonometric $A^{(1)}_{n-1}$ vertex model. The solutions can be expressed in terms of intertwinner matrix and its inverse, which intertwine two trigonometric R-matrices. In addition to a {\it discrete} (positive integer) parameter $l$, $1\leq l\leq n$, the solution contains $n+2$ {\it continuous} boundary parameters.

hep-th↗
arXiv2004

Primary fields and screening currents of gl(2|2) non-unitary conformal field theory

The non-semisimple $gl(2|2)_k$ current superalgebra in the standard basis and the corresponding non-unitary conformal field theory are investigated. Infinite families of primary fields corresponding to all finite-dimensional irreducible typical and atypical representations of $gl(2|2)$ and three (two even and one odd) screening currents of the first kind are constructed explicitly in terms of ten free fields.

hep-th↗
arXiv2004

A Unified and Complete Construction of All Finite Dimensional Irreducible Representations of gl(2|2)

Representations of the non-semisimple superalgebra $gl(2|2)$ in the standard basis are investigated by means of the vector coherent state method and boson-fermion realization. All finite-dimensional irreducible typical and atypical representations and lowest weight (indecomposable) Kac modules of $gl(2|2)$ are constructed explicitly through the explicit construction of all $gl(2)\oplus gl(2)$ particle states (multiplets) in terms of boson and fermion creation operators in the super-Fock space. This gives a unified and complete treatment of finite-dimensional representations of $gl(2|2)$ in explicit form, essential for the construction of primary fields of the corresponding current superalgebra at arbitrary level.

math.QA↗
arXiv2004

Coherent State Construction of Representations of osp(2|2) and Primary Fields of osp(2|2) Conformal Field Theory

Representations of the superalgebra $osp(2|2)$ and current superalgebra $osp(2|2)^{(1)}_k$ in the standard basis are investigated. All finite-dimensional typical and atypical representations of $osp(2|2)$ are constructed by the vector coherent state method. Primary fields of the non-unitary conformal field theory associated with $osp(2|2)^{(1)}_k$ in the standard basis are constructed for arbitrary level $k$.

hep-th↗
arXiv2004

Quantum Doubles from a Class of Noncocommutative Weak Hopf Algebras

The concept of biperfect (noncocommutative) weak Hopf algebras is introduced and their properties are discussed. A new type of quasi-bicrossed products are constructed by means of weak Hopf skew-pairs of the weak Hopf algebras which are generalizations of the Hopf pairs introduced by Takeuchi. As a special case, the quantum double of a finite dimensional biperfect (noncocommutative) weak Hopf algebra is built. Examples of quantum doubles from a Clifford monoid as well as a noncommutative and noncocommutative weak Hopf algebra are given, generalizing quantum doubles from a group and a noncommutative and noncocommutative Hopf algebra, respectively. Moreover, some characterisations of quantum doubles of finite dimensional biperfect weak Hopf algebras are obtained.

math.QA↗
arXiv2003

Finite matrix model of quantum Hall fluids on $S^2$

Based on Haldane's spherical geometrical formalism of two-dimensional quantum Hall fluids, the relation between the noncommutative geometry of $S^2$ and the two-dimensional quantum Hall fluids is exhibited. If the number of particles $N$ is infinitely large, two-dimensional quantum Hall physics can be precisely described in terms of the noncommutative U(1) Chern-Simons theory proposed by Susskind, like in the case of plane. However, for the finite number of particles on two-sphere, the matrix-regularized version of noncommutative U(1) Chern-Simons theory involves in spinor oscillators. We establish explicitly such a finite matrix model on two-sphere as an effective description of fractional quantum Hall fluids of finite extent. The complete sets of physical quantum states of this matrix model are determined, and the properties of quantum Hall fluids related to them are discussed. We also describe how the low-lying excitations are constructed in terms of quasiparticle and quasihole excitations in the matrix model. It is shown that there consistently exists a Haldane's hierarchical structure of two-dimensional quantum Hall fluid states in the matrix model. These hierarchical fluid states are generated by the parent fluid state for particles by condensing the quasiparticle and quasihole excitations level by level, without any requirement of modifications of the matrix model.

