arXiv subjects

Mahito Kohmoto

Publications and source records attributed to Mahito Kohmoto.

47 records · Page 3Linked to original sources

arXiv1997

Vortex lattice transition in D-wave superconductors

Making use of the extended Ginzburg Landau theory, which includes the fourth order derivative term, we study the vortex state in a magnetic field parallel to the $ c$ axis. The vortex core structure is distorted due to this higher order term, which reveals t he fourfold symmetry. Futher, this distortion gives rise to the core interaction energy, which favo rs a square lattice tilted by $45^\circ$ from the $a$ axis. The critical field of this transition is determined. The magnetization diverges at the transition. This suggests the transition is of the fi rst order.

cond-mat↗

arXiv1996

Correlations in one-dimensional disordered electronic systems with interaction

We investigate the effects of randomness in a strongly correlated electron model in one-dimension at half-filling. The ground state correlation functions are exactly written by products of 3$\times$3 transfer matrices and are evaluated numerically. The correlation lengths depend on randomness when the interaction is effectively weak. On the contrary, they are completely insensitive to randomness when the interaction is effectively strong.

cond-mat.str-el↗

arXiv1996

Current and charge distributions of the fractional quantum Hall liquids with edges

An effective Chern-Simons theory for the quantum Hall states with edges is studied by treating the edge and bulk properties in a unified fashion. An exact steady-state solution is obtained for a half-plane geometry using the Wiener-Hopf method. For a Hall bar with finite width, it is proved that the charge and current distributions do not have a diverging singularity. It is shown that there exists only a single mode even for the hierarchical states, and the mode is not localized exponentially near the edges. Thus this result differs from the edge picture in which electrons are treated as strictly one dimensional chiral Luttinger liquids.

cond-mat↗

arXiv1996

Quasiperiodic Modulated-Spring Model

We study the classical vibration problem of a chain with spring constants which are modulated in a quasiperiodic manner, {\it i. e.}, a model in which the elastic energy is $\sum_j k_j( u_{j-1}-{u_j})^2$, where $k_j=1+Δcos[2πσ(j-1/2)+θ]$ and $σ$ is an irrational number. For $Δ< 1$, it is shown analytically that the spectrum is absolutely continuous, {\it i.e.}, all the eigen modes are extended. For $Δ=1$, numerical scaling analysis shows that the spectrum is purely singular continuous, {\it i.e.}, all the modes are critical.

cond-mat↗

arXiv1996

Disordered Critical Wave functions in Random Bond Models in Two Dimensions -- Random Lattice Fermions at $E=0$ without Doubling

Random bond Hamiltonians of the $π$ flux state on the square lattice are investigated. It has a special symmetry and all states are paired except the ones with zero energy. Because of this, there are always zero-modes. The states near $E=0$ are described by massless Dirac fermions. For the zero-mode, we can construct a random lattice fermion without a doubling and quite large systems ( up to $801 \times 801$) are treated numerically. We clearly demonstrate that the zero-mode is given by a critical wave function. Its multifractal behavior is also compared with the effective field theory.

cond-mat↗

arXiv1995

Exact ground-state correlation functions of the one-dimensional strongly correlated electron models with the resonating-valence-bond ground state

We investigate the one-dimensional strongly correlated electron models which have the resonating-valence-bond state as the exact ground state. The correlation functions are evaluated exactly using the transfer matrix method for the geometric representations of the valence-bond states. In this method, we only treat matrices with small dimensions. This enables us to give analytical results. It is shown that the correlation functions decay exponentially with distance. The result suggests that there is a finite excitation gap, and that the ground state is insulating. Since the corresponding non-interacting systems may be insulating or metallic, we can say that the gap originates from strong correlation. The persistent currents of the present models are also investigated and found to be exactly vanishing.

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↗

arXiv1995

Hidden Massive Spectators in the Effective Field Theory for Integral Quantum Hall Transitions

Integral quantum Hall plateau transitions in a planar lattice system due to gap collapse can be described by an effective field theory with Dirac fermions. We discuss how to reproduce the correct integral values for the Hall conductance, $σ_{xy}$, before and after the plateau transition, which are dictated by the microscopic topological invariant. In addition to the massless Dirac fermions that appear at gap closing, the matching condition of $σ_{xy}$ requires the introduction of massive Dirac fermions, as "spectators", in the effective field theory. For non-interacting electrons on the lattice, we give a general prescription to determine these massive "spectators", based on microscopic information on the vortices in the magnetic Brillouin zone which are closely related to edge states. Our description is demonstrated in a model with both nearest-neighbor and next-nearest-neighbor hoppings.

cond-mat↗

arXiv1995

Edge and Bulk of the Fractional Quantum Hall Liquids

An effective Chern-Simons theory for the Abelian quantum Hall states with edges is proposed to study the edge and bulk properties in a unified fashion. We impose a condition that the currents do not flow outside the sample. With this boundary condition, the action remains gauge invariant and the edge modes are naturally derived. We find that the integer coupling matrix $K$ should satisfy the condition $\sum_I(K^{-1})_{IJ} = ν/m$ ($ν$: filling of Landau levels, $m$: the number of gauge fields ) for the quantum Hall liquids. Then the Hall conductance is always quantized irrespective of the detailed dynamics or the randomness at the edge.

cond-mat↗

arXiv1995

Conductivity of 2D lattice electrons in an incommensurate magnetic field

We consider conductivities of two-dimensional lattice electrons in a magnetic field. We focus on systems where the flux per plaquette $ϕ$ is irrational (incommensurate flux). To realize the system with the incommensurate flux, we consider a series of systems with commensurate fluxes which converge to the irrational value. We have calculated a real part of the longitudinal conductivity $σ_{xx}(ω)$. Using a scaling analysis, we have found $\Reσ_{xx}(ω)$ behaves as $1/ω^γ$ \,$(γ=0.55)$ when $ϕ=τ,(τ=\frac{\sqrt{5}-1}{2})$ and the Fermi energy is near zero. This behavior is closely related to the known scaling behavior of the spectrum.

cond-mat↗

arXiv1994

Explicit Solutions of the Bethe Ansatz Equations for Bloch Electrons in a Magnetic Field

For Bloch electrons in a magnetic field, explicit solutions are obtained at the center of the spectrum for the Bethe ansatz equations recently proposed by Wiegmann and Zabrodin. When the magnetic flux per plaquette is $1/Q$ where $Q$ is an odd integer, distribution of the roots is uniform on the unit circle in the complex plane. For the semi-classical limit, $ Q\rightarrow\infty$, the wavefunction obeys the power low and is given by $|ψ(x)|^2=(2/ \sin πx)$ which is critical and unnormalizable. For the golden mean flux, the distribution of roots has the exact self-similarity and the distribution function is nowhere differentiable. The corresponding wavefunction also shows a clear self-similar structure.

cond-mat↗