Theory of RIXS in strongly correlated electron systems: Mott gap excitations in cuprates

We theoretically examine the momentum dependence of resonant inelastic x-ray scattering (RIXS) spectrum for one-dimensional and two-dimensional cuprates based on the single-band Hubbard model with realistic parameter values. The spectrum is calculated by using the numerical diagonalization technique for finite-size clusters. We focus on excitations across the Mott gap and clarify spectral features coming from the excitations as well as the physics behind them. Good agreement between the theoretical and existing experimental results clearly demonstrates that the RIXS is a potential tool to study the momentum-dependent charge excitations in strongly correlated electron systems.Comment: 9 pages, 8 figures, Proceedings of 5th International Conference on Inelastic X-ray Scattering (IXS 2004

Moebius Structure of the Spectral Space of Schroedinger Operators with Point Interaction

The Schroedinger operator with point interaction in one dimension has a U(2) family of self-adjoint extensions. We study the spectrum of the operator and show that (i) the spectrum is uniquely determined by the eigenvalues of the matrix U belonging to U(2) that characterizes the extension, and that (ii) the space of distinct spectra is given by the orbifold T^2/Z_2 which is a Moebius strip with boundary. We employ a parametrization of U(2) that admits a direct physical interpretation and furnishes a coherent framework to realize the spectral duality and anholonomy recently found. This allows us to find that (iii) physically distinct point interactions form a three-parameter quotient space of the U(2) family.Comment: 16 pages, 2 figure

Exact diagonalization study of optical conductivity in two-dimensional Hubbard model

The optical conductivity \sigma(\omega) in the two-dimensional Hubbard model is examined by applying the exact diagonalization technique to small square clusters with periodic boundary conditions up to \sqrt{20} X \sqrt{20} sites. Spectral-weight distributions at half filling and their doping dependence in the 20-site cluster are found to be similar to those in a \sqrt{18} X \sqrt{18} cluster, but different from 4 X 4 results. The results for the 20-site cluster enable us to perform a systematic study of the doping dependence of the spectral-weight transfer from the region of the Mott-gap excitation to lower-energy regions. We discuss the dependence of the Drude weight and the effective carrier number on the electron density at a large on-site Coulomb interaction.Comment: 5 pages, 5 figure

Lattice study of semileptonic form factors with twisted boundary conditions

We apply twisted boundary conditions to lattice QCD simulations of three-point correlation functions in order to access spatial components of hadronic momenta different from the integer multiples of 2 pi / L. We calculate the vector and scalar form factors relevant to the K -> pi semileptonic decay and consider all the possible ways of twisting one of the quark lines in the three-point functions. We show that the momentum shift produced by the twisted boundary conditions does not introduce any additional noise and easily allows to determine within a few percent statistical accuracy the form factors at quite small values of the four-momentum transfer, which are not accessible when periodic boundary conditions are considered. The use of twisted boundary conditions turns out to be crucial for a precise determination of the form factor at zero-momentum transfer, when a precise lattice point sufficiently close to zero-momentum transfer is not accessible with periodic boundary conditions.Comment: latex 15 pages, 4 figures and 3 tables; modified intro and discussions of the results; version to appear in PR

Entanglement of Indistinguishable Particles

We present a general criterion for entanglement of N indistinguishable particles decomposed into arbitrary s subsystems based on the unambiguous measurability of correlation. Our argument provides a unified viewpoint on the entanglement of indistinguishable particles, which is still unsettled despite various proposals made mainly for the s = 2 case. Even though entanglement is defined only with reference to the measurement setup, we find that the so-called i.i.d. states form a special class of bosonic states which are universally separable.Comment: 6 pages, 3 figures, major revisio

Temperature dependence of spinon and holon excitations in one-dimensional Mott insulators

Motivated by the recent angle-resolved photoemission spectroscopy (ARPES) measurements on one-dimensional Mott insulators, SrCuO${}_{2}$ and Na${}_{0.96}$V${}_{2}$O${}_{5}$, we examine the single-particle spectral weight of the one-dimensional (1D) Hubbard model at half-filling. We are particularly interested in the temperature dependence of the spinon and holon excitations. For this reason, we have performed the dynamical density matrix renormalization group and determinantal quantum Monte Carlo (QMC) calculations for the single-particle spectral weight of the 1D Hubbard model. In the QMC data, the spinon and holon branches become observable at temperatures where the short-range antiferromagnetic correlations develop. At these temperatures, the spinon branch grows rapidly. In the light of the numerical results, we discuss the spinon and holon branches observed by the ARPES experiments on SrCuO${}_{2}$. These numerical results are also in agreement with the temperature dependence of the ARPES results on Na${}_{0.96}$V${}_{2}$O${}_{5}$.Comment: 8 pages, 8 figure

Resonant Two-Magnon Raman Scattering and Photoexcited States in Two-Dimensional Mott Insulators

We investigate the resonant two-magnon Raman scattering in two-dimensional (2D) Mott insulators by using a half-filled 2D Hubbard model in the strong coupling limit. By performing numerical diagonalization calculations for small clusters, we find that the Raman intensity is enhanced when the incoming photon energy is not near the optical absorption edge but well above it, being consistent with experimental data. The absence of resonance near the gap edge is associated with the presence of background spins, while photoexcited states for resonance are found to be characterized by the charge degree of freedom. The resonance mechanism is different from those proposed previously.Comment: REVTeX4, 4 pages, 3 figures, to be published in Phys. Rev. Let

Multi-population genetic algorithms with immigrants scheme for dynamic shortest path routing problems in mobile ad hoc networks

Copyright @ Springer-Verlag Berlin Heidelberg 2010.The static shortest path (SP) problem has been well addressed using intelligent optimization techniques, e.g., artificial neural networks, genetic algorithms (GAs), particle swarm optimization, etc. However, with the advancement in wireless communications, more and more mobile wireless networks appear, e.g., mobile ad hoc network (MANET), wireless mesh network, etc. One of the most important characteristics in mobile wireless networks is the topology dynamics, that is, the network topology changes over time due to energy conservation or node mobility. Therefore, the SP problem turns out to be a dynamic optimization problem in mobile wireless networks. In this paper, we propose to use multi-population GAs with immigrants scheme to solve the dynamic SP problem in MANETs which is the representative of new generation wireless networks. The experimental results show that the proposed GAs can quickly adapt to the environmental changes (i.e., the network topology change) and produce good solutions after each change.This work was supported by the Engineering and Physical Sciences Research Council(EPSRC) of UK under Grant EP/E060722/1

Theoretical study of angle-resolved two-photon photoemission in two-dimensional insulating cuprates

We propose angle-resolved two-photon photoemission spectroscopy (AR-2PPES) as a technique to detect the location of the bottom of the upper Hubbard band (UHB) in two-dimensional insulating cuprates. The AR-2PPES spectra are numerically calculated for small Hubbard clusters. When the pump photon excites an electron from the lower Hubbard band, the bottom of the UHB is less clear, but when an electron in the nonbonding oxygen band is excited, the bottom of the UHB can be identified clearly, accompanied with additional spectra originated from the spin-wave excitation at half filling.Comment: 5 pages, 4 figure