10 research outputs found
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 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
Vortices in Schwinger-Boson Mean-Field Theory of Two-Dimensional Quantum Antiferromagnets
In this paper we study the properties of vortices in two dimensional quantum
antiferromagnets with spin magnitude S on a square lattice within the framework
of Schwinger-boson mean field theory. Based on a continuum description, we show
that vortices are stable topological excitations in the disordered state of
quantum antiferromagnets. Furthermore, we argue that vortices can be divided
into two kinds: the first kind always carries zero angular momentum and are
bosons, whereas the second kind carries angular momentum S under favourable
conditions and are fermions if S is half-integer. A plausible consequence of
our results relating to RVB theories of High-Tc superconductors is pointed out.Comment: 25 page
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(MN) 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