Rank $n$ swapping algebra for $operatorname{PGL}_n$ Fock-Goncharov $mathcal{X}$ moduli space

The {em rank $n$ swapping algebra} is a Poisson algebra defined on the set of ordered pairs of points of the circle using linking numbers, whose geometric model is given by a certain subspace of $(mathbb{K}^n times mathbb{K}^{n*})^r/operatorname{GL}(n,mathbb{K})$. For any ideal triangulation of $D_k$---a disk with $k$ points on its boundary, using determinants, we find an injective Poisson algebra homomorphism from the fraction algebra generated by the Fock--Goncharov coordinates for $mathcal{X}_{operatorname{PGL}_n,D_k}$ to the rank $n$ swapping multifraction algebra for $r=kcdot(n-1)$ with respect to the (Atiyah--Bott--)Goldman Poisson bracket and the swapping bracket. This is the building block of the general surface case. Two such injective Poisson algebra homomorphisms related to two ideal triangulations $mathcal{T}$ and $mathcal{T}$ are compatible with each other under the flips.

Swapping algebra, Virasoro algebra and discrete integrable system

We induce a Poisson algebra ${cdot,cdot}_{mathcal{C}_{n,N}}$ on the configuration space $mathcal{C}_{n,N}$ of $N$ twisted polygons in $mathbb{RP}^{n-1}$ from the swapping algebra cite{L12}, which is found coincide with Faddeev-Takhtajan-Volkov algebra for $n=2$. There is another Poisson algebra ${cdot,cdot}_{S2}$ on $mathcal{C}_{2,N}$ induced from the first Adler-Gelfand-Dickey Poissson algebra by Miura transformation. By observing that these two Poisson algebras are asymptotically related to the dual to the Virasoro algebra, finally, we prove that ${cdot,cdot}_{mathcal{C}_{2,N}}$ and ${cdot,cdot}_{S2}$ are Schouten commute.

Rank $n$ swapping algebra for the $operatorname{PSL}(n, mathbb{R})$ Hitchin component

F. Labourie [arXiv:1212.5015] characterized the Hitchin components for $operatorname{PSL}(n, mathbb{R})$ for any $n>1$ by using the swapping algebra, where the swapping algebra should be understood as a ring equipped with a Poisson bracket. We introduce the rank $n$ swapping algebra, which is the quotient of the swapping algebra by the $(n+1)times(n+1)$ determinant relations. The main results are the well-definedness of the rank $n$ swapping algebra and the cross-ratio in its fraction algebra. As a consequence, we use the sub fraction algebra of the rank $n$ swapping algebra generated by these cross-ratios to characterize the $operatorname{PSL}(n, mathbb{R})$ Hitchin component for a fixed $n>1$. We also show the relation between the rank $2$ swapping algebra and the cluster $mathcal{X}_{operatorname{PGL}(2,mathbb{R}),D_k}$-space.

Electronic structure in one-Fe Brillouin zone of iron-pnictide superconductor CsFe$_2$As$_2$

The multiband nature of iron-pnictide superconductors is one of the keys to the understanding of their intriguing behavior. The electronic and magnetic properties heavily rely on the multiband interactions between different electron and hole pockets near the Fermi level. At the fundamental level, though many theoretical models were constructed on the basis of the so-called 1-Fe Brillouin zone (BZ) with an emphasis of the basic square lattice of iron atoms, most electronic structure measurements were interpreted in the 2-Fe BZ. Whether the 1-Fe BZ is valid in a real system is still an open question. Using angle-resolved photoemission spectroscopy (ARPES), here we show in an extremely hole-doped iron-pnictide superconductor CsFe$_2$As$_2$ that the distribution of electronic spectral weight follows the 1-Fe BZ, and that the emerging band structure bears some features qualitatively different from theoretical band structures of the 1-Fe BZ. Our analysis suggests that the interlayer separation is an important tuning factor for the physics of FeAs layers, the increase of which can reduce the coupling between Fe and As and lead to the emergence of the electronic structure in accord with the 1-Fe symmetry of the Fe square lattice. Our finding puts strong constraints on the theoretical models constructed on the basis of the 1-Fe BZ.

Minority-spin $t_{2g}$ states and the degree of spin polarization in ferromagnetic metallic La$_{2-2x}$Sr$_{1+2x}$Mn$_2$O$_7$ ($x=0.38$)

Using angle-resolved photoemission spectroscopy (ARPES), we investigate the electronic band structure and Fermi surface of ferromagnetic La$_{2-2x}$Sr$_{1+2x}$Mn$_2$O$_7$ ($x=0.38$). Besides the expected two hole pockets and one electron pocket of majority-spin $e_g$ electrons, we show an extra electron pocket around the $Gamma$ point. A comparison with first-principles spin-polarized band-structure calculations shows that the extra electron pocket arises from $t_{2g}$ electrons of minority-spin character, indicating this compound is not a complete half-metallic ferromagnet, with similar expectations for lightly-doped cubic manganites. However, our data suggest that a complete half-metallic state is likely to be reached as long as the bandwidth is mildly reduced. Moreover, the band-resolved capability of ARPES enables us to investigate the band structure effects on spin polarization for different experimental conditions.

Evolution of band structure from optimally doped to heavily overdoped Co-substituted NaFeAs

Using angle-resolved photoemission spectroscopy, we studied the electronic structure of NaFe$_{1-x}$Co$_x$As from an optimally doped superconducting compound ($x=0.028$) to a heavily overdoped non-superconducting one ($x=0.109$). Similar to the case of 122 type iron pnictides, our data suggest that Co dopant in NaFe$_{1-x}$Co$_x$As supplies extra charge carriers and shifts the Fermi level accordingly. In the $x=0.109$ compound, the hole-like bands around the zone center $Gamma$ move to deeper binding energies and an electron pocket appears instead. The overall band renormalization remains basically the same throughout the doping range we studied, suggesting that the local magnetic/electronic correlations are not affected by carrier doping. We speculate that a balance between itinerant properties of mobile carriers and local interactions may play an important role for the superconductivity.

Non-monotonic Fermi surface evolution and its correlation with stripe ordering in bilayer manganites

In correlated electron systems such as cuprate superconductors and colossal magnetoresistive (CMR) oxides there is often a tendency for a nanoscale self-organization of electrons that can give rise to exotic properties and to extreme non-linear responses. The driving mechanisms for this self-organization are highly debated, especially in the CMR oxides in which two types of self-organized stripes of charge and orbital order coexist with each other. By utilizing angle-resolved photoemission spectroscopy measurements over a wide doping range, we show that one type of stripe is exclusively linked to long flat portions of nested Fermi surface, while the other type prefers to be commensurate with the real space lattice but also may be driven away from this by the Fermi surface. Complementarily, the Fermi surface also appears to be driven away from its non-interacting value at certain doping levels, giving rise to a host of unusual electronic properties.

Disentanglement in a quantum critical environment

We study the dynamical process of disentanglement of two qubits and two qutrits coupled to an Ising spin chain in a transverse field, which exhibits a quantum phase transition. We use the concurrence and negativity to quantify entanglement of two qubits and two qutrits, respectively. Explicit connections between the concurrence (negativity) and the decoherence factors are given for two initial states, the pure maximally entangled state and the mixed Werner state. We find that the concurrence and negativity decay exponentially with fourth power of time in the vicinity of critical point of the environmental system.