arXiv subjects
Publications and source records attributed to Tadahiro Miyao.
We study the ground state properties of the Holstein-Hubbard model on some bipartite lattices at half-filling; The ground state is proved to exhibit ferrimagnetism whenever the electron-phonon interaction is not so strong. In addition, the antiferromagnetic long range order is shown to exist in the ground state. In contrast to this, we prove the absence of the long range charge order.
Nagaoka's theorem on ferromagnetism in the Hubbard model is extended to the Holstein-Hubbard model. This shows that Nagaoka's ferromagnetism is stable even if the electron-phonon interaction is taken into account. We also prove that Nagaoka's ferromagnetism is stable under the influence of the quantized radiation field.
This study investigated the extended Holstein--Hubbard model at half-filling as a model for describing interplay of the electron-electron and electron-phonon couplings. When the electron-phonon and nearest-neighbor electron-electron interactions are strong, we prove the existence of long-range charge order at sufficiently low temperature in three or more dimensions. As a result, we rigorously justify the phase competition between the antiferromagnetic and charge orders.
We rigorously investigated the charge-charge correlation function of the ionic Hubbard model in two dimensions by reflection positivity. We prove the existence of charge-density waves for large staggered potential $Δ$ (i.e., $\fracΔ{2}+2V>U$) at low temperatures, where $U$ and $V$ are the on-site and nearest-neighbor Coulomb repulsions, respectively. The results are consistent with previous numerical simulation results. We argue that the absence of charge-density waves for $Δ=0$ and $U$ are large enough (i.e., $U>\fracΔ{2}$+2V).
We present a general framework of Griffiths inequalities for quantum systems. Our approach is based on operator inequalities associated with self-dual cones and provides a consistent viewpoint of the Griffiths inequality. As examples, we discuss the quantum Ising model, quantum rotor model, Bose--Hubbard model, Hubbard model, and spin-1/2 quantum Heisenberg model. We present a model-independent structure that governs the correlation inequalities.
The Holstein model has been widely accepted as a model comprising electrons interacting with phonons; analysis of this model's ground states was accomplished two decades ago. However, the results were obtained without completely taking repulsive Coulomb interactions into account. Recent progress has made it possible to treat such interactions rigorously; in this paper, we study the Holstein--Hubbard model with repulsive Coulomb interactions. The ground state properties of the model are investigated; in particular, the ground state of the Hamiltonian is proven to be unique for an even number of electrons on a bipartite connected lattice. In addition, we provide a rigorous upper bound on charge susceptibility.
We propose a new method of constructing the quantum Griffiths inequality. From a viewpoint of operator inequalities, we first study the quantum rotor model. This viewpoint clarifies important connections between the reflection positivity and the Griffiths inequality. Next we apply our method to the spin-$1/2$ quantum Heisenberg model. Finally we point out a model-independent structure which governs the correlation inequalities.
We extend the Kubo-Kishi theorem concerning the charge susceptibility of the Hubbard model in the following way: (i) The electron-photon interaction is taken into account. (ii) Not only on-site but also general Coulomb repulsion is considered.
In condensed matter physics, the polaron has been fascinating subject. It is described by the Hamiltonian of H. Fröhlich. In this paper, the Fröhlich Hamiltonian is investigated from a viewpoint of the self-dual cone analysis proposed in Miyao (2011). This point of view clarifies the monotonicity of polaron energy, i.e., denoting the lowest energy of the Fröhlich Hamiltonian with the ultraviolet cutoff $Λ$ by $E_Λ$, we prove $E_Λ>E_{Λ'}$ for $Λ<Λ'$.
We construct a general theory of operator monotonicity and apply it to the Fröhlich polaron hamiltonian. This general theory provides a consistent viewpoint of the Fröhlich model.
We study the ground state energy for a system of two hydrogen atoms coupled to the quantized Maxwell field in the limit $α\to 0$ together with the relative distance between the atoms increasing as $α^{-γ} R$, $γ> 0$. In particular we determine explicitly the crossover function from the $R^{-6}$ van der Waals potential to the $R^{-7}$ retarded van der Waals potential, which takes place at scale $α^{-2} R$.
The retarded van-der-Waals potential, as first obtained by Casimir and Polder, is usually computed on the basis of nonrelativistic QED. The hamiltonian describes two infinitely heavy nuclei, charge $e$, separated by a distance $R$ and two spinless electrons, charge $-e$, nonrelativistically coupled to the quantized radiation field. Casimir and Polder use the dipole approximation and small coupling to the Maxwell field. We employ here the full hamiltonian and determine the asymptotic strength of the leading $-R^{-7}$ potential, which is valid for all $e$. Our computation is based on a path integral representation and expands in $1/R$, rather than in $e$.
Degeneracy of the eigenvalues of the Pauli-Fierz Hamiltonian with spin 1/2 is proven by the Kramers degeneracy theorem. The Pauli-Fierz Hamiltonian at fixed total momentum is also investigated.
We consider a charged particle, spin 1/2, with relativistic kinetic energy and minimally coupled to the quantized Maxwell field. Since the total momentum is conserved, the Hamiltonian admits a fiber decomposition as $H(P)$, $P\in \BbbR^3$. We study the spectrum of $H(P)$. In particular we prove that, for non-zero photon mass, the ground state is exactly two-fold degenerate and separated by a gap, uniformly in $P$, from the rest of the spectrum.
Within the framework of nonrelativisitic quantum electrodynamics we consider a single nucleus and $N$ electrons coupled to the radiation field. Since the total momentum $P$ is conserved, the Hamiltonian $H$ admits a fiber decomposition with respect to $P$ with fiber Hamiltonian $H(P)$. A stable atom, resp. ion, means that the fiber Hamiltonian $H(P)$ has an eigenvalue at the bottom of its spectrum. We establish the existence of a ground state for $H(P)$ under (i) an explicit bound on $P$, (ii) a binding condition, and (iii) an energy inequality. The binding condition is proven to hold for a heavy nucleus and the energy inequality for spinless electrons.