Universality of Entropy Scaling in 1D Gap-less Models

We consider critical models in one dimension. We study the ground state in thermodynamic limit [infinite lattice]. Following Bennett, Bernstein, Popescu, and Schumacher, we use the entropy of a sub-system as a measure of entanglement. We calculate the entropy of a part of the ground state. At zero temperature it describes entanglement of this part with the rest of the ground state. We obtain an explicit formula for the entropy of the subsystem at low temperature. At zero temperature we reproduce a logarithmic formula of Holzhey, Larsen and Wilczek. Our derivation is based on the second law of thermodynamics. The entropy of a subsystem is calculated explicitly for Bose gas with delta interaction, the Hubbard model and spin chains with arbitrary value of spin.Comment: A section on spin chains with arbitrary value of spin is included. The entropy of a subsystem is calculated explicitly as a function of spin. References update

Energy-level correlations in chiral symmetric disordered systems: Corrections to the universal results

We investigate the deviation of the level-correlation functions from the universal form for the chiral symmetric classes. Using the supersymmetric nonlinear sigma model we formulate the perturbation theory. The large energy behavior is compared with the result of the diagrammatic perturbation theory. We have the diffuson and cooperon contributions even in the average density of states. For the unitary and orthogonal classes we get the small energy behavior that suggests a weakening of the level repulsion. For the symplectic case we get a result with opposite tendency.Comment: 7 pages, revtex, 2 eps figures, references added, some minor change

Quantum Spin Chains and Riemann Zeta Function with Odd Arguments

Riemann zeta function is an important object of number theory. It was also used for description of disordered systems in statistical mechanics. We show that Riemann zeta function is also useful for the description of integrable model. We study XXX Heisenberg spin 1/2 anti-ferromagnet. We evaluate a probability of formation of a ferromagnetic string in the anti-ferromagnetic ground state in thermodynamics limit. We prove that for short strings the probability can be expressed in terms of Riemann zeta function with odd arguments.Comment: LaTeX, 7 page

Theoretical Analysis of Resonant Inelastic X-Ray Scattering Spectra in LaMnO3

We analyze the resonant inelastic x-ray scattering (RIXS) spectra at the K edge of Mn in the antiferromagnetic insulating manganite LaMnO3. We make use of the Keldysh-type Green-function formalism, in which the RIXS intensity is described by a product of an incident-photon-dependent factor and a density-density correlation function in the 3d states. We calculate the former factor using the 4p density of states given by an ab initio band structure calculation and the latter using a multi-orbital tight-binding model. The ground state of the model Hamiltonian is evaluated within the Hartree-Fock approximation. Correlation effects are treated within the random phase approximation (RPA). We obtain the RIXS intensity in a wide range of energy-loss 2-15 eV. The spectral shape is strongly modified by the RPA correlation, showing good agreement with the experiments. The incident-photon-energy dependence also agrees well with the experiments. The present mechanism that the RIXS spectra arise from band-to-band transitions to screen the core-hole potential is quite different from the orbiton picture previously proposed, enabling a comprehensive understanding of the RIXS spectra.Comment: 20 pages, 10 figures, To be published in PR

Dynamics of a single exciton in strongly correlated bilayers

We formulated an effective theory for a single interlayer exciton in a bilayer quantum antiferromagnet, in the limit that the holon and doublon are strongly bound onto one interlayer rung by the Coulomb force. Upon using a rung linear spin wave approximation of the bilayer Heisenberg model, we calculated the spectral function of the exciton for a wide range of the interlayer Heisenberg coupling \alpha=J_{\perp}/Jz. In the disordered phase at large \alpha, a coherent quasiparticle peak appears representing free motion of the exciton in a spin singlet background. In the N\'{e}el phase, which applies to more realistic model parameters, a ladder spectrum arises due to Ising confinement of the exciton. The exciton spectrum is visible in measurements of the dielectric function, such as c-axis optical conductivity measurements.Comment: 28 pages, 12 figure

Proximity-driven source of highly spin-polarized ac current on the basis of superconductor/weak ferromagnet/superconductor voltage-biased Josephson junction

We theoretically investigate an opportunity to implement a source of highly spin-polarized ac current on the basis of superconductor/weak ferromagnet/superconductor (SFS) voltage-biased junction in the regime of essential proximity effect and calculate the current flowing through the probe electrode tunnel coupled to the ferromagnetic interlayer region. It is shown that while the polarization of the dc current component is generally small in case of weak exchange field of the ferromagnet, there is an ac component of the current in the system. This ac current is highly spin-polarized and entirely originated from the non-equilibrium proximity effect in the interlayer. The frequency of the current is controlled by the voltage applied to SFS junction. We discuss a possibility to obtain a source of coherent ac currents with a certain phase shift between them by tunnel coupling two probe electrodes at different locations of the interlayer region.Comment: 8 pages, 5 figure

Non-regular eigenstate of the XXX model as some limit of the Bethe state

For the one-dimensional XXX model under the periodic boundary conditions, we discuss two types of eigenvectors, regular eigenvectors which have finite-valued rapidities satisfying the Bethe ansatz equations, and non-regular eigenvectors which are descendants of some regular eigenvectors under the action of the SU(2) spin-lowering operator. It was pointed out by many authors that the non-regular eigenvectors should correspond to the Bethe ansatz wavefunctions which have multiple infinite rapidities. However, it has not been explicitly shown whether such a delicate limiting procedure should be possible. In this paper, we discuss it explicitly in the level of wavefunctions: we prove that any non-regular eigenvector of the XXX model is derived from the Bethe ansatz wavefunctions through some limit of infinite rapidities. We formulate the regularization also in terms of the algebraic Bethe ansatz method. As an application of infinite rapidity, we discuss the period of the spectral flow under the twisted periodic boundary conditions.Comment: 53 pages, no figur

Anisotropy of the upper critical field in superconductors with anisotropic gaps. Anisotropy parameters of MgB2

The upper critical field Hc2 is evaluated for weakly-coupled two-band superconductors. By modeling the actual bands and the gap distribution of MgB2 by two Fermi surface spheroids with average parameters of the real material, we show that H_{c2,ab}/H_{c2,c} increases with decreasing temperature in agreement with available data.Comment: 4 pages, 2 figure

Cosmic Rays at the highest energies

After a century of observations, we still do not know the origin of cosmic rays. I will review the current state of cosmic ray observations at the highest energies, and their implications for proposed acceleration models and secondary astroparticle fluxes. Possible sources have narrowed down with the confirmation of a GZK-like spectral feature. The anisotropy observed by the Pierre Auger Observatory may signal the dawn of particle astronomy raising hopes for high energy neutrino observations. However, composition related measurements point to a different interpretation. A clear resolution of this mystery calls for much larger statistics than the reach of current observatories.Comment: 8 pages, 4 figures, in the Proceedings of TAUP 201

Ensemble Inequivalence and the Spin-Glass Transition

We report on the ensemble inequivalence in a many-body spin-glass model with integer spin. The spin-glass phase transition is of first order for certain values of the crystal field strength and is dependent whether it was derived in the microcanonical or the canonical ensemble. In the limit of infinitely many-body interactions, the model is the integer-spin equivalent of the random-energy model, and is solved exactly. We also derive the integer-spin equivalent of the de Almeida-Thouless line.Comment: 19 pages, 7 figure