Classification of the phases of 1D spin chains with commuting Hamiltonians

We consider the class of spin Hamiltonians on a 1D chain with periodic boundary conditions that are (i) translational invariant, (ii) commuting and (iii) scale invariant, where by the latter we mean that the ground state degeneracy is independent of the system size. We correspond a directed graph to a Hamiltonian of this form and show that the structure of its ground space can be read from the cycles of the graph. We show that the ground state degeneracy is the only parameter that distinguishes the phases of these Hamiltonians. Our main tool in this paper is the idea of Bravyi and Vyalyi (2005) in using the representation theory of finite dimensional C^*-algebras to study commuting Hamiltonians.Comment: 8 pages, improved readability, added exampl

The correlation energy functional within the GW-RPA approximation: exact forms, approximate forms and challenges

In principle, the Luttinger-Ward Green's function formalism allows one to compute simultaneously the total energy and the quasiparticle band structure of a many-body electronic system from first principles. We present approximate and exact expressions for the correlation energy within the GW-RPA approximation that are more amenable to computation and allow for developing efficient approximations to the self-energy operator and correlation energy. The exact form is a sum over differences between plasmon and interband energies. The approximate forms are based on summing over screened interband transitions. We also demonstrate that blind extremization of such functionals leads to unphysical results: imposing physical constraints on the allowed solutions (Green's functions) is necessary. Finally, we present some relevant numerical results for atomic systems.Comment: 3 figures and 3 tables, under review at Physical Review

The Importance of Worldviews on Women’s Leadership to HRD

Problem: The challenges faced by women in leadership, to some extent, appear throughout the word, across country-based cultures and religious traditions, even where there has been progress. The eight articles that comprise this issue raise questions related to women in leadership, providing a cross-case opportunity to explore what might yet be needed to empower women in leadership roles in business, politics, non-government organizations, academia, and the family. The Solution: There are no easy solutions that emerge from our analysis across these eight articles. Worldviews influence women in leadership; from these articles, we understand the influences better and glimpse opportunities for improving the status of women leaders, globally, as well as within specific countries and religious traditions. We also suggest perspectives that might lead to valuable studies that will help/pave the way for developing future women leaders. Stakeholders: HR scholars and practitioners, potential and current women leaders, and those working with or accommodating women leaders in multiple contexts are the main stakeholders of this issue. Furthermore, because this is the concluding article to this issue, all of the stakeholders listed with each article will be interested in our overall conclusions to this issue

Operator-valued Schatten spaces and quantum entropies

Operator-valued Schatten spaces were introduced by G. Pisier as a noncommutative counterpart of vector-valued $\ell_p$-spaces. This family of operator spaces forms an interpolation scale which makes it a powerful and convenient tool in a variety of applications. In particular, as the norms coming from this family naturally appear in the definition of certain entropic quantities in Quantum Information Theory (QIT), one may apply Pisier's theory to establish some features of those quantities. Nevertheless, it could be quite challenging to follow the proofs of the main results of this theory from the existing literature. In this article, we attempt to fill this gap by presenting the underlying concepts and ideas of Pisier's theory in an almost self-contained way which we hope to be more accessible, especially for the QIT community at large. Furthermore, we describe some applications of this theory in QIT. In particular, we prove a new uniform continuity bound for the quantum conditional R\'enyi entropy.Comment: 41 page

Graph Concatenation for Quantum Codes

Graphs are closely related to quantum error-correcting codes: every stabilizer code is locally equivalent to a graph code, and every codeword stabilized code can be described by a graph and a classical code. For the construction of good quantum codes of relatively large block length, concatenated quantum codes and their generalizations play an important role. We develop a systematic method for constructing concatenated quantum codes based on "graph concatenation", where graphs representing the inner and outer codes are concatenated via a simple graph operation called "generalized local complementation." Our method applies to both binary and non-binary concatenated quantum codes as well as their generalizations.Comment: 26 pages, 12 figures. Figures of concatenated [[5,1,3]] and [[7,1,3]] are added. Submitted to JM

Regioselective iodination of aryl amines using 1,4-dibenzyl-1,4-diazoniabicyclo [2.2.2] octane dichloroiodate in solution and under solvent-free conditions

1,4-Dibenzyl-1,4-diazoniabicyclo[2.2.2]octane dichloroiodate is an efficient and regioselective reagent for iodination of aryl amines. A wide variety of aryl amines in reaction with this reagent afforded regioselectively iodinated products. The iodination reaction can be carried out in solution or under solvent-free condition at room temperature. KEY WORDS:  Regioselective iodination, Aryl amines, 1,4-Dibenzyl-1,4-diazoniabicyclo [2.2.2] octane dichloroiodate,  Solvent-free conditions Bull. Chem. Soc. Ethiop. 2015, 29(1), 157-162DOI: http://dx.doi.org/10.4314/bcse.v29i1.1

Approximating the Set of Separable States Using the Positive Partial Transpose Test

The positive partial transpose test is one of the main criteria for detecting entanglement, and the set of states with positive partial transpose is considered as an approximation of the set of separable states. However, we do not know to what extent this criterion, as well as the approximation, are efficient. In this paper, we show that the positive partial transpose test gives no bound on the distance of a density matrix from separable states. More precisely, we prove that, as the dimension of the space tends to infinity, the maximum trace distance of a positive partial transpose state from separable states tends to 1. Using similar techniques, we show that the same result holds for other well-known separability criteria such as reduction criterion, majorization criterion and symmetric extension criterion. We also bring an evidence that the sets of positive partial transpose states and separable states have totally different shapes.Comment: 12 pages, published versio