On Models with Inverse-Square Exchange

A one-dimensional quantum N-body system of either fermions or bosons with $SU(n)$ colors interacting via inverse-square exchange is presented in this article. A class of eigenstates of both the continuum and lattice version of the model Hamiltonians is constructed in terms of the Jastrow-product type wave function. The class of states we construct in this paper corresponds to the ground state and the low energy excitations of the model that can be described by the effective harmonic fluid Hamiltonian. By expanding the energy about the ground state we find the harmonic fluid parameters (i.e. the charge, spin velocities, etc.), explicitly. The correlation exponent and the compressibility of are also found. As expected the general harmonic relation(i.e. $v_S=(v_Nv_J)^{1/2}$) is satisfied among the charge and spin velocities.Comment: 26 page

Hydrodynamic theory of surface excitations of three-dimensional topological insulators

Edge excitations of a fractional quantum Hall system can be derived as surface excitations of an incompressible quantum droplet using one dimensional chiral bosonization. Here we show that an analogous approach can be developed to characterize surface states of three-dimensional time reversal invariant topological insulators. The key ingredient of our theory is the Luther's multidimensional bosonization construction.Comment: 4 pages, published versio

Coordinate Representation of the Two-Spinon wavefunction and Spinon Interaction

By deriving and studying the coordinate representation for the two-spinon wavefunction, we show that spinon excitations in the Haldane-Shastry model interact. The interaction is given by a short-range attraction and causes a resonant enhancement in the two-spinon wavefunction at short separations between the spinons. We express the spin susceptibility for a finite lattice in terms of the resonant enhancement, given by the two-spinon wavefunction at zero separation. In the thermodynamic limit, the spinon attraction turns into the square-root divergence in the dynamical spin susceptibility.Comment: 19 pages, 5 .eps figure

Bosonization of One-Dimensional Exclusons and Characterization of Luttinger Liquids

We achieve a bosonization of one-dimensional ideal gas of exclusion statistics $\lambda$ at low temperatures, resulting in a new variant of $c=1$ conformal field theory with compactified radius $R=\sqrt{1/\lambda}$. These ideal excluson gases exactly reproduce the low-$T$ critical properties of Luttinger liquids, so they can be used to characterize the fixed points of the latter. Generalized ideal gases with mutual statistics and non-ideal gases with Luttinger-type interactions have also similar behavior, controlled by an effective statistics varying in a fixed-point line.Comment: 13 pages, revte

Microscopic origin of the next generation fractional quantum Hall effect

Most of the fractions observed to date belong to the sequences $\nu=n/(2pn\pm 1)$ and $\nu=1-n/(2pn\pm 1)$, $n$ and $p$ integers, understood as the familiar {\em integral} quantum Hall effect of composite fermions. These sequences fail to accommodate, however, many fractions such as $\nu=4/11$ and 5/13, discovered recently in ultra-high mobility samples at very low temperatures. We show that these "next generation" fractional quantum Hall states are accurately described as the {\em fractional} quantum Hall effect of composite fermions

Fermi liquid features of the one-dimensional Luttinger liquid

We show that the one-dimensional (1D) electron systems can also be described by Landau's phenomenological Fermi-liquid theory. Most of the known results derived from the Luttinger-liquid theory can be retrieved from the 1D Fermi-liquid theory. Exact correspondence between the Landau parameters and Haldane parameters is established. The exponents of the dynamical correlation functions and the impurity problem are also discussed based on the finite size corrections of elementary excitations with the predictions of the conformal field theory, which provides a bridge between the 1D Fermi-liquid and the Luttinger liquid.Comment: RevTeX, 5 pages, published versio

Laughlin State on Stretched and Squeezed Cylinders and Edge Excitations in Quantum Hall Effect

We study the Laughlin wave function on the cylinder. We find it only describes an incompressible fluid when the two lengths of the cylinder are comparable. As the radius is made smaller at fixed area, we observe a continuous transition to the charge density wave Tao-Thouless state. We also present some exact properties of the wave function in its polynomial form. We then study the edge excitations of the quantum Hall incompressible fluid modeled by the Laughlin wave function. The exponent describing the fluctuation of the edge predicted by recent theories is shown to be identical with numerical calculations. In particular, for $\nu=1/3$, we obtain the occupation amplitudes of edge state $n(k)$ for 4-10 electron size systems. When plotted as a function of the scaled wave vector they become essentially free of finite-size effects. The resulting curve obtains a very good agreement with the appropriate infinite-size Calogero-Sutherland model occupation numbers. Finally, we numerically obtain $n(k)$ of the edge excitations for some pairing states which may be relevant to the $\nu=5/2$ incompressible Hall state.Comment: 25 pages revtex, 9 uuencoded figures, submitted separately, also available from first author. CSULA-94-1

New Types of Off-Diagonal Long Range Order in Spin-Chains

We discuss new possibilities for Off-Diagonal Long Range Order (ODLRO) in spin chains involving operators which add or delete sites from the chain. For the Heisenberg and Inverse Square Exchange models we give strong numerical evidence for the hidden ODLRO conjectured by Anderson \cite{pwa_conj}. We find a similar ODLRO for the XY model (or equivalently for free fermions in one spatial dimension) which we can demonstrate rigorously, as well as numerically. A connection to the singlet pair correlations in one dimensional models of interacting electrons is made and briefly discussed.Comment: 13 pages, Revtex v3.0, 2 PostScript figures include

Semiclassical Solution of One Dimensional Model of Kondo Insulator

The model of Kondo chain with $M$-fold degenerate band of conduction electrons of spin 1/2 interacting with localized spins $S$ is studied for the case when the electronic band is half filled. It is shown that the spectrum of spin excitations in the continuous limit is described by the O(3) nonlinear sigma model with the topological term with $\theta = \pi(2S - M)$. For a case $|M - 2S| =$(even) the system is an insulator and single electron excitations at low energies are massive spin polarons. Otherwise the density of states has a pseudogap and vanishes only at the Fermi level. The relevance of this picture to higher dimensional Kondo insulators is discussed.Comment: 10 pages, LaTe