hep-th↗
arXiv2003

On osp(2|2) conformal field theories

We study the conformal field theories corresponding to current superalgebras $osp(2|2)^{(1)}_k$ and $osp(2|2)^{(2)}_k$. We construct the free field realizations, screen currents and primary fields of these current superalgebras at general level $k$. All the results for $osp(2|2)^{(2)}_k$ are new, and the results for the primary fields of $osp(2|2)^{(1)}_k$ also seem to be new. Our results are expected to be useful in the supersymmetric approach to Gaussian disordered systems such as random bond Ising model and Dirac model.

hep-th↗
arXiv2002

$gl(2|2)$ Current Superalgebra and Non-unitary Conformal Field Theory

Motivated by application of current superalgebras in the study of disordered systems such as the random XY and Dirac models, we investigate $gl(2|2)$ current superalgebra at general level $k$. We construct its free field representation and corresponding Sugawara energy-momentum tensor in the non-standard basis. Three screen currents of the first kind are also presented.

hep-th↗
arXiv2002

R-matrices and Tensor Product Graph Method

A systematic method for constructing trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of any two affinizable representations of a quantum algebra or superalgebra has been developed by the Brisbane group and its collaborators. This method has been referred to as the Tensor Product Graph Method. Here we describe applications of this method to untwisted and twisted quantum affine superalgebras.

hep-th↗
arXiv2002

$A^{(2)}_2$ Parafermions: A New Conformal Field Theory

A new parafermionic algebra associated with the homogeneous space $A^{(2)}_2/U(1)$ and its corresponding $Z$-algebra have been recently proposed. In this paper, we give a free boson representation of the $A^{(2)}_2$ parafermion algebra in terms of seven free fields. Free field realizations of the parafermionic energy-momentum tensor and screening currents are also obtained. A new algebraic structure is discovered, which contains a $W$-algebra type primary field with spin two.

hep-th↗
arXiv2002

Supersymmetric t-J Gaudin Models and KZ Equations

Supersymmetric t-J Gaudin models with both periodic and open boundary conditions are constructed and diagonalized by means of the algebraic Bethe ansatz method. Off-shell Bethe ansatz equations of the Gaudin systems are derived, and used to construct and solve the KZ equations associated with $sl(2|1)^{(1)}$ superalgebra.

nlin.SI↗
arXiv2002

Twisted Parafermions

A new type of nonlocal currents (quasi-particles), which we call twisted parafermions, and its corresponding twisted $Z$-algebra are found. The system consists of one spin-1 bosonic field and six nonlocal fields of fractional spins. Jacobi-type identities for the twisted parafermions are derived, and a new conformal field theory is constructed from these currents. As an application, a parafermionic representation of the twisted affine current algebra $A^{(2)}_2$ is given.

hep-th↗
arXiv2001

Twisted $sl(3, {\bf C})^{(2)}_k$ Current Algebra: Free Field Representation and Screening Currents

Motivated by applications of twisted current algebras in description of the entropy of $Ads_3$ black hole, we investigate the simplest twisted current algebra $sl(3,{\bf C})^{(2)}_k$. Free field representation of the twisted algebra and the corresponding twisted Sugawara energy-momentum tensor are obtained by using three $(β,γ)$ pairs and two scalar fields. Primary fields and two screening currents of the first kind are presented.

hep-th↗
arXiv2001

Elliptic Gaudin models and elliptic KZ Equations

The Gaudin models based on the face-type elliptic quantum groups and the $XYZ$ Gaudin models are studied. The Gaudin model Hamiltonians are constructed and are diagonalized by using the algebraic Bethe ansatz method. The corresponding face-type Knizhnik-Zamolodchikov equations and their solutions are given.

nlin.SI↗
arXiv2001

On the Construction of Integrable Gaudin Models with Boundaries

We propose a general method for constructing boundary integrable Gaudin models associated with (twisted) affine algebras ${\cal G}^{(k)} (k=1, 2)$, where ${\cal G}$ is a simple Lie algebra or superalgebra. Many new integrable Gaudin models with boundaries are constructed using this approach.

nlin.SI↗
arXiv2001

q-deformed Supersymmetric t-J Model with a Boundary

The q-deformed supersymmetric t-J model on a semi-infinite lattice is diagonalized by using the level-one vertex operators of the quantum affine superalgebra $U_q[\hat{sl(2|1)}]$. We give the bosonization of the boundary states. We give an integral expression of the correlation functions of the boundary model, and derive the difference equations which they satisfy.

nlin.SI↗