arXiv subjects

Yasuhiro Hatsugai

Publications and source records attributed to Yasuhiro Hatsugai.

143 records · Page 8Linked to original sources

arXiv2003

Zero-energy edge states and chiral symmetry breaking at edges of graphite sheets

Two-dimensional graphite sheets with a certain type of edges are known to support boundary states localized near the edges. Forming a flat band with a sharp peak in the density of states at the Fermi energy, they can trigger a magnetic instability or a distortion of the lattice in the presence of electron-electron or electron-phonon interactions. We shall discuss a relationship between chiral symmetry, which is the origin of the zero-energy edge states, and several types of induced orders such as spin density waves or lattice distortions. We also investigate electron correlation effects on the edge states for a wrapped quasi one-dimensional geometry, i.e., carbon nanotube, by means of the renormalization group and the open boundary bosonization.

cond-mat.str-el↗

arXiv2003

Dielectric response of the interacting 1D spinless fermions with disorder

Dielectric responces of the one-dimentional electron system is investigated numerically. We treat an interacting one-dimentional spinless fermion model with disorder by using the Density Matrix Renormalization Group(DMRG) method which is extended for nonuniform systems. We apply an electric field $E$ to the system and calculate dielectric responces. Dielectric responce of the Mott insulator and the Anderson insulator are calculated respectively. Steplike behaviors in $P-E$ curve are obtained which corresponds to breakdown of the insulating behavior. For the Mott insulator, the steps originate from generation of kink-pairs. For the Anderson insulator on the other hand, the origin of the steps is a crossing of the localized one particle energy levels. We also treat random systems with interaction. From one parameter scaling analysis of the susceptibility $χ$, the metal-insulator transition in attractively interacting region is confirmed and a phase diagram of the random spinless fermion model is obtained.

cond-mat.dis-nn↗

arXiv2003

Correlation effects of carbon nanotubes at boundaries: Spin polarization induced by zero-energy boundary states

When a carbon nanotube is truncated with a certain type of edges, boundary states localized near the edges appear at the fermi level. Starting from lattice models, low energy effective theories are constructed which describe electron correlation effects on the boundary states. We then focus on a thin metallic carbon nanotube which supports one or two boundary states, and discuss physical consequences of the interaction between the boundary states and bulk collective excitations. By the renormalization group analyses together with the open boundary bosonization, we show that the repulsive bulk interactions suppress the charge fluctuations at boundaries, and assist the spin polarization.

cond-mat.mes-hall↗

arXiv2002

Topological Origin of Zero-Energy Edge States in Particle-Hole Symmetric Systems

A criterion to determine the existence of zero-energy edge states is discussed for a class of particle-hole symmetric Hamiltonians. A ``loop'' in a parameter space is assigned for each one-dimensional bulk Hamiltonian, and its topological properties, combined with the chiral symmetry, play an essential role. It provides a unified framework to discuss zero-energy edge modes for several systems such as fully gapped superconductors, two-dimensional d-wave superconductors, and graphite ribbons. A variants of the Peierls instability caused by the presence of edges is also discussed.

cond-mat.supr-con↗

arXiv2001

Topological Quantum Phase Transitions in Superconductivity on Lattices

Topological quantum phase transitions in superconductivity are discussed on two dimensional lattices. The main focus is on the Chern number for superconducting states. Each superconductivity is characterized by the Chern number, and the quantum phase transition is associated with topological changes of the quasiparticle Bloch function in the Brillouin zone. For the superconducting case, the Chern number has several equivalent but different topological expressions given by vortices, the Dirac monopole and strings. We demonstrate quantum phase transitions by these topological quantities both for singlet and triplet cases.

cond-mat.supr-con↗

arXiv2001

Singular Density of States of Disordered Dirac Fermions in the Chiral Models

The Dirac fermion in the random chiral models is studied which includes the random gauge field model and the random hopping model. We focus on a connection between continuum and lattice models to give a clear perspective for the random chiral models. Two distinct structures of density of states (DoS) around zero energy, one is a power-law dependence on energy in the intermediate energy range and the other is a diverging one at zero energy, are revealed by an extensive numerical study for large systems up to $250\times 250$. For the random hopping model, our finding of the diverging DoS within very narrow energy range reconciles previous inconsistencies between the lattice and the continuum models.

