When the Fermi level lies in a gap, the Hall conductivity of three-dimensional electrons in a
periodic potential is expressed in a topologically invariant form with a set of three integers. If …

We established a large class of exactly soluble spin liquids and chiral spin liquids on three-
dimensional helix lattices by introducing Kitaev-type's spin coupling. In the chiral spin …

We calculate the distribution of single-particle states for a spinless electron hopping on a two-
dimensional square lattice in the presence of random magnetic flux. The flux is taken to be …

A class of the symmetrically frustrated SU (N) models is constructed for quantum magnets
based on the generators of the SU (N) group. The total Hamiltonian lacks SU (N) symmetry …

There is a class of electronic liquids in dimensions greater than 1 that shows all essential
properties of one-dimensional electronic physics. These are topological liquids—correlated …

Abstract We discuss three topics:(1) the construction of effective Lagrangians for the Hall
and anyon fluids,(2) the generalization of the chiral spin liquid to three dimensions and to …

A three-dimensional generalization of the wave function of Girvin et al. is constructed by
taking the N→∞ limit of a solution of the two-dimensional massless Dirac equation with an …

The present state of the gauge theory of high-temperature superconductivity in strongly-
correlated two-dimensional spin systems is reviewed. Basic ideas on the statistics of …

This is a monograph on geometrical and topological features which arise in various
quantization procedures. Quantization schemes consider the feasibility of arriving at a …

抄録 Energy spectrum of electrons on three-dimensional lattice (two-dimensional lattices
coupled with interlayer hoppings) in the magnetic field along the (1, 1, 1) direction is …