Non-Poissonian level spacing statistics of classically integrable quantum systems based on the Berry-Robnik approach

Along the line of thoughts of Berry and Robnik\cite{[1]}, we investigated the gap distribution function of systems with infinitely many independent components, and discussed the level-spacing distribution of classically integrable quantum systems. The level spacing distribution is classified into three cases: Case 1: Poissonian if $\bar{\mu}(+\infty)=0$, Case 2: Poissonian for large $S$, but possibly not for small $S$ if $0<\bar{\mu}(+\infty)< 1$, and Case 3: sub-Poissonian if $\bar{\mu}(+\infty)=1$. Thus, even when the energy levels of individual components are statistically independent, non-Poisson level spacing distributions are possible.Comment: 5 pages, 0 figur

Long-Range Spectral Statistics of Classically Integrable Systems --Investigation along the Line of the Berry-Robnik Approach--

Extending the argument of Ref.\citen{[4]} to the long-range spectral statistics of classically integrable quantum systems, we examine the level number variance, spectral rigidity and two-level cluster function. These observables are obtained by applying the approach of Berry and Robnik\cite{[0]} and the mathematical framework of Pandey \cite{[2]} to systems with infinitely many components, and they are parameterized by a single function $\bar{c}$, where $\bar{c}=0$ corresponds to Poisson statistics, and $\bar{c}\not=0$ indicates deviations from Poisson statistics. This implies that even when the spectral components are statistically independent, non-Poissonian spectral statistics are possible.Comment: 13 pages, 4 figure

Flat-Bands on Partial Line Graphs -- Systematic Method for Generating Flat-Band Lattice Structures

We introduce a systematic method for constructing a class of lattice structures that we call ``partial line graphs''.In tight-binding models on partial line graphs, energy bands with flat energy dispersions emerge.This method can be applied to two- and three-dimensional systems. We show examples of partial line graphs of square and cubic lattices. The method is useful in providing a guideline for synthesizing materials with flat energy bands, since the tight-binding models on the partial line graphs provide us a large room for modification, maintaining the flat energy dispersions.Comment: 9 pages, 4 figure

Stability of ferromagnetism in the Hubbard model on the kagom\'e lattice

The Hubbard model on the kagom\'e lattice has highly degenerate ground states (the flat lowest band) in the corresponding single-electron problem and exhibits the so-called flat-band ferromagnetism in the many-electron ground states as was found by Mielke. Here we study the model obtained by adding extra hopping terms to the above model. The lowest single-electron band becomes dispersive, and there is no band gap between the lowest band and the other band. We prove that, at half-filling of the lowest band, the ground states of this perturbed model remain saturated ferromagnetic if the lowest band is nearly flat.Comment: 4 pages, 1 figur

Exact many-electron ground states on the diamond Hubbard chain

Exact ground states of interacting electrons on the diamond Hubbard chain in a magnetic field are constructed which exhibit a wide range of properties such as flat-band ferromagnetism and correlation induced metallic, half-metallic or insulating behavior. The properties of these ground states can be tuned by changing the magnetic flux, local potentials, or electron density.Comment: 4 pages, 2 figure

Gapless Excitation above a Domain Wall Ground State in a Flat Band Hubbard Model

We construct a set of exact ground states with a localized ferromagnetic domain wall and with an extended spiral structure in a deformed flat-band Hubbard model in arbitrary dimensions. We show the uniqueness of the ground state for the half-filled lowest band in a fixed magnetization subspace. The ground states with these structures are degenerate with all-spin-up or all-spin-down states under the open boundary condition. We represent a spin one-point function in terms of local electron number density, and find the domain wall structure in our model. We show the existence of gapless excitations above a domain wall ground state in dimensions higher than one. On the other hand, under the periodic boundary condition, the ground state is the all-spin-up or all-spin-down state. We show that the spin-wave excitation above the all-spin-up or -down state has an energy gap because of the anisotropy.Comment: 26 pages, 1 figure. Typos are fixe

Magnetic field effects on two-dimensional Kagome lattices

Magnetic field effects on single-particle energy bands (Hofstadter butterfly), Hall conductance, flat-band ferromagnetism, and magnetoresistance of two-dimensional Kagome lattices are studied. The flat-band ferromagnetism is shown to be broken as the flat-band has finite dispersion in the magnetic field. A metal-insulator transition induced by the magnetic field (giant negative magnetoresistance) is predicted. In the half-filled flat band, the ferromagnetic-paramagnetic transition and the metal-insulator one occur simultaneously at a magnetic field for strongly interacting electrons. All of the important magnetic fields effects should be observable in mesoscopic systems such as quantum dot superlattices.Comment: 10 pages, 4 figures, and 1 tabl

Cr-doping effect on the orbital fluctuation of heavily doped Nd1-xSrxMnO3 (x ~ 0.625)

We have investigated the Cr-doping effect of Nd0.375Sr0.625MnO3 near the phase boundary between the x2-y2 and 3z2-r2 orbital ordered states, where a ferromagnetic correlation and concomitant large magnetoresistance are observed owing to orbital fluctuation. Cr-doping steeply suppresses the ferromagnetic correlation and magnetoresistance in Nd0.375Sr0.625Mn1-yCryO3 with 0 < y < 0.05, while they reappear in 0.05 < y < 0.10. Such a reentrant behavior implies that a phase boundary is located at y = 0.05, or a phase crossover occurs across y = 0.05.Comment: 3 pages, 3 figures, to be published in Journal of Applied Physic

An Information--Theoretic Equality Implying the Jarzynski Relation

We derive a general information-theoretic equality for a system undergoing two projective measurements separated by a general temporal evolution. The equality implies the non-negativity of the mutual information between the measurement outcomes of the earlier and later projective measurements. We show that it also contains the Jarzynski relation between the average exponential of the thermodynamical work and the exponential of the difference between the initial and final free energy. Our result elucidates the information-theoretic underpinning of thermodynamics and explains why the Jarzynski relation holds identically both quantumly as well as classically.Comment: 2 pages, no figure