Exact calculation of the ground-state dynamical spin correlation function of a S=1/2 antiferromagnetic Heisenberg chain with free spinons

We calculate the exact dynamical magnetic structure factor S(Q,E) in the ground state of a one-dimensional S=1/2 antiferromagnet with gapless free S=1/2 spinon excitations, the Haldane-Shastry model with inverse-square exchange, which is in the same low-energy universality class as Bethe's nearest-neighbor exchange model. Only two-spinon excited states contribute, and S(Q,E) is found to be a very simple integral over these states.Comment: 11 pages, LaTeX, RevTeX 3.0, cond-mat/930903

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

Exact Dynamical Correlation Functions of Calogero-Sutherland Model and One-Dimensional Fractional Statistics

One-dimensional model of non-relativistic particles with inverse-square interaction potential known as Calogero-Sutherland Model (CSM) is shown to possess fractional statistics. Using the theory of Jack symmetric polynomial the exact dynamical density-density correlation function and the one-particle Green's function (hole propagator) at any rational interaction coupling constant $\lambda = p/q$ are obtained and used to show clear evidences of the fractional statistics. Motifs representing the eigenstates of the model are also constructed and used to reveal the fractional {\it exclusion} statistics (in the sense of Haldane's ``Generalized Pauli Exclusion Principle''). This model is also endowed with a natural {\it exchange } statistics (1D analog of 2D braiding statistics) compatible with the {\it exclusion} statistics. (Submitted to PRL on April 18, 1994)Comment: Revtex 11 pages, IASSNS-HEP-94/27 (April 18, 1994

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

Adiabatic Ground-State Properties of Spin Chains with Twisted Boundary Conditions

We study the Heisenberg spin chain with twisted boundary conditions, focusing on the adiabatic flow of the energy spectrum as a function of the twist angle. In terms of effective field theory for the nearest-neighbor model, we show that the period 2 (in unit $2\pi$) obtained by Sutherland and Shastry arises from irrelevant perturbations around the massless fixed point, and that this period may be rather general for one-dimensional interacting lattice models at half filling. In contrast, the period for the Haldane-Shastry spin model with $1/r^2$ interaction has a different and unique origin for the period, namely, it reflects fractional statistics in Haldane's sense.Comment: 6 pages, revtex, 3 figures available on request, to appear in J. Phys. Soc. Jp

Sex ratio and unisexual sterility in hybrid animals

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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

Breakdown of Luttinger liquid state in one-dimensional frustrated spinless fermion model

Haldane hypothesis about the universality of Luttinger liquid (LL) behavior in conducting one-dimensional (1D) fermion systems is checked numerically for spinless fermion model with next-nearest-neighbor interactions. It is shown that for large enough interactions the ground state can be gapless (metallic) due to frustrations but not be LL. The exponents of correlation functions for this unusual conducting state are found numerically by finite-size method.Comment: 3 pages, 4 figures, RevTe

Properties of Non-Abelian Fractional Quantum Hall States at Filling ν=kr\nu=\frac{k}{r}

We compute the physical properties of non-Abelian Fractional Quantum Hall (FQH) states described by Jack polynomials at general filling $\nu=\frac{k}{r}$. For $r=2$, these states are identical to the $Z_k$ Read-Rezayi parafermions, whereas for $r>2$ they represent new FQH states. The $r=k+1$ states, multiplied by a Vandermonde determinant, are a non-Abelian alternative construction of states at fermionic filling $2/5, 3/7, 4/9...$. We obtain the thermal Hall coefficient, the quantum dimensions, the electron scaling exponent, and show that the non-Abelian quasihole has a well-defined propagator falling off with the distance. The clustering properties of the Jack polynomials, provide a strong indication that the states with $r>2$ can be obtained as correlators of fields of \emph{non-unitary} conformal field theories, but the CFT-FQH connection fails when invoked to compute physical properties such as thermal Hall coefficient or, more importantly, the quasihole propagator. The quasihole wavefuntion, when written as a coherent state representation of Jack polynomials, has an identical structure for \emph{all} non-Abelian states at filling $\nu=\frac{k}{r}$.Comment: 2 figure

Single-particle Green's functions of the Calogero-Sutherland model at couplings \lambda = 1/2, 1, and 2

At coupling strengths lambda = 1/2, 1, or 2, the Calogero-Sutherland model (CSM) is related to Brownian motion in a Wigner-Dyson random matrix ensemble with orthogonal, unitary, or symplectic symmetry. Using this relation in conjunction with superanalytic techniques developed in mesoscopic conductor physics, we derive an exact integral representation for the CSM two-particle Green's function in the thermodynamic limit. Simple closed expressions for the single-particle Green's functions are extracted by separation of points. For the advanced part, where a particle is added to the ground state and later removed, a sum of two contributions is found: the expected one with just one particle excitation present, plus an extra term arising from fractionalization of the single particle into a number of elementary particle and hole excitations.Comment: 19 REVTeX page