cond-mat.mes-hall↗

arXiv2000

Numerical Replica Limit for the Density Correlation of the Random Dirac Fermion

The zero mode wave function of a massless Dirac fermion in the presence of a random gauge field is studied. The density correlation function is calculated numerically and found to exhibit power law in the weak randomness with the disorder dependent exponent. It deviates from the power law and the disorder dependence becomes frozen in the strong randomness. A classical statistical system is employed through the replica trick to interpret the results and the direct evaluation of the replica limit is demonstrated numerically. The analytic expression of the correlation function and the free energy are also discussed with the replica symmetry breaking and the Liouville field theory.

cond-mat.dis-nn↗

arXiv1997

Near Critical States of Random Dirac Fermions

Random Dirac fermions in a two-dimensional space are studied numerically. We realize them on a square lattice using the $π$-flux model with random hopping. The system preserves two symmetries, the time-reversal symmetry and the symmetry denoted by ${{\cal H},γ}=0$ with a $4\times 4$ matrix $γ$ in an effective field theory. Although it belongs to the orthogonal ensemble, the zero-energy states do not localize and become critical. The density of states vanishes at zero energy as $\sim E^α$ and the exponent $α$ changes with strength of the randomness, which implies the existence of the critical line. Rapid growth of the localization length near zero energy is suggested and the eigenstates near zero energy exhibit anomalous behaviour which can be interpreted as a critical slowing down in the available finite-size system. The level-spacing distributions close to zero energy deviate from both the Wigner surmise and the Poissonian, and exhibit critical behaviour which reflects the existence of critical states at zero energy.

cond-mat↗

arXiv1997

Gap Opening Transition and Fractal Ground State Phase Diagram in One Dimensional Fermions with Long Range Interaction : Mott Transition as a Quantum Phase Transition of Infinite Order

The metal-insulator transition in one dimensional fermionic systems with long-range interaction is investigated. We have focused on an excitation spectrum by the exact diagonalization technique in sectors with different momentum quantum numbers. At rational fillings, we have demonstrated gap opening transitions from the Tomonaga-Luttinger liquid to the Mott insulator associated with a discrete symmetry breaking by changing the interaction strength. Finite interaction range is crucial to have the Mott transition at a rational filling away from the half filling. It is consistent with the strong coupling picture where the Mott gap exists at any rational fillings with sufficiently strong interaction. The critical regions as a quantum phase transition are also investigated numerically. Non-analytic behavior of the Mott gap is the characteristic in the weak coupling. It is of the order of the interaction in the strong coupling. It implies that the metal-insulator transition of the model is of the infinite order as a quantum phase transition at zero temperature. Fractal nature of the ground state phase diagram is also revealed.

cond-mat.str-el↗

arXiv1996

Quantum Coherence of Edge States in the Quantum Hall Effect -- Topological Invariants and Edge State Mixing --

Edge states in the integral quantum Hall effect on a lattice are reviewed from a topological point of view. For a system with edges which is realized inevitably in an experimental situation, the Hall conductance $σ_{xy}$ is given by a winding number of the edge state on a complex energy surface. A relation between two topological invariants (bulk and edge) is also clarified. In a macroscopic system, mixture of the edge states are exponentially small and negligible. Quantum Coherence between the two edge states gives the quantization of $σ_{xy}$. However, when the system is mesoscopic, the mixture between the edges states plays a physical role. We focus on this point and show numerical results.

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

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↗

arXiv1993

Chiral Operator Product Algebra and Edge Excitations of a Fractional Quantum Hall Droplet

In this paper we study the spectrum of low-energy edge excitations of a fractional quantum Hall (FQH) droplet. We show how to generate, by conformal field theory (CFT) techniques, the many-electron wave functions for the edge states. And we propose to classify the spectrum of the edge states by the same chiral operator product algebra (OPA) that appears in the CFT description of the ground state in the bulk. This bulk-edge correspondence is suggested particularly for FQH systems that support quasiparticle obeying non-abelian braid statistics, including the $ν=5/2$ Haldane-Rezayi state. Numerical diagonalization to count the low-lying edge states has been done for several non-abelian FQH systems, showing good agreement in all cases with the chiral OPA predictions. The specific heat of the edge excitations in those non-abelian states is also calculated.

cond-mat↗