Direct Calculation of Spin-Stiffness for Spin-1/2 Heisenberg Models

The spin-stiffness of frustrated spin-1/2 Heisenberg models in one and two dimensions is computed for the first time by exact diagonalizations on small clusters that implement spin-dependent twisted boundary conditions. Finite-size extrapolation to the thermodynamic limit yields a value of $0.14\pm 0.01$ for the spin-stiffness of the unfrustrated planar antiferromagnet. We also present a general discussion of the linear-response theory for spin-twists, which ultimately leads to the moment sum-rule.Comment: 11 pgs, TeX, LA-UR-94-94 (to be published in Phys. Rev. B

Quantum spin Hamiltonians for the SU(2)_k WZW model

We propose to use null vectors in conformal field theories to derive model Hamiltonians of quantum spin chains and corresponding ground state wave function(s). The approach is quite general, and we illustrate it by constructing a family of Hamiltonians whose ground states are the chiral correlators of the SU(2)_k WZW model for integer values of the level k. The simplest example corresponds to k=1 and is essentially a nonuniform generalization of the Haldane-Shastry model with long-range exchange couplings. At level k=2, we analyze the model for N spin 1 fields. We find that the Renyi entropy and the two-point spin correlator show, respectively, logarithmic growth and algebraic decay. Furthermore, we use the null vectors to derive a set of algebraic, linear equations relating spin correlators within each model. At level k=1, these equations allow us to compute the two-point spin correlators analytically for the finite chain uniform Haldane-Shastry model and to obtain numerical results for the nonuniform case and for higher-point spin correlators in a very simple way and without resorting to Monte Carlo techniques.Comment: 38 pages, 6 figure

Seiberg-Witten and "Polyakov-like" magnetic bion confinements are continuously connected

We study four-dimensional N=2 supersymmetric pure-gauge (Seiberg-Witten) theory and its N=1 mass perturbation by using compactification S**1 x R**3. It is well known that on R**4 (or at large S**1) the perturbed theory realizes confinement through monopole or dyon condensation. At small S**1, we demonstrate that confinement is induced by a generalization of Polyakov's three-dimensional instanton mechanism to a locally four-dimensional theory - the magnetic bion mechanism - which also applies to a large class of nonsupersymmetric theories. Using a large- vs. small-L Poisson duality, we show that the two mechanisms of confinement, previously thought to be distinct, are in fact continuously connected.Comment: 49 pages, 5 figure

Continuum limit of gl(M∣\vertN) spin chains

We study the spectrum of an integrable antiferromagnetic Hamiltonian of the gl(M|N) spin chain of alternating fundamental and dual representations. After extensive numerical analysis, we identify the vacuum and low lying excitations and with this knowledge perform the continuum limit, while keeping a finite gap. All gl(n+N|N) spin chains with n,N>0 are shown to possess in the continuum limit 2n-2 multiplets of massive particles which scatter with gl(n) Gross-Neveu like S-matrices, namely their eigenvalues do not depend on N. We argue that the continuum theory is the gl(M|N) Gross-Neveu model. We then look for remaining particles in the gl(2m|1) chains. The results suggest there is a continuum of such particles, which in order to be fully understood require finite volume calculations