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Y. Hatsugai

Publications and source records attributed to Y. Hatsugai.

54 records · Page 3Linked to original sources
arXiv2001

Mott Transition in the Two-Dimensional Flux Phase

Effects of the electron-electron interaction in the two-dimensional flux phase are investigated. We treat the half-filled Hubbard model with a magnetic flux $π$ per plaquette by the quantum Monte Carlo method. When the interaction is small, an antiferromagnetic long-range does not exist and the charge fluctuation is different from that of the Mott insulator It suggests that the Mott transition occurs at finite strength of the interaction in the flux phase, which is in contrast to the standard Hubbard model.

cond-mat.str-el↗
arXiv2000

Duality in the Azbel-Hofstadter problem and the two-dimensional d-wave superconductivity with a magnetic field

A single-parameter family of lattice-fermion model is constructed. It is a deformation of the Azbel-Hofstadter problem by a parameter $h={$B%((BDelta}/t$ (quantum parameter). A topological number is attached to each energy band. A duality between the classical limit ($h=+0$) and the quantum limit ($h=1$) is revealed in the energy spectrum and the topological number. The model has a close relation to the two-dimensional d-wave superconductivity with a magnetic field. Making use of the duality and a topological argument, we shed light on how the quasiparticles with a magnetic field behave especially in the quantum limit.

cond-mat.supr-con↗
arXiv2000

Numerical study of disorder effects on the three-dimensional Hubbard model

Combined effects of interactions and disorder are investigated using a finite temperature quantum Monte Carlo technique for the three-dimensional Hubbard model with random potentials of a finite range. Temperature dependence of the charge compressibility shows that the Mott gap collapses beyond a finite disorder strength. This is a quantum phase transition from an incompressible phase to a compressible phase driven by disorder. We calculate the antiferromagnetic structure factor in the presence of disorder as well. Strong antiferromagnetic correlation, which is characteristic of the Mott insulator, is destroyed by a finite amount of disorder.

cond-mat.str-el↗
arXiv1999

Landau Levels from the Bethe Ansatz Equations

The Bethe ansatz (BA) equations for the two-dimensional Bloch electrons in a uniform magnetic field are treated in the weak field limit. We have calculated energies near the lower boundary of the energy spectrum up to the first nontrivial order. It corresponds to calculating a finite size correction for the excitation energies of the BA solvable lattice models and gives the Landau levels in the present problem.

cond-mat.mes-hall↗
arXiv1999

Sum Rule of the Hall Conductance in Random Quantum Phase Transition

The Hall conductance $σ_{xy}$ of two-dimensional {\it lattice} electrons with random potential is investigated. The change of $σ_{xy}$ due to randomness is focused on. It is a quantum phase transition where the {\it sum rule} of $σ_{xy}$ plays an important role. By the {\it string} (anyon) gauge, numerical study becomes possible in sufficiently weak magnetic field regime which is essential to discuss the floating scenario in the continuum model. Topological objects in the Bloch wavefunctions, charged vortices, are obtained explicitly. The anomalous plateau transitions ($Δσ_{xy}= 2,3,... >1$) and the trajectory of delocalized states are discussed.

cond-mat.dis-nn↗
arXiv1999

Transitions from the Quantum Hall State to the Anderson Insulator: Fa te of Delocalized States

Transitions between the quantum Hall state and the Anderson insulator are studied in a two dimensional tight binding model with a uniform magnetic field and a random potential. By the string (anyon) gauge, the weak magnetic field regime is explored numerically. The regime is closely related to the continuum model. The change of the Hall conductance and the trajectoy of the delocalized states are investigated by the topological arguments and the Thouless number study.

cond-mat.dis-nn↗
arXiv1999

Plateaux Transitions in the Pairing Model:Topology and Selection Rule

Based on the two-dimensional lattice fermion model, we discuss transitions between different pairing states. Each phase is labeled by an integer which is a topological invariant and characterized by vortices of the Bloch wavefunction. The transitions between phases with different integers obey a selection rule. Basic properties of the edge states are revealed. They reflect the topological character of the bulk. Transitions driven by randomness are also discussed numerically.

cond-mat.mes-hall↗
arXiv1998

Collapse of Charge Gap in Random Mott Insulators

Effects of randomness on interacting fermionic systems in one dimension are investigated by quantum Monte-Carlo techniques. At first, interacting spinless fermions are studied whose ground state shows charge ordering. Quantum phase transition due to randomness is observed associated with the collapse of the charge ordering. We also treat random Hubbard model focusing on the Mott gap. Although the randomness closes the Mott gap and low-lying states are created, which is observed in the charge compressibility, no (quasi-) Fermi surface singularity is formed. It implies localized nature of the low-lying states.

cond-mat.str-el↗
arXiv1998

Scaling near random criticality in two-dimensional Dirac fermions

Recently the existence of a random critical line in two dimensional Dirac fermions is confirmed. In this paper, we focus on its scaling properties, especially in the critical region. We treat Dirac fermions in two dimensions with two types of randomness, a random site (RS) model and a random hopping (RH) model. The RS model belongs to the usual orthogonal class and all states are localized. For the RH model, there is an additional symmetry expressed by ${\{}{\cal H},γ{\}}=0$. Therefore, although all non-zero energy states localize, the localization length diverges at the zero energy. In the weak localization region, the generalized Ohm's law in fractional dimensions, $d^{*}(<2)$, has been observed for the RH model.

cond-mat.dis-nn↗
arXiv1997

Exclusonic Quasiparticles and Thermodynamics of Fractional Quantum Hall Liquids

Quasielectrons and quasiholes in the fractional quantum Hall liquids obey fractional (including nontrivial mutual) exclusion statistics. Their statistics matrix can be determined from several possible state-counting scheme, involving different assumptions on statistical correlations. Thermal activation of quasiparticle pairs and thermodynamic properties of the fractional quantum Hall liquids near fillings $1/m$ ($m$ odd) at low temperature are studied in the approximation of generalized ideal gas. The existence of hierarchical states in the fractional quantum Hall effect is shown to be a manifestation of the exclusonic nature of the relevant quasiparticles. For magnetic properties, a paramagnetism-diamagnetism transition appears to be possible at finite temperature.

cond-mat.mes-hall↗
arXiv1997

Simple Exactly Solvable Models of non-Fermi Liquids

We generalize the model of Hatsugai and Kohmoto [J. Phys. Soc. Jpn, 61, 2056 (1992)] and find ground states which do not show the properties of Fermi liquids. We work in two space dimensions, but it is straightforward to generalize to higher dimensions. The ground state is highly degenerate and there is no discontinuity in the momentum distribution; i.e., there is no Fermi surface. The Green's function generically has a branch cut.

cond-mat.str-el↗
arXiv1996

Mutual Exclusion Statistics in Exactly Solvable Models in One and Higher Dimensions at Low Temperatures

We study statistical characterization of the many-body states in exactly solvable models with internal degrees of freedom. The models under consideration include the isotropic and anisotropic Heisenberg spin chain, the Hubbard chain, and a model in higher dimensions which exhibits the Mott metal-insulator transition. It is shown that the ground state of these systems is all described by that of a generalized ideal gas of particles (called exclusons) which have mutual exclusion statistics, either between different rapidities or between different species. For the Bethe ansatz solvable models, the low temperature properties are well described by the excluson description if the degeneracies due to string solutions with complex rapidities are taken into account correctly. {For} the Hubbard chain with strong but finite coupling, charge-spin separation is shown for thermodynamics at low temperatures. Moreover, we present an exactly solvable model in arbitrary dimensions which, in addition to giving a perspective view of spin-charge separation, constitutes an explicit example of mutual exclusion statistics in more than two dimensions.

cond-mat↗
arXiv1995

Quantum Group, Bethe Ansatz and Bloch Electrons in a Magnetic Field

The wave functions for two dimensional Bloch electrons in a uniform magnetic field at the mid-band points are studied with the help of the algebraic structure of the quantum group $U_q(sl_2)$. A linear combination of its generators gives the Hamiltonian. We obtain analytical and numerical solutions for the wave functions by solving the Bethe Ansatz equations, proposed by Wiegmann and Zabrodin on the basis of above observation. The semi-classical case with the flux per plaquette $ϕ=1/Q$ is analyzed in detail, by exploring a structure of the Bethe Ansatz equations. We also reveal the multifractal structure of the Bethe Ansatz solutions and corresponding wave functions when $ϕ$ is irrational, such as the golden or silver mean.

cond-mat↗
arXiv1995

Exact Results on Superconductivity due to Interband Coupling

We present a family of exactly solvable models at arbitrary filling in any dimensions which exhibit novel superconductivity with interband pairing. By the use of the hidden $SU(2)$ algebra the Hamiltonians were diagonalized explicitly. The zero-temperature phase diagrams and the thermodynamic properties are discussed. Several new properties are revealed which are different from those of the BCS-type superconductor.

cond-mat↗
arXiv1994

Universal Correlations in the random matrices and 1D particles with long range interactions in a confinement potential

We study the correlations between eigenvalues of the large random matrices by a renormalization group approach. The results strongly support the universality of the correlations proposed by Brézin and Zee. Then we apply the results to the ground state of the 1D particles with long range interactions in a confinement potential. We obtain the exact ground state. We also show the existence of a transition similar to a phase separation. Before and after the transition, we obtain the density-density correlation explicitly. The correlation shows nontrivial universal behavior.

cond-mat↗
arXiv1994

Universal Behavior of Correlations between Eigenvalues of Random Matrices

The universal connected correlations proposed recently between eigenvalues of unitary random matrices is examined numerically. We perform an ensemble average by the Monte Carlo sampling. Although density of eigenvalues and a bare correlation of the eigenvalues are not universal, the connected correlation shows a universal behavior after smoothing.

cond-mat↗
arXiv1993

Phase diagram of the S=1/2 quantum spin chain with bond alternation

We study the ground state properties of the bond alternating $S=1/2$ quantum spin chain whose Hamiltonian is H=\sum_j (S_{2j}^x S_{2j+1}^x +S_{2j}^y S_{2j+1}^y +λS_{2j}^z S_{2j+1}^z ) +β\sum_j {\bf S}_{2j-1} \cdot {\bf S}_{2j} . When $β=0$, the ground state is a collection of local singlets with a finite excitation gap. In the limit of strong ferromagnetic coupling $β\to - \infty$, this is equivalent to the $S=1 \ XXZ$ Hamiltonian. It has several ground state phases in the $λ$-$β$ plane including the gapful Haldane phase. They are characterized by a full breakdown, partial breakdowns and a non-breakdown of the hidden discrete $Z_2 \times Z_2$ symmetry. The ground state phase diagram is obtained by series expansions.

cond-mat↗