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

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

Impurities in S=1/2 Heisenberg Antiferromagnetic Chains: Consequences for Neutron Scattering and Knight Shift

Non-magnetic impurities in an S=1/2 Heisenberg antiferromagnetic chain are studied using boundary conformal field theory techniques and finite-temperature quantum Monte Carlo simulations. We calculate the static structure function, S_imp(k), measured in neutron scattering and the local susceptibility, chi_i measured in Knight shift experiments. S_imp(k) becomes quite large near the antiferromagnetic wave-vector, and exhibits much stronger temperature dependence than the bulk structure function. \chi_i has a large component which alternates and increases as a function of distance from the impurity.Comment: 8 pages (revtex) + one postscript file with 6 figures. A complete postscript file with all figures + text (10pages) is available from http://fy.chalmers.se/~eggert/struct.ps or by request from [email protected] Submitted to Phys. Rev. Let

S(k) for Haldane Gap Antiferromagnets: Large-scale Numerical Results vs. Field Theory and Experiment

The structure function, S(k), for the s=1, Haldane gap antiferromagnetic chain, is measured accurately using the recent density matrix renormalization group method, with chain-length 100. Excellent agreement with the nonlinear $\sigma$ model prediction is obtained, both at $k\approx \pi$ where a single magnon process dominates and at $k\approx 0$ where a two magnon process dominates. We repeat our calculation with crystal field anisotropy chosen to model NENP, obtaining good agreement with both field theory predictions and recent experiments. Correlation lengths, gaps and velocities are determined for both polarizations.Comment: 11 pages, 3 postscript figures included, REVTEX 3.0, UBCTP-93-02

Susceptibility of the Spin 1/2 Heisenberg Antiferromagnetic Chain

Highly accurate results are presented for the susceptibility, $\chi (T)$ of the $s=1/2$ Heisenberg antiferromagnetic chain for all temperatures, using the Bethe ansatz and field theory methods. After going through a rounded peak, $\chi (T)$ approaches its asympotic zero-temperature value with infinite slope.Comment: 8 pages and 3 postscript figures appended (uuencoded), Revtex, Report #:UBCTP-94-00

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

Kondo effect due to a hydrogen impurity in graphene: A multichannel Kondo problem with diverging hybridization

We consider the Kondo effect, arising from a hydrogen impurity in graphene. As a first approximation, the strong covalent bond to a carbon atom removes that carbon atom without breaking the C3 rotation symmetry, and we retain only the Hubbard interaction on the three nearest neighbors of the removed carbon atom which then behave as magnetic impurities. These three impurity spins are coupled to three conduction channels with definite helicity, two of which support a diverging local density of states (LDOS) ∝1/[|ω|ln2(Λ/|ω|)] near the Dirac point ω→0 even though the bulk density of states vanishes linearly. We study the resulting three-impurity multichannel Kondo model using the numerical renormalization group method. For weak potential scattering, the ground state of the Kondo model is a particle-hole symmetric spin-1/2 doublet, with ferromagnetic coupling between the three impurity spins; for moderate potential scattering, the ground state becomes a particle-hole asymmetric spin singlet, with antiferromagnetic coupling between the three impurity spins. This behavior is inherited by the Anderson model containing the hydrogen impurity and all four carbon atoms in its vicinity

Critical properties of the double-frequency sine-Gordon model with applications

We study the properties of the double-frequency sine--Gordon model in the vicinity of the Ising quantum phase transition displayed by this model. Using a mapping onto a generalised lattice quantum Ashkin-Teller model, we obtain critical and nearly-off-critical correlation functions of various operators. We discuss applications of the double-sine-Gordon model to one-dimensional physical systems, like spin chains in a staggered external field and interacting electrons in a staggered potential.Comment: 51 pages, Latex fil

Impurities in s=1s=1 Heisenberg Antiferromagnets

The $s=1$ Heisenberg Antiferromagnet is studied in the presence of two kinds of local impurities. First, a perturbed antiferromagnetic bond with $J'\ne J$ at the center of an even-length open chain is considered. Using the density matrix renormalization group method we find that, for sufficiently strong or weak $J'$, a bound state is localized at the impurity site, giving rise to an energy level in the Haldane gap. The energy of the bound state is in agreement with perturbative results, based on $s=1/2$ chain-end excitations, both in the weak and strong coupling limit. In a region around the uniform limit, $J'=J$, no states are found with energy below the Haldane gap. Secondly, a $s=1/2$ impurity at the center of an otherwise even-length open chain is considered. The coupling to the $s=1/2$ impurity is varied. Bound states in the Haldane gap are found {\it only} for sufficiently weak (antiferromagnetic) coupling. For a $s=1/2$ impurity coupled with a strong (antiferromagnetic) bond, {\it no} states are found in the Haldane. Our results are in good qualitative agreement with recent experiments on doped NENP and Y$_2$BaNiO$_5$.Comment: 29 pages, RevTeX 3.0, 12 uuencoded postscript figures include