Topological phases and delocalization of quantum walks in random environments

We investigate one-dimensional (1D) discrete time quantum walks (QWs) with spatially or temporally random defects as a consequence of interactions with random environments. We focus on the QWs with chiral symmetry in a topological phase, and reveal that chiral symmetry together with bipartite nature of the QWs brings about intriguing behaviors such as coexistence of topologically protected edge states at zero energy and Anderson transitions in the 1D chiral class at non-zero energy in their dynamics. Contrary to the previous studies, therefore, the spatially disordered QWs can avoid complete localization due to the Anderson transition. It is further confirmed that the edge states are robust for spatial disorder but not for temporal disorder.Comment: 7 pages, 7 figure

Mott transitions in two-orbital Hubbard systems

We investigate the Mott transitions in two-orbital Hubbard systems. Applying the dynamical mean field theory and the self-energy functional approach, we discuss the stability of itinerant quasi-particle states in each band. It is shown that separate Mott transitions occur at different Coulomb interaction strengths in general. On the other hand, if some special conditions are satisfied for the interactions, spin and orbital fluctuations are equally enhanced at low temperatures, resulting in a single Mott transition. The phase diagrams are obtained at zero and finite temperatures. We also address the effect of the hybridization between two orbitals, which induces the Kondo-like heavy fermion states in the intermediate orbital-selective Mott phase.Comment: 21 Pages, 17 Figures, to appear in Progress of Theoretical Physics (YKIS2004 Proceedings

Spin Chains with Periodic Array of Impurities

We investigate the spin chain model composed of periodic array of two kinds of spins $S_1$ and $S_2$, which allows us to study the spin chains with impurities as well as the alternating spin chains in a unified fashion. By using the Lieb-Shultz-Mattis theorem, we first study the model rigorously, and then by mapping it to the non-linear sigma model, we extensively investigate low-energy properties with particular emphasis on the competition between the massive and massless phases.Comment: 5 pages, revtex, To appear in PR

Systematic Analysis of Frustration Effects in Anisotropic Checkerboard Lattice Hubbard Model

We study the ground state properties of the geometrically frustrated Hubbard model on the anisotropic checkerboard lattice with nearest-neighbor hopping $t$ and next nearest-neighbor hopping $t'$. By using the path-integral renormalization group method, we study the phase diagram in the parameter space of the Hubbard interaction $U$ and the frustration-control parameter $t'/t$. Close examinations of the effective hopping, the double occupancy, the momentum distribution and the spin/charge correlation functions allow us to determine the phase diagram at zero temperature, where the plaquette-singlet insulator emerges besides the antiferromagnetic insulator and the paramagnetic metal. Spin-liquid insulating states without any kind of symmetry breaking cannot be found in our frustrated model.Comment: 7pages, 5figure

Zero-temperature Phase Diagram of Two Dimensional Hubbard Model

We investigate the two-dimensional Hubbard model on the triangular lattice with anisotropic hopping integrals at half filling. By means of a self-energy functional approach, we discuss how stable the non-magnetic state is against magnetically ordered states in the system. We present the zero-temperature phase diagram, where the normal metallic state competes with magnetically ordered states with $(\pi, \pi)$ and $(2\pi/3, 2\pi/3)$ structures. It is shown that a non-magnetic Mott insulating state is not realized as the ground state, in the present framework, but as a meta-stable state near the magnetically ordered phase with $(2\pi/3, 2\pi/3)$ structure.Comment: 4 pages, 4 figure

Character Sequence Models for ColorfulWords

We present a neural network architecture to predict a point in color space from the sequence of characters in the color's name. Using large scale color--name pairs obtained from an online color design forum, we evaluate our model on a "color Turing test" and find that, given a name, the colors predicted by our model are preferred by annotators to color names created by humans. Our datasets and demo system are available online at colorlab.us

Exact Drude weight for the one-dimensional Hubbard model at finite temperatures

The Drude weight for the one-dimensional Hubbard model is investigated at finite temperatures by using the Bethe ansatz solution. Evaluating finite-size corrections to the thermodynamic Bethe ansatz equations, we obtain the formula for the Drude weight as the response of the system to an external gauge potential. We perform low-temperature expansions of the Drude weight in the case of half-filling as well as away from half-filling, which clearly distinguish the Mott-insulating state from the metallic state.Comment: 9 pages, RevTex, To appear in J. Phys.

Renormalized Harmonic-Oscillator Description of Confined Electron Systems with Inverse-Square Interaction

An integrable model for SU($\nu$) electrons with inverse-square interaction is studied for the system with confining harmonic potential. We develop a new description of the spectrum based on the {\it renormalized harmonic-oscillators} which incorporate interaction effects via the repulsion of energy levels. This approach enables a systematic treatment of the excitation spectrum as well as the ground-state quantities.Comment: RevTex, 7 page

Criteria of off-diagonal long-range order in Bose and Fermi systems based on the Lee-Yang cluster expansion method

The quantum-statistical cluster expansion method of Lee and Yang is extended to investigate off-diagonal long-range order (ODLRO) in one- and multi-component mixtures of bosons or fermions. Our formulation is applicable to both a uniform system and a trapped system without local-density approximation and allows systematic expansions of one- and multi-particle reduced density matrices in terms of cluster functions which are defined for the same system with Boltzmann statistics. Each term in this expansion can be associated with a Lee-Yang graph. We elucidate a physical meaning of each Lee-Yang graph; in particular, for a mixture of ultracold atoms and bound dimers, an infinite sum of the ladder-type Lee-Yang 0-graphs is shown to lead to Bose-Einstein condensation of dimers below the critical temperature. In the case of Bose statistics, an infinite series of Lee-Yang 1-graphs is shown to converge and gives the criteria of ODLRO at the one-particle level. Applications to a dilute Bose system of hard spheres are also made. In the case of Fermi statistics, an infinite series of Lee-Yang 2-graphs is shown to converge and gives the criteria of ODLRO at the two-particle level. Applications to a two-component Fermi gas in the tightly bound limit are also made.Comment: 21 pages, 10 figure

Correlated electron transport through double quantum dots coupled to normal and superconducting leads

We study Andreev transport through double quantum dots connected in series normal and superconducting (SC) leads, using the numerical renormalization group. The ground state of this system shows a crossover between a local Cooper-pairing singlet state and a Kondo singlet state, which is caused by the competition between the Coulomb interaction and the SC proximity. We show that the ground-state properties reflect this crossover especially for small values of the inter-dot coupling $t$, while in the opposite case, for large $t$, another singlet with an inter-dot character becomes dominant. We find that the conductance for the local SC singlet state has a peak with the unitary-limit value $4e^2/h$. In contrast, the Andreev reflection is suppressed in the Kondo regime by the Coulomb interaction. Furthermore, the conductance has two successive peaks in the transient region of the crossover. It is further elucidated that the gate voltage gives a different variation into the crossover. Specifically, as the energy level of the dot that is coupled to the normal lead varies, the Kondo screening cloud is deformed to a long-range singlet bond.Comment: 11 pages, 10 figure