arXiv subjects

Kensuke Tamura

Publications and source records attributed to Kensuke Tamura.

5 recordsLinked to original sources

arXiv2026

Another proof of the result on rotation compatible planar covers

Negami's Planar Cover Conjecture asserts that a connected graph has a finite planar cover if and only if it can be embedded on the projective plane. While this statement has already been proven for rotation compatible planar covers, namely covers equipped with a certain condition on the rotation system, the existing proof relies on advanced algebraic and topological methods. In this paper, we provide another proof of this result, focusing primarily on combinatorial arguments based on a structural analysis with respect to a spanning tree in the base graph.

math.CO↗

arXiv2023

Flat-band ferromagnetism in the SU($N$) Hubbard and Kondo lattice models

We develop a general theory of flat-band ferromagnetism in the SU($N$) Fermi-Hubbard model, which describes the behavior of $N$-component fermions with SU($N$) symmetric interactions. We focus on the case where the single-particle spectrum has a flat band and establish a necessary and sufficient condition for the SU($N$) Hubbard model to exhibit ferromagnetism when the number of particles is the same as the degeneracy. We show that the occurrence of ferromagnetism is equivalent to the irreducibility of the projection matrix onto the space of single-particle ground states. We also demonstrate that this result can be exploited to establish a rigorous result for the ferromagnetic SU($N$) Kondo lattice model with a flat band. Specifically, we prove that when the SU($N$) Hubbard model is ferromagnetic, the ferromagnetic SU($N$) Kondo lattice model with the same hopping matrix also exhibits SU($N$) ferromagnetism.

cond-mat.str-el↗

arXiv2022

Quantum many-body scars of spinless fermions with density-assisted hopping in higher dimensions

We introduce a class of spinless fermion models that exhibit quantum many-body scars (QMBS) originating from kinetic constraints in the form of density-assisted hopping. The models can be defined on any lattice in any dimension and allow for spatially varying interactions. We construct a tower of exact eigenstates with finite energy density, and we demonstrate that these QMBS are responsible for the nonthermal nature of the system by studying the entanglement entropy and correlation functions. The quench dynamics from certain initial states is also investigated, and it is confirmed that the QMBS induce nonthermalizing dynamics. As another characterization of the QMBS, we give a parent Hamiltonian for which the QMBS are unique ground states. We also prove the uniqueness rigorously.

quant-ph↗

arXiv2020

Ferromagnetism in $d$-dimensional SU($n$) Hubbard models with nearly flat bands

We present rigorous results for the SU($n$) Fermi-Hubbard models with finite-range hopping in $d$ ($\ge 2$) dimensions. The models are defined on a class of decorated lattices. We first study the models with flat bands at the bottom of the single-particle spectrum and prove that the ground states exhibit SU($n$) ferromagnetism when the number of particles is equal to the number of unit cells. We then perturb the models by adding particular hopping terms and make the bottom bands dispersive. Under the same filling condition, it is proved that the ground states remain SU($n$) ferromagnetic when the bottom bands are sufficiently flat and the Coulomb repulsion is sufficiently large.

cond-mat.str-el↗

arXiv2020

Ferromagnetism in the SU($n$) Hubbard model with a nearly flat band

We present rigorous results for the SU($n$) Fermi-Hubbard model on the railroad-trestle lattice. We first study the model with a flat band at the bottom of the single-particle spectrum and prove that the ground states exhibit SU($n$) ferromagnetism when the total fermion number is the same as the number of unit cells. We then perturb the model by adding extra hopping terms and make the flat band dispersive. Under the same filling condition, it is proved that the ground states of the perturbed model remain SU($n$) ferromagnetic when the bottom band is nearly flat. This is the first rigorous example of the ferromagnetism in nonsingular SU($n$) Hubbard models in which both the single-particle density of states and the on-site repulsive interaction are finite.

cond-mat.str-el↗