Tunneling in Quantum Wires: a Boundary Conformal Field Theory Approach

Tunneling through a localized barrier in a one-dimensional interacting electron gas has been studied recently using Luttinger liquid techniques. Stable phases with zero or unit transmission occur, as well as critical points with universal fractional transmission whose properties have only been calculated approximately, using a type of ``$\epsilon$-expansion''. It may be possible to calculate the universal properties of these critical points exactly using the recent boundary conformal field theory technique, although difficulties arise from the $\infty$ number of conformal towers in this $c=4$ theory and the absence of any apparent ``fusion'' principle. Here, we formulate the problem efficiently in this new language, and recover the critical properties of the stable phases.Comment: 32 pages, REVTEX 3.0, 1 postscript file appended, UBCTP-93-2

Phase Diagram of the 1/2-1/2-1-1 Spin Chain by the Nonlinear Sigma Model

We examine a periodic mixed spin chain with spin magnitudes 1/2 and 1 which are arrayed as 1/2-1/2-1-1. The three independent parameters are ratios of the four exchange couplings. We determine phase boundaries in the parameter space by using the gapless condition which was previously derived by mapping a general inhomogeneous spin chain to the nonlinear sigma model. We find two gapless boundaries separating three disordered phases. The features of the phases are explained in terms of singlet clusters.Comment: 2 pages, 2 Postscript figures, Submitted to Physica B (Proceedings of the 22nd International Conference on Low temperature Physics

Majorana Fermions, Exact Mapping between Quantum Impurity Fixed Points with four bulk Fermion species, and Solution of the ``Unitarity Puzzle''

Several Quantum Impurity problems with four flavors of bulk fermions have zero temperature fixed points that show non fermi liquid behavior. They include the two channel Kondo effect, the two impurity Kondo model, and the fixed point occurring in the four flavor Callan-Rubakov effect. We provide a unified description which exploits the SO(8) symmetry of the bulk fermions. This leads to a mapping between correlation functions of the different models. Furthermore, we show that the two impurity Kondo fixed point and the Callan-Rubakov fixed point are the same theory. All these models have the puzzling property that the S matrix for scattering of fermions off the impurity seems to be non unitary. We resolve this paradox showing that the fermions scatter into collective excitations which fit into the spinor representation of SO(8). Enlarging the Hilbert space to include those we find simple linear boundary conditions. Using these boundary conditions it is straightforward to recover all partition functions, boundary states and correlation functions of these models.Comment: 19 pages, latex, revtex

Naturalness Versus Supersymmetric Non-renormalization Theorems

We give an intuitive proof of a new non-renormalization theorem in supersymmetric field theories. It applies both perturbatively and non-perturbatively. The superpotential is not renormalized in perturbation theory but receives non-perturbative corrections. However, these non-perturbative corrections are {\it not} generic functions of the fields consistent with the symmetries. Certain invariant terms are not generated. This violation of naturalness has applications to dynamical supersymmetry breaking.Comment: 14 pages, RU-93-4

On a Renormalization Group Approach to Dimensional Crossover

A recently proposed renormalization group approach to dimensional crossover in quasi-one-dimensional quantum antiferromagnets is improved and then shown to give identical results, in some cases, to those obtained earlier.Comment: 8 pages, Rev Tex, no figure

Non-Hermitian Luttinger Liquids and Vortex Physics

As a model of two thermally excited flux liquids connected by a weak link, we study the effect of a single line defect on vortex filaments oriented parallel to the surface of a thin planar superconductor. When the applied field is tilted relative to the line defect, the physics is described by a nonhermitian Luttinger liquid of interacting quantum bosons in one spatial dimension with a point defect. We analyze this problem using a combination of analytic and numerical density matrix renormalization group methods, uncovering a delicate interplay between enhancement of pinning due to Luttinger liquid effects and depinning due to the tilted magnetic field. Interactions dramatically improve the ability of a single columnar pin to suppress vortex tilt when the Luttinger liquid parameter g is less than or equal to one.Comment: 4 pages, 5 eps figures, minor changes made, one reference adde

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

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

Non-Fermi Liquid Fixed Point in 2+1 Dimensions

We construct models of excitations about a Fermi surface that display calculable deviations from Fermi liquid behavior in the low-energy limit. They arise as a consequence of coupling to a Chern-Simons gauge field, whose fluctations are controlled through a ${1\over{k^x}}$ interaction. The Fermi liquid fixed point is shown to be unstable in the infrared for $x<1$, and an infrared-stable fixed point is found in a $(1-x)$-expansion, analogous to the $\epsilon$-expansion of critical phenomena. $x=1$ corresponds to Coulomb interactions, and in this case we find a logarithmic approach to zero coupling. We describe the low-energy behavior of metals in the universality class of the new fixed point, and discuss its possible application to the compressible $\nu={1\over2}$ quantum Hall state and to the normal state of copper-oxide superconductors.Comment: 24 pages, 2 figures uuencoded at end, use Phyzzx and epsf, PUPT 1438, IASSNS-HEP 93/8