arXiv subjects

Akinori Tanaka

Publications and source records attributed to Akinori Tanaka.

44 records · Page 3Linked to original sources

arXiv2008

Ferromagnetic Pairing States on Two-Coupled Chains

We propose a concrete model which exhibits ferromagnetism and electron-pair condensation simultaneously. The model is defined on two chains and consists of the electron hopping term, the on-site Coulomb repulsion, and a ferromagnetic interaction which describes ferromagnetic coupling between two electrons, one on a bond in a chain and the other on a site in the other chain. It is rigorously shown that the model has fullypolarized ferromagnetic pairing ground states. The higher dimensional version of the model is also presented.

cond-mat.supr-con↗

arXiv2007

d-Wave Pairing State in Terms of the Zhang-Rice Singlets

In cuprate superconductors doping is believed to create holes on the O-sites, which couple antiferromagnetically with holes on the Cu-sites to form the so-called Zhang-Rice singlets. Here we study a d-wave pairing state based on the Zhang-Rice singlet states. Upper and lower bounds of an off-diagonal long-range order parameter with d-wave symmetry for this state are estimated. We also introduce a concrete model with on-site Coulomb repulsion and kinds of antiferromagnetic interactions whose ground state is this d-wave pairing state.

cond-mat.str-el↗

arXiv2007

Metallic ferromagnetism in the Hubbard model: A rigorous example

We present the first rigorous example of the Hubbard model in any dimensions which exhibits metallic ferromagnetism. The model is a genuine Hubbard model with short-range hopping and on-site Coulomb repulsion, and has multi single-electron bands. In the limit where the band gap and the Coulomb repulsion become infinite, we prove that the ground states are completely ferromagnetic and at the same time conducting.

cond-mat.str-el↗

arXiv2005

Physical realization of the four color problem in quantum systems

A multi-component electron model on a lattice is constructed whose ground state exhibits a spontaneous ordering which follows the rule of map-coloring used in the solution of the four color problem. The number of components is determined by the Euler characteristics of a certain surface into which the lattice is embedded. Combining the concept of chromatic polynomials with the Heawood-Ringel-Youngs theorem, we derive an index theorem relating the degeneracy of the ground state with a hidden topology of the lattice. The system exhibits coloring transition and hidden-topological structure transition. The coloring phase exhibits a topological order.

cond-mat.str-el↗

arXiv2005

Extended Hubbard Model with Unconventional Pairing in Two Dimensions

We rigorously prove that an extended Hubbard model with attraction in two dimensions has an unconventional pairing ground state for any electron filling. The anisotropic spin-0 or anisotropic spin-1 pairing symmetry is realized, depending on a phase parameter characterizing the type of local attractive interactions. In both cases the ground state is unique. It is also shown that in a special case, where there are no electron hopping terms, the ground state has Ising-type Néel order at half-filling, when on-site repulsion is furthermore added. Physical applications are mentioned.

cond-mat.str-el↗

arXiv2003

A Model of Strongly Correlated Electrons with Condensed Resonating-Valence-Bond Ground States

We propose a new exactly solvable model of strongly correlated electrons. The model is based on a $d$-$p$ model of the CuO$_2$ plane with infinitely large repulsive interactions on Cu-sites, and it contains additional correlated-hopping, pair-hopping and charge-charge interactions of electrons. For even numbers of electrons less than or equal to 2/3-filling, we construct the exact ground states of the model, all of which have the same energy and each of which is the unique ground state for a fixed electron number. It is shown that these ground states are the resonating-valence-bond states which are also regarded as condensed states in which all electrons are in a single two-electron state. We also show that the ground states exhibit off-diagonal long-range order.

cond-mat.str-el↗

arXiv2003

Exact Electron-Pairing Ground States of Tight-Binding Models with Local Attractive Interactions

We present a class of exactly solvable models of correlated electrons. The models are defined in any dimension $d$ and consist of electron-hopping terms and local attractive interactions between electrons. For each even number of electrons less than or equal to $1/(d+1)$-filling, we find the exact ground state in which all electrons form pairs of a certain type, and thus the models exhibit an electron-pair condensation.

cond-mat.str-el↗

arXiv2002

Stability of ferromagnetism in the Hubbard model on the kagomé lattice

The Hubbard model on the kagomé 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.

cond-mat.str-el↗