Finite-size scaling for the S=1/2 Heisenberg Antiferromagnetic Chain

Corrections to the asymptotic correlation function in a Heisenberg spin-1/2 antiferromagnetic spin chain are known to vanish slowly (logarithmically) as a function of the distance r or the chain size L. This leads to significant differences with numerical results. We calculate the sub-leading logarithmic corrections to the finite-size correlation function, using renormalization group improved perturbation theory, and compare the result with numerical data.Comment: 7 pages Revtex, 3 figure

Fine structure of the asymptotic expansion of cyclic integrals

The asymptotic expansion of $n$-dimensional cyclic integrals was expressed as a series of functionals acting on the symmetric function involved in the cyclic integral. In this article, we give an explicit formula for the action of these functionals on a specific class of symmetric functions. These results are necessary for the computation of the O(1) part in the long-distance asymptotic behavior of correlation functions in integrable models.Comment: 13 page

Proposal for a Simple Model of Dynamical SUSY Breaking

We discuss supersymmetric $SU(2)$ gauge theory with a single matter field in the $I=3/2$ representation. This theory has a moduli space of exactly degenerate vacua. Classically it is the complex plane with an orbifold singularity at the origin. There seem to be two possible candidates for the quantum theory at the origin. In both the global chiral symmetry is unbroken. The first is interacting quarks and gluons at a non-trivial infrared fixed point -- a non-Abelian Coulomb phase. The second, which we consider more likely, is a confining phase where the singularity is simply smoothed out. If this second, more likely, possibility is realized, supersymmetry will dynamically break when a tree level superpotential is added. This would be the simplest known gauge theory which dynamically breaks supersymmetry.Comment: 6 page

Boundary Critical Phenomena in SU(3) "Spin" Chains

SU(3)-invariant "spin" chains with a single impurity, such as a modified exchange coupling on one link, are analyzed using boundary conformal field theory techniques. These chains are equivalent to a special case of the "tJV" model, i.e. the t-J model with a nearest neighbour repulsion added. In the continuum limit they are equivalent to two free bosons at a special value of the compactification radii. The SU(3) symmetry, which is made explicit in this formulation, provides insight into the exact solution of a non-trivial boundary critical point found earlier in another formulation of this model as a theory of quantum Brownian motion.Comment: 19 pages, Rev Te

Exact Correlation Amplitude for the S=1/2 Heisenberg Antiferromagnetic Chain

The exact amplitude for the asymptotic correlation function in the S=1/2 Heisenberg antiferromagnetic chain is determined: goes to (-1)^r delta^{ab}(ln r)^{1/2}/[(2 pi)^{3/2}r]. The behaviour of the correlation functions for small xxz anisotropy and the form of finite-size corrections to the correlation function are also analysed.Comment: 8 pages, 3 figures, added reference and discussio

Response of finite spin-S Heisenberg chains to local perturbations

We consider the properties of finite isotropic antiferromagnetic Heisenberg chains with S=1/2, 1, 3/2 spins when a weak magnetic field is applied on a few sites, using White's density matrix renormalization group (DMRG) method. For the S=1 chain there exists only one length scale in the system which determines the behavior of the one- and two-point correlation functions both around the local perturbation and near the free boundary. For the critical, half-odd-integer spin cases the exponent of the spin-spin correlation function was found to be $\eta=1$, and the exponent of the decay of the site magnetization around the perturbed site is $x_m =\eta /2$. Close to a free boundary, however, the behavior is completely different for S=1/2 and $S > 1/2$.Comment: 13 pages, 7 figure

Neel order in doped quasi one-dimensional antiferromagnets

We study the Neel temperature of quasi one-dimensional S=1/2 antiferromagnets containing non-magnetic impurities. We first consider the temperature dependence of the staggered susceptibility of finite chains with open boundary conditions, which shows an interesting difference for even and odd length chains. We then use a mean field theory treatment to incorporate the three dimensional inter-chain couplings. The resulting Neel temperature shows a pronounced drop as a function of doping by up to a factor of 5.Comment: 4 pages in revtex4 format including 2 epsf-embedded figures. The latest version in PDF format is available from http://fy.chalmers.se/~eggert/papers/staggered.pd

Non-Fermi liquid behavior in Kondo models

Despite the fact that the low energy behavior of the basic Kondo model cannot be studied perturbatively it was eventually shown by Wilson, Anderson, Nozieres and others to have a simple "local Fermi liquid theory" description. That is, electronic degrees of freedom become effectively non-interacting in the zero energy limit. However, generalized versions of the Kondo model involving more than one channel or impurity may exhibit low energy behavior of a less trivial sort which can, nonetheless, be solved exactly using either Bethe ansatz or conformal field theory and bosonization techniques. Now the low energy limit exhibits interacting many body behavior. For example, processes in which a single electron scatters off the impurity into a multi electron-hole state have a non-vanishing (and sometimes large) amplitude at zero energy. This corresponds to a rare solveable example of non-Fermi liquid behavior. Essential features of these phenomena are reviewed.Comment: A brief review submitted to the special issue of J. Phys. Soc. of Japan, "Kondo effect -- 40 years after the discovery

Phase diagram of a 1 dimensional spin-orbital model

We study a 1 dimensional spin-orbital model using both analytical and numerical methods. Renormalization group calculations are performed in the vicinity of a special integrable point in the phase diagram with SU(4) symmetry. These indicate the existence of a gapless phase in an extended region of the phase diagram, missed in previous studies. This phase is SU(4) invariant at low energies apart from the presence of different velocities for spin and orbital degrees of freedom. The phase transition into a gapped dimerized phase is in a generalized Kosterlitz-Thouless universality class. The phase diagram of this model is sketched using the density matrix renormalization group technique.Comment: 11 pages, 5 figures, new references adde

Runaway Dynamics and Supersymmetry Breaking

Supersymmetric SU(N_C) gauge theories possess runaway-type superpotentials for N_F < N_C, where N_F is the flavor number of massless quarks. We show that the runaway behavior can be stabilized for N_F nearly equal to N_C by introducing singlets with the aid of perturbative corrections to the Kahler potential, generating (local) minima of supersymmetry breaking.Comment: 6 page