arXiv subjects

Tohru Koma

Publications and source records attributed to Tohru Koma.

45 records · Page 3Linked to original sources

arXiv1999

Spectral Gaps of Quantum Hall Systems with Interactions

A two-dimensional quantum Hall system without disorder for a wide class of interactions including any two-body interaction with finite range is studied by using the Lieb-Schultz-Mattis method [{\it Ann. Phys. (N.Y.)} {\bf 16}: 407 (1961)]. The model is defined on an infinitely long strip with a fixed large width, and the Hilbert space is restricted to the lowest $(n_{\rm max}+1)$ Landau levels with a large integer $n_{\rm max}$. We proved that, for a non-integer filling $ν$ of the Landau levels, either (i) there is a symmetry breaking at zero temperature or (ii) there is only one infinite-volume ground state with a gapless excitation. We also proved the following two theorems: (a) If a pure infinite-volume ground state has a non-zero excitation gap for a non-integer filling $ν$, then a translational symmetry breaking occurs at zero temperature. (b) Suppose that there is no non-translationally invariant infinite-volume ground state. Then, if a pure infinite-volume ground state has a non-zero excitation gap, the filling factor $ν$ must be equal to a rational number. Here the ground state is allowed to have a periodic structure which is a consequence of the translational symmetry breaking. We also discuss the relation between our results and the quantized Hall conductance, and phenomenologically explain why odd denominators of filling fractions $ν$ giving the quantized Hall conductance, are favored exclusively.

cond-mat.mes-hall↗

arXiv1999

Insensitivity of Quantized Hall Conductance to Disorder and Interactions

A two-dimensional quantum Hall system is studied for a wide class of potentials including single-body random potentials and repulsive electron-electron interactions. We assume that there exists a non-zero excitation gap above the ground state(s), and then the conductance is derived from the linear perturbation theory with a sufficiently weak electric field. Under these two assumptions, we proved that the Hall conductance $σ_{xy}$ and the diagonal conductance $σ_{yy}$ satisfy $|σ_{xy}+e^2ν/h|\le{\rm const.}L^{-1/12}$ and $|σ_{yy}|\le{\rm const.}L^{-1/12}$. Here $e^2/h$ is the universal conductance with the charge $-e$ of electron and the Planck constant $h$; $ν$ is the filling factor of the Landau level, and $L$ is the linear dimension of the system. In the thermodymanic limit, our results show $σ_{xy}=-e^2ν/h$ and $σ_{yy}=0$. The former implies that integral and fractional filling factors $ν$ with a gap lead to, respectively, integral and fractional quantizations of the Hall conductance.

cond-mat.mes-hall↗

arXiv1998

Scattering of Conduction Electrons by a Ferromagnetic Domain Wall

We study the scattering of an electron by a ferromagnetic domain wall of the quantum Heisenberg-Ising model (XXZ model) with certain boundary conditions. The spin of the electron interacts with the spins of the XXZ model by the Hund coupling. Using the exact domain wall ground states of the XXZ model, we analytically obtain the exact effective Schrödinger equation for conduction electrons. This equation coincides with a conventional phenomenological Schrödinger equation which was derived in a classical treatment of spins of a domain wall. By solving the Schrödinger equation numerically, we have calculated the transmission coefficient which is a function of the Hund coupling and of the anisotropy of the XXZ model. It turns out that the transmission coefficient is vanishing in the low energy limit for the electron.

cond-mat.stat-mech↗

arXiv1998

The complete set of ground states of the ferromagnetic XXZ chains

We show that the well-known translation invariant ground states and the recently discovered kink and antikink ground states are the complete set of pure infinite-volume ground states (in the sense of local stability) of the spin-S ferromagnetic XXZ chains with Hamiltonian H=-sum_x [ S^1_x S^1_{x+1} + S^2_x S^2_{x+1} + Delta S^3_x S^3_{x+1} ], for all Delta >1, and all S=1/2,1,3/2,.... For the isotropic model (Delta =1) we show that all ground states are translation invariant. For the proof of these statements we propose a strategy for demonstrating completeness of the list of the pure infinite-volume ground states of a quantum many-body system, of which the present results for the XXX and XXZ chains can be seen as an example. The result for Delta>1 can also be proved by an easy extension to general $S$ of the method used in [T. Matsui, Lett. Math. Phys. 37 (1996) 397] for the spin-1/2 ferromagnetic XXZ chain with $Δ>1$. However, our proof is different and does not rely on the existence of a spectral gap. In particular, it also works to prove absence of non-translationally invariant ground states for the isotropic chains (Delta=1), which have a gapless excitation spectrum. Our results show that, while any small amount of the anisotropy is enough to stabilize the domain walls against the quantum fluctuations, no boundary condition exists that would stabilize a domain wall in the isotropic model (Delta=1).

cond-mat.stat-mech↗

arXiv1997

Decay of Superconducting and Magnetic Correlations in One- and Two-Dimensional Hubbard Models

In a general class of one and two dimensional Hubbard models, we prove upper bounds for the two-point correlation functions at finite temperatures for electrons, for electron pairs, and for spins. The upper bounds decay exponentially in one dimension, and with power laws in two dimensions. The bounds rule out the possibility of the corresponding condensation of superconducting electron pairs, and of the corresponding magnetic ordering. Our method is general enough to cover other models such as the t-J model.

cond-mat.stat-mech↗

arXiv1997

Symmetry Breaking and Finite Size Effects in Quantum Many-Body Systems

We consider a quantum many-body system on a lattice with a continuous symmetry which exhibits a spontaneous symmetry breaking in its infinite volume ground states, but in which the order operator does not commute with the Hamiltonian. A typical example is the Heisenberg antiferromagnet with a Neel order. In the corresponding finite system, the symmetry breaking is usually "obscured" by "quantum fluctuation" and one gets a symmetric ground state with a long range order. In such a situation, we prove that there exist ever increasing numbers of low-lying eigenstates whose excitation energies are bounded by a constant times 1/N, where N denotes the number of sites. By forming linear combinations of these low-lying states and the (finite-volume) ground state, and by taking infinite volume limits, we construct infinite volume ground states with explicit symmetry breaking. Our general theorems do not only shed light on the nature ofsymmetry breaking in quantum many-body systems, but provide indispensable information for numerical approaches to these systems. We also discuss applications of our general results to a variety of examples. The present paper is intended to be accessible to the readers without background in mathematical approaches to quantum many-body systems.

cond-mat.stat-mech↗

arXiv1997

Classical XY Model in 1.99 Dimensions

We consider the classical XY model (O(2) nonlinear sigma-model) on a class of lattices with the (fractal) dimensions 1<D<2. The Berezinskii's harmonic approximation suggests that the model undergoes a phase transition in which the low temperature phase is characterized by stretched exponential decay of correlations. We prove an exponentially decaying upper bound for the two-point correlation functions at non-zero temperatures, thus excluding the possibility of such a phase transition.

cond-mat.stat-mech↗

arXiv1995

The spectral gap of the ferromagnetic XXZ chain

We prove that the spectral gap of the spin-1/2 ferromagnetic XXZ chain with Hamiltonian $H=-\sum_x S^{(1)}_xS^{(1)}_{x+1}+S^{(2)}_xS^{(2)}_{x+1} +ΔS^{(3)}_xS^{(3)}_{x+1}$, is given by $Δ-1$ for all $Δ\geq 1$. This is the gap in the spectrum of the infinite chain in any of its ground states, the translation invariant ones as well as the kink ground states, which contain an interface between an {\it up} and a {\it down} region. In particular, this shows that the lowest magnon energy is not affected by the presence of a domain wall. This surprising fact is a consequence of the $SU_q(2)$ quantum group symmetry of the model.

cond-mat↗

arXiv1995

Mutual Exclusion Statistics in the Exactly Solvable Model of the Mott Metal-Insulator Transition

We study statistical characterization of the many-body states in the exactly solvable model with internal degree of freedom in more than one dimension. The model exhibits the Mott metal-insulator transition. It is shown that the ground state is described by that of a generalized ideal gas of particles (called exclusons) which have mutual exclusion statistics between different species. In addition to giving a perspective view of spin-charge separation, the model constitutes an explicit example of mutual exclusion statistics in more than two dimensions.

cond-mat↗