arXiv subjects

M. Kohmoto

Publications and source records attributed to M. Kohmoto.

24 records · Page 2Linked to original sources

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↗

arXiv1994

Critical and bicritical properties of Harper's equation with next nearest neighbor coupling

We have exploited a variety of techniques to study the universality and stability of the scaling properties of Harper's equation, the equation for a particle moving on a tight-binding square lattice in the presence of a gauge field, when coupling to next nearest sites is added. We find, from numerical and analytical studies, that the scaling behavior of the total width of the spectrum and the multifractal nature of the spectrum are unchanged, provided the next nearest neighbor coupling terms are below a certain threshold value. The full square symmetry of the Hamiltonian is not required for criticality, but the square diagonals should remain as reflection lines. A bicritical line is found at the boundary between the region in which the nearest neighbor terms dominate and the region in which the next nearest neighbor terms dominate. On the bicritical line a different critical exponent for the width of the spectrum and different multifractal behavior are found. In the region in which the next nearest neighbor terms dominate the behavior is still critical if the Hamiltonian is invariant under reflection in the directions parallel to the sides of the square, but a new length scale enters, and the behavior is no longer universal but shows strongly oscillatory behavior. For a flux per unit cell equal to $1/q$ the measure of the spectrum is proportional to $1/q$ in this region, but if it is a ratio of Fibonacci numbers the measure decreases with a rather higher inverse power of the denominator.

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↗