arXiv subjects

Andreas W. W. Ludwig

Publications and source records attributed to Andreas W. W. Ludwig.

81 records · Page 5Linked to original sources

arXiv1999

Random Defect Lines in Conformal Minimal Models

We analyze the effect of adding quenched disorder along a defect line in the 2D conformal minimal models using replicas. The disorder is realized by a random applied magnetic field in the Ising model, by fluctuations in the ferromagnetic bond coupling in the Tricritical Ising model and Tricritical Three-state Potts model (the $ϕ_{12}$ operator), etc.. We find that for the Ising model, the defect renormalizes to two decoupled half-planes without disorder, but that for all other models, the defect renormalizes to a disorder-dominated fixed point. Its critical properties are studied with an expansion in $\eps \propto 1/m$ for the mth Virasoro minimal model. The decay exponents $X_N=\frac{N}{2}(1-\frac{9(3N-4)}{4(m+1)^2}+ \mathcal{O}(\frac{3}{m+1})^3)$ of the Nth moment of the two-point function of $ϕ_{12}$ along the defect are obtained to 2-loop order, exhibiting multifractal behavior.This leads to a typical decay exponent $X_{\rm typ}={1/2} (1+\frac{9}{(m+1)^2}+\mathcal{O}(\frac{3}{m+1})^3)$. One-point functions are seen to have a non-self-averaging amplitude. The boundary entropy is larger than that of the pure system by order 1/m^3. As a byproduct of our calculations, we also obtain to 2-loop order the exponent $\tilde{X}_N=N(1-\frac{2}{9π^2}(3N-4)(q-2)^2+\mathcal{O}(q-2)^3)$ of the Nth moment of the energy operator in the q-state Potts model with bulk bond disorder.

cond-mat.dis-nn↗

arXiv1999

Schwinger-Keldysh Approach to Disordered and Interacting Electron Systems: Derivation of Finkelstein's Renormalization Group Equations

We develop a dynamical approach based on the Schwinger-Keldysh formalism to derive a field-theoretic description of disordered and interacting electron systems. We calculate within this formalism the perturbative RG equations for interacting electrons expanded around a diffusive Fermi liquid fixed point, as obtained originally by Finkelstein using replicas. The major simplifying feature of this approach, as compared to Finkelstein's is that instead of $N \to 0$ replicas, we only need to consider N=2 species. We compare the dynamical Schwinger-Keldysh approach and the replica methods, and we present a simple and pedagogical RG procedure to obtain Finkelstein's RG equations.

cond-mat.dis-nn↗

arXiv1999

Exact exponents for the spin quantum Hall transition

We consider the spin quantum Hall transition which may occur in disordered superconductors with unbroken SU(2) spin-rotation symmetry but broken time-reversal symmetry. Using supersymmetry, we map a model for this transition onto the two-dimensional percolation problem. The anisotropic limit is an sl(2|1) supersymmetric spin chain. The mapping gives exact values for critical exponents associated with disorder-averages of several observables in good agreement with recent numerical results.

cond-mat.mes-hall↗

arXiv1996

Relating c<0 and c>0 Conformal Field Theories

A `canonical mapping' is established between the c=-1 system of bosonic ghosts and the c=2 complex scalar theory and, a similar mapping between the c=-2 system of fermionic ghosts and the c=1 Dirac theory. The existence of this mapping is suggested by the identity of the characters of the respective theories. The respective c<0 and c>0 theories share the same space of states, whereas the spaces of conformal fields are different. Upon this mapping from their c<0 counterparts, the (c>0) complex scalar and the Dirac theories inherit hidden nonlocal sl(2) symmetries.

hep-th↗

arXiv1995

SPINON BASIS FOR (sl2^)_k INTEGRABLE HIGHEST WEIGHT MODULES AND NEW CHARACTER FORMULAS

In this note we review the spinon basis for the integrable highest weight modules of sl2^ at levels k\geq1, and give the corresponding character formula. We show that our spinon basis is intimately related to the basis proposed by Foda et al. in the principal gradation of the algebra. This gives rise to new identities for the q-dimensions of the integrable modules.

hep-th↗

arXiv1995

Conformal Field Theory Approach to the 2-Impurity Kondo Problem: Comparison with Numerical Renormalization Group Results

Numerical renormalization group and conformal field theory work indicate that the two impurity Kondo Hamiltonian has a non-Fermi liquid critical point separating the Kondo-screening phase from the inter-impurity singlet phase when particle-hole (P-H) symmetry is maintained. We clarify the circumstances under which this critical point occurs, pointing out that there are two types of P-H symmetry. Only one of them guarantees the occurance of the critical point. Much of the previous numerical work was done on models with the other type of P-H symmetry. We analyse this critical point using the boundary conformal field theory technique. The finite-size spectrum is presented in detail and compared with about 50 energy levels obtained using the numerical renormalization group. Various Green's functions, general renormalization group behaviour, and a hidden $SO(7)$ are analysed.

cond-mat↗

arXiv1995

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.

cond-mat↗

arXiv1994

Affine and Yangian Symmetries in $SU(2)_1$ Conformal Field Theory

In these lectures, we study and compare two different formulations of $SU(2)$, level $k=1$, Wess-Zumino-Witten conformal field theory. The first, conventional, formulation employs the affine symmetry of the model; in this approach correlation functions are derived from the so-called Knizhnik-Zamolodchikov equations. The second formulation is based on an entirely different algebraic structure, the so-called Yangian $Y(sl_2)$. In this approach, the Hilbert space of the theory is obtained by repeated application of modes of the so-called spinon field, which has $SU(2)$ spin $j=\thalf$ and obeys fractional (semionic) statistics. We show how this new formulation, which can be generalized to many other rational conformal field theories, can be used to compute correlation functions and to obtain new expressions for the Virasoro and affine characters in the theory. [Lectures given at the 1994 Trieste Summer School on High Energy Physics and Cosmology, Trieste, July 1994.]

hep-th↗

arXiv1994

The Fermi Edge Singularity and Boundary Condition Changing Operators

The boundary conformal field theory approach to quantum impurity problems is used to study the Fermi edge singularity, occuring in the X-ray adsorption probablility. The deep-hole creation operator, in the effective low-energy theory, changes the boundary condition on the conduction electrons. By a conformal mapping, the dimension of such an operator is related to the groundstate energy for a finite system with different boundary conditions at the two ends. The Fermi edge singularity is solved using this method, for the Luttinger liquid including back-scattering and for the multi-channel Kondo problem.

cond-mat↗