Tardos fingerprinting is better than we thought

We review the fingerprinting scheme by Tardos and show that it has a much better performance than suggested by the proofs in Tardos' original paper. In particular, the length of the codewords can be significantly reduced. First we generalize the proofs of the false positive and false negative error probabilities with the following modifications: (1) we replace Tardos' hard-coded numbers by variables and (2) we allow for independently chosen false positive and false negative error rates. It turns out that all the collusion-resistance properties can still be proven when the code length is reduced by a factor of more than 2. Second, we study the statistical properties of the fingerprinting scheme, in particular the average and variance of the accusations. We identify which colluder strategy forces the content owner to employ the longest code. Using a gaussian approximation for the probability density functions of the accusations, we show that the required false negative and false positive error rate can be achieved with codes that are a factor 2 shorter than required for rigid proofs. Combining the results of these two approaches, we show that the Tardos scheme can be used with a code length approximately 5 times shorter than in the original construction.Comment: Modified presentation of result

Cooper pairs and exclusion statistics from coupled free-fermion chains

We show how to couple two free-fermion chains so that the excitations consist of Cooper pairs with zero energy, and free particles obeying (mutual) exclusion statistics. This behavior is reminiscent of anyonic superconductivity, and of a ferromagnetic version of the Haldane-Shastry spin chain, although here the interactions are local. We solve this model using the nested Bethe ansatz, and find all the eigenstates; the Cooper pairs correspond to exact-string or ``0/0'' solutions of the Bethe equations. We show how the model possesses an infinite-dimensional symmetry algebra, which is a supersymmetric version of the Yangian symmetry algebra for the Haldane-Shastry model.Comment: 16 pages. v2: includes explicit expression for super-Yangian generato

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

Interaction and thermodynamics of spinons in the XX chain

The mapping between the fermion and spinon compositions of eigenstates in the one-dimensional spin-1/2 XX model on a lattice with N sites is used to describe the spinon interaction from two different perspectives: (i) For finite N the energy of all eigenstates is expressed as a function of spinon momenta and spinon spins, which, in turn, are solutions of a set of Bethe ansatz equations. The latter are the basis of an exact thermodynamic analysis in the spinon representation of the XX model. (ii) For N -> infinity the energy per site of spinon configurations involving any number of spinon orbitals is expressed as a function of reduced variables representing momentum, filling, and magnetization of each orbital. The spins of spinons in a single orbital are found to be coupled in a manner well described by an Ising-like equivalent-neighbor interaction, switching from ferromagnetic to antiferromagnetic as the filling exceeds a critical level. Comparisons are made with results for the Haldane-Shastry model.Comment: 16 pages, 3 figure

Integrals of motion of the Haldane Shastry Model

In this letter we develop a method to construct all the integrals of motion of the $SU(p)$ Haldane-Shastry model of spins, equally spaced around a circle, interacting through a $1/r^2$ exchange interaction. These integrals of motion respect the Yangian symmetry algebra of the Hamiltonian.Comment: 13 pages, REVTEX v3.

Lineshape predictions via Bethe ansatz for the one-dimensional spin-1/2 Heisenberg antiferromagnet in a magnetic field

The spin fluctuations parallel to the external magnetic field in the ground state of the one-dimensional (1D) s=1/2 Heisenberg antiferromagnet are dominated by a two-parameter set of collective excitations. In a cyclic chain of N sites and magnetization 0<M_z<N/2, the ground state, which contains 2M_z spinons, is reconfigured as the physical vacuum for a different species of quasi-particles, identifiable in the framework of the coordinate Bethe ansatz by characteristic configurations of Bethe quantum numbers. The dynamically dominant excitations are found to be scattering states of two such quasi-particles. For N -> \infty, these collective excitations form a continuum in (q,\omega)-space with an incommensurate soft mode. Their matrix elements in the dynamic spin structure factor S_{zz}(q,\omega) are calculated directly from the Bethe wave functions for finite N. The resulting lineshape predictions for N -> \infty complement the exact results previously derived via algebraic analysis for the exact 2-spinon part of S_{zz}(q,\omega) in the zero-field limit. They are directly relevant for the interpretation of neutron scattering data measured in nonzero field on quasi-1D antiferromagnetic compounds.Comment: 10 page

Dynamical density-density correlations in one-dimensional Mott insulators

The dynamical density-density correlation function is calculated for the one-dimensional, half-filled Hubbard model extended with nearest neighbor repulsion using the Lanczos algorithm for finite size systems and analytically for large on site repulsion compared to hopping amplitudes. At the zone boundary an excitonic feature exists for any finite nearest neighbor repulsion and exhausts most of the spectral weight, even for parameters where no exciton is visible at zero momentum.Comment: 5 pages, REVTeX, epsf, 3 postscript figure

Quasiparticles governing the zero-temperature dynamics of the 1D spin-1/2 Heisenberg antiferromagnet in a magnetic field

The T=0 dynamical properties of the one-dimensional (1D) $s=1/2$ Heisenberg antiferromagnet in a uniform magnetic field are studied via Bethe ansatz for cyclic chains of $N$ sites. The ground state at magnetization $0<M_z<N/2$, which can be interpreted as a state with $2M_z$ spinons or as a state of $M_z$ magnons, is reconfigured here as the vacuum for a different species of quasiparticles, the {\em psinons} and {\em antipsinons}. We investigate three kinds of quantum fluctuations, namely the spin fluctuations parallel and perpendicular to the direction of the applied magnetic field and the dimer fluctuations. The dynamically dominant excitation spectra are found to be sets of collective excitations composed of two quasiparticles excited from the psinon vacuum in different configurations. The Bethe ansatz provides a framework for (i) the characterization of the new quasiparticles in relation to the more familiar spinons and magnons, (ii) the calculation of spectral boundaries and densities of states for each continuum, (iii) the calculation of transition rates between the ground state and the dynamically dominant collective excitations, (iv) the prediction of lineshapes for dynamic structure factors relevant for experiments performed on a variety of quasi-1D antiferromagnetic compounds, including KCuF$_3$, Cu(C$_4$H$_4$N$_2)(NO_3)_2$, and CuGeO$_3$.Comment: 13 pages, 12 figure