Hierarchical Mean-Field Theories in Quantum Statistical Mechanics

We present a theoretical framework and a calculational scheme to study the coexistence and competition of thermodynamic phases in quantum statistical mechanics. The crux of the method is the realization that the microscopic Hamiltonian, modeling the system, can always be written in a hierarchical operator language that unveils all symmetry generators of the problem and, thus, possible thermodynamic phases. In general one cannot compute the thermodynamic or zero-temperature properties exactly and an approximate scheme named ``hierarchical mean-field approach'' is introduced. This approach treats all possible competing orders on an equal footing. We illustrate the methodology by determining the phase diagram and quantum critical point of a bosonic lattice model which displays coexistence and competition between antiferromagnetism and superfluidity.Comment: 4 pages, 2 psfigures. submitted Phys. Rev.

Superconductivity from correlated hopping

We consider a chain described by a next-nearest-neighbor hopping combined with a nearest-neighbor spin flip. In two dimensions this three-body term arises from a mapping of the three-band Hubbard model for CuO$_2$ planes to a generalized $t-J$ model and for large O-O hopping favors resonance-valence-bond superconductivity of predominantly $d$-wave symmetry. Solving the ground state and low-energy excitations by analytical and numerical methods we find that the chain is a Luther-Emery liquid with correlation exponent $K_{\rho} = (2-n)^2/2$, where $n$ is the particle density.Comment: 10 pages, RevTeX 3.0 + 2 PostScript figs. Accepted for publication in Phys.Rev.

Unveiling Order behind Complexity: Coexistence of Ferromagnetism and Bose-Einstein Condensation

We present an algebraic framework for identifying the order parameter and the possible phases of quantum systems that is based on identifying the local dimension $N$ of the quantum operators and using the SU(N) group representing the generators of generalized spin-particle mappings. We illustrate this for $N$=3 by presenting for any spatial dimension the exact solution of the bilinear-biquadratic $S$=1 quantum Heisenberg model at a high symmetry point. Through this solution we rigorously show that itinerant ferromagnetism and Bose-Einstein condensation may coexist.Comment: 5 pages, 1 psfigur

Quasiparticle photoemission intensity in doped two-dimensional quantum antiferromagnets

Using the self-consistent Born approximation, and the corresponding wave function of the magnetic polaron, we calculate the quasiparticle weight corresponding to destruction of a real electron (in contrast to creation of a spinless holon), as a funtion of wave vector for one hole in a generalized $t-J$ model and the strong coupling limit of a generalized Hubbard model. The results are in excellent agreement with those obtained by exact diagonalization of a sufficiently large cluster. Only the Hubbard weigth compares very well with photoemission measurements in Sr_2CuO_2Cl_2.Comment: 11 pages, latex, 3 figure

Charge and spin inhomogeneous phases in the Ferromagnetic Kondo Lattice Model

We study numerically the one-dimensional ferromagnetic Kondo lattice. This model is widely used to describe nickel and manganese perovskites. Due to the competition between double and super-exchange, we find a region where the formation of magnetic polarons induces a charge-ordered state. This ordering is present even in the absence of any inter-site Coulomb repulsion. There is an insulating gap associated to the charge structure formation. We also study the insulator-metal transition induced by a magnetic field which removes simultaneously both charge and spin ordering.Comment: 7 pages, 11 figure

Pairing Correlations in a Generalized Hubbard Model for the Cuprates

Using numerical diagonalization of a 4x4 cluster, we calculate on-site s, extended s and d pairing correlation functions (PCF) in an effective generalized Hubbard model for the cuprates, with nearest-neighbor correlated hopping and next nearest-neighbor hopping t'. The vertex contributions (VC) to the PCF are significantly enhanced, relative to the t-t'-U model. The behavior of the PCF and their VC, and signatures of anomalous flux quantization, indicate superconductivity in the d-wave channel for moderate doping and in the s-wave channel for high doping and small U.Comment: 5 pages, 5 figure

Ferromagnetism in the Strong Hybridization Regime of the Periodic Anderson Model

We determine exactly the ground state of the one-dimensional periodic Anderson model (PAM) in the strong hybridization regime. In this regime, the low energy sector of the PAM maps into an effective Hamiltonian that has a ferromagnetic ground state for any electron density between half and three quarters filling. This rigorous result proves the existence of a new magnetic state that was excluded in the previous analysis of the mixed valence systems.Comment: Accepted in Phys. Rev.

Efficiency of free energy calculations of spin lattices by spectral quantum algorithms

Quantum algorithms are well-suited to calculate estimates of the energy spectra for spin lattice systems. These algorithms are based on the efficient calculation of the discrete Fourier components of the density of states. The efficiency of these algorithms in calculating the free energy per spin of general spin lattices to bounded error is examined. We find that the number of Fourier components required to bound the error in the free energy due to the broadening of the density of states scales polynomially with the number of spins in the lattice. However, the precision with which the Fourier components must be calculated is found to be an exponential function of the system size.Comment: 9 pages, 4 figures; corrected typographical and minor mathematical error

Generalizations of entanglement based on coherent states and convex sets

Unentangled pure states on a bipartite system are exactly the coherent states with respect to the group of local transformations. What aspects of the study of entanglement are applicable to generalized coherent states? Conversely, what can be learned about entanglement from the well-studied theory of coherent states? With these questions in mind, we characterize unentangled pure states as extremal states when considered as linear functionals on the local Lie algebra. As a result, a relativized notion of purity emerges, showing that there is a close relationship between purity, coherence and (non-)entanglement. To a large extent, these concepts can be defined and studied in the even more general setting of convex cones of states. Based on the idea that entanglement is relative, we suggest considering these notions in the context of partially ordered families of Lie algebras or convex cones, such as those that arise naturally for multipartite systems. The study of entanglement includes notions of local operations and, for information-theoretic purposes, entanglement measures and ways of scaling systems to enable asymptotic developments. We propose ways in which these may be generalized to the Lie-algebraic setting, and to a lesser extent to the convex-cones setting. One of our original motivations for this program is to understand the role of entanglement-like concepts in condensed matter. We discuss how our work provides tools for analyzing the correlations involved in quantum phase transitions and other aspects of condensed-matter systems.Comment: 37 page

Identification of stingless bees (Hymenoptera: Apidae) in Kenya using Morphometrics and DNA barcoding

Stingless bees are important pollinators of wild plants and crops. The identity of stingless bee species in Africa has not been fully documented. The present study explored the utility of morphometrics and DNA barcoding for identification of African stingless bee populations, and to further employ these tools to identify potential cryptic variation within species. Stingless bee samples were collected from three ecological zones, namely Kakamega Forest, Mwingi and Arabuko-Sokoke Forest, which are geographically distant and cover high, medium and low altitudes, respectively. Forewing and hind leg morphometric characters were measured to determine the extent of morphological variation between the populations. DNA barcodes were generated from the mitochondrial cytochrome c-oxidase I (COI) gene. Principal Component Analysis (PCA) on the morphometric measurements separated the bee samples into three clusters: (1) Meliponula bocandei; (2) Meliponula lendliana + Plebeina hildebrandti; (3) Dactylurina schmidti + Meliponula ferruginea black + Meliponula ferruginea reddish brown, but Canonical Variate Analysis (CVA) separated all the species except the two morphospecies (M. ferruginea reddish brown and black). The analysis of the COI sequences showed that DNA barcoding can be used to identify all the species studied and revealed remarkable genetic distance (7.3%) between the two M. ferruginea morphs. This is the first genetic evidence that M. ferruginea black and M. ferruginea reddish brown are separate species