Persistent spin current and entanglement in the anisotropic spin ring i

We investigate the ground state persistent spin current and the pair entanglement in one-dimensional antiferromagnetic anisotropic Heisenberg ring with twisted boundary conditions. Solving Bethe ansatz equations numerically, we calculate the dependence of the ground state energy on the total magnetic flux through the ring, and the resulting persistent current. Motivated by recent development of quantum entanglement theory, we study the properties of the ground state concurrence under the influence of the flux through the anisotropic Heisenberg ring. We also include an external magnetic field and discuss the properties of the persistent current and the concurrence in the presence of the magnetic field.Comment: 5 pages, 8 figure

Large-N scaling behavior of the quantum fisher information in the Dicke model

Quantum Fisher information (QFI) of the reduced two-atom state is employed to capture the quantum criticality of the superradiant phase transition in the Dicke model in the infinite size and finite-$N$ systems respectively. The analytical expression of the QFI of its ground state is evaluated explicitly. And finite-size scaling analysis is performed with the large accessible system size due to the effective bosonic coherent-state technique. We also investigate the large-size scaling behavior of the scaled QFI of the reduced $N$-atom state and show the accurate exponent.Comment: 6pages,2figure

Representations of Hopf Ore extensions of group algebras and pointed Hopf algebras of rank one

In this paper, we study the representation theory of Hopf-Ore extensions of group algebras and pointed Hopf algebras of rank one over an arbitrary field $k$. Let H=kG(\chi, a,\d) be a Hopf-Ore extension of $kG$ and $H'$ a rank one quotient Hopf algebra of $H$, where $k$ is a field, $G$ is a group, $a$ is a central element of $G$ and $\chi$ is a $k$-valued character for $G$ with $\chi(a)\neq 1$. We first show that the simple weight modules over $H$ and $H'$ are finite dimensional. Then we describe the structures of all simple weight modules over $H$ and $H'$, and classify them. We also consider the decomposition of the tensor product of two simple weight modules over $H'$ into the direct sum of indecomposable modules. Furthermore, we describe the structures of finite dimensional indecomposable weight modules over $H$ and $H'$, and classify them. Finally, when $\chi(a)$ is a primitive $n$-th root of unity for some $n>2$, we determine all finite dimensional indecomposable projective objects in the category of weight modules over $H'$.Comment: arXiv admin note: substantial text overlap with arXiv:1206.394