Local Entanglement and quantum phase transition in spin models

Due to the phase interference of electromagnetic wave, one can recover the total image of one object from a small piece of holograph, which records the interference pattern of two laser light reflected from it. Similarly, the quantum superposition principle allows us to derive the global phase diagram of quantum spin models by investigating a proper local measurement. In the present paper, we study the two-site entanglement in the antifferomagnetic spin models with both spin-1/2 and 1. We show that its behaviors reveal some important information on the global properties and the quantum phase transition of these systems.Comment: 6 pages, 7 figure

Entanglement and quantum phase transitions

We examine several well known quantum spin models and categorize behavior of pairwise entanglement at quantum phase transitions. A unified picture on the connection between the entanglement and quantum phase transition is given.Comment: 4 pages, 3 figure

Reaction-Diffusion-Branching Models of Stock Price Fluctuations

Several models of stock trading [P. Bak et al, Physica A {\bf 246}, 430 (1997)] are analyzed in analogy with one-dimensional, two-species reaction-diffusion-branching processes. Using heuristic and scaling arguments, we show that the short-time market price variation is subdiffusive with a Hurst exponent $H=1/4$. Biased diffusion towards the market price and blind-eyed copying lead to crossovers to the empirically observed random-walk behavior ($H=1/2$) at long times. The calculated crossover forms and diffusion constants are shown to agree well with simulation data.Comment: 4 pages, 3 figure

The ground state entanglement in the XXZXXZ model

In this paper, we investigate spin entanglement in the $XXZ$ model defined on a $d$-dimensional bipartite lattice. The concurrence, a measure of the entanglement between two spins, is analyzed. We prove rigorously that the ground state concurrence reaches maximum at the isotropic point. For dimensionality $d \ge 2$, the concurrence develops a cusp at the isotropic point and we attribute it to the existence of magnetic long-range order.Comment: 5 pages, 2 figure

Constrain on possible pairing symmetry in a two-orbital model of FeAs-based superconductors

In this work, we establish a few exact identities through commutation of intra-orbital and inter-orbital on-site pairings with a two-orbital model describing newly discovered FeAs-based superconductors. Applying the conclusion drawn from rigorous relation and physical interpretation, we give constraints on the possible symmetries of the superconducting pairing of the model. Hence the favorable pairings in newly discovered high-temperature oxypnictide superconductors are proposed.Comment: 5 pages, 2 figure

Matrix Product State and Quantum Phase Transitions in the One-Dimensional Extended Quantum Compass Model

The matrix product state (MPS) is utilized to study the ground state properties and quantum phase transitions (QPTs) of the one-dimensional quantum compass model (QCM). The MPS wavefunctions are argued to be very efficient descriptions of QCM ground states, and are numerically determined by imaginary time projections. The ground state energy, correlations, quantum entanglement and its spectrum, local and nonlocal order parameters, etc., are calculated and studied in details. It is revealed that the bipartite and block entanglement entropies, as well as the nearest neighbor correlation functions can be used to detect the second-order QPTs, but not the first-order ones, while fidelity detections can recognize both. The entanglement spectrum is extracted from the MPS wavefunction, and found to be doubly degenerate in disordered phases of QCM, where non-local string order parameters exist. Moreover, with linearized tensor renormalization group method, the specific heat curves are evaluated and their low temperature behaviors are investigated.Comment: 12 pages, 19 figure

Some exact results for the multicomponent t-J model

We present a generalization of the Sutherland's multicomponent model. Our extension includes both the ferromagnetic and the antiferromagnetic t-J model for any value of the exchange coupling J and the hopping parameter t. We prove rigorously that for one dimensional chains the ground-state of the generalized model is non-degenerate. As a consequence, the ordering of energy levels of the antiferromagnetic t-J model is determined. Our result rigorously proves and extends the analysis carried out by Sutherland in establishing the phase diagram of the model as a function of the number of components.Comment: 11 pages, RevTeX 3.0, no figure

Charged and spin-excitation gaps in half-filled strongly correlated electron systems: A rigorous result

By exploiting the particle-hole symmetries of the Hubbard model, the periodic Anderson model and the Kondo lattice model at half-filling and applying a generalized version of Lieb's spin-reflection positivity method, we show that the charged gaps of these models are always larger than their spin excitation gaps. This theorem confirms the previous results derived by either the variational approach or the density renormalization group approach.Comment: 20 pages, no figur

Divergent Evolution of TRC Genes in Mammalian Niche Adaptation

Mammals inhabit a wide variety of ecological niches, which in turn can be affected by various ecological factors, especially in relation to immunity. The canonical TRC repertoire (TRAC, TRBC, TRGC, and TRDC) codes C regions of T cell receptor chains that form the primary antigen receptors involved in the activation of cellular immunity. At present, little is known about the correlation between the evolution of mammalian TRC genes and ecological factors. In this study, four types canonical of TRC genes were identified from 37 mammalian species. Phylogenetic comparative methods (phyANOVA and PGLS) and selective pressure analyses among different groups of ecological factors (habitat, diet, and sociality) were carried out. The results showed that habitat was the major ecological factor shaping mammalian TRC repertoires. Specifically, trade-off between TRGC numbers and positive selection of TRAC and the balanced evolutionary rates between TRAC and TRDC genes were speculated as two main mechanisms in adaption to habitat and sociality. Overall, our study suggested divergent mechanisms for the evolution of TRCs, prompting mammalian immunity adaptions within diverse niches

Osteocalcin Ameliorates Motor Dysfunction in a 6-Hydroxydopamine-Induced Parkinson’s Disease Rat Model Through AKT/GSK3β Signaling

Osteoblasts derived osteocalcin (OCN) is recently reported to be involved in dopaminergic neuronal development. As dopaminergic neuronal injury in the substantia nigra (SN) is a pathological hallmark of Parkinson’s disease (PD), we investigated whether OCN could exert protective effects on 6-hydroxydopamine (6-OHDA)-induced PD rat model. Our data showed that the OCN level in the cerebrospinal fluid (CSF) in PD rat models was significantly lower than that in controls. Intervention with OCN could improve the behavioral dysfunction in PD rat models and reduce the tyrosine hydroxylase (TH) loss in the nigrostriatal system. In addition, OCN could inhibit the astrocyte and microglia proliferation in the SN of PD rats. In vitro studies showed that OCN significantly ameliorated the neurotoxicity of 6-OHDA through the AKT/GSK3β signaling pathway. In summary, OCN plays a protective role against parkinsonian neurodegeneration in the PD rat model, suggesting a potential therapeutic use of OCN in PD