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

Unconventional Superconducting Symmetry in a Checkerboard Antiferromagnet

We use a renormalized mean field theory to study the Gutzwiller projected BCS states of the extended Hubbard model in the large $U$ limit, or the $t$-$t'$-$J$-$J'$ model on a two-dimensional checkerboard lattice. At small $t'/t$, the frustration due to the diagonal terms of $t'$ and $J'$ does not alter the $d_{x^2-y^2}$-wave pairing symmetry, and the negative (positive) $t'/t$ enhances (suppresses) the pairing order parameter. At large $t'/t$, the ground state has an extended s-wave symmetry. At the intermediate $t'/t$, the ground state is $d+id$ or $d+is$-wave with time reversal symmetry broken.Comment: 6 pages, 6 figure