Birgit Wehefritz-Kaufmann

Integrable quantum field theories with OSP(m/2n) symmetries

We conjecture the factorized scattering description for OSP(m/2n)/OSP(m − 1/2n) supersphere sigma models and OSP(m/2n) Gross–Neveu models. The non-unitarity of these field theories translates into a lack of ‘physical unitarity’ of the S-matrices, which are instead unitary with respect to the non-positive scalar product inherited from the orthosymplectic structure. Nevertheless, we find that formal thermodynamic Bethe ansatz calculations appear meaningful, reproduce the correct central charges, and agree with perturbative calculations. This paves the way to a more thorough study of these and other models with supergroup symmetries using the S-matrix approach.  2002 Elsevier Science B.V. All rights reserved.

Thermodynamics of the complex su(3) Toda theory

Abstract We present the first computation of the thermodynamic properties of the complex su (3) Toda theory. This is possible thanks to a new string hypothesis, which involves bound states that are non-self-conjugate solutions of the Bethe equations. Our method provides equivalently the solution of the su (3) generalization of the XXZ chain. In the repulsive regime, we confirm that the scattering theory proposed over the past few years – made only of solitons with non-diagonal S matrices – is complete. But we show that unitarity does not follow, contrary to early claims, eigenvalues of the monodromy matrix not being pure phases. In the attractive regime, we find that the proposed minimal solution of the bootstrap equations is actually far from being complete. We discuss some simple values of the couplings, where, instead of the few conjectured breathers, a very complex structure (involving E 6 , or two E 8 ) of bound states is necessary to close the bootstrap.

Integrable quantum field theories with supergroup symmetries: the OSP(1/2) case

As a step to understand general patterns of integrability in 1 + 1 quantum field theories with supergroup symmetry, we study in details the case of OSP(1/2). Our results include the solutions of natural generalizations of models with ordinary group symmetry: the UOSP(1/2)k WZW model with a current–current perturbation, the UOSP(1/2) principal chiral model, and the UOSP(1/2) ⊗ UOSP(1/2)/UOSP(1/2) coset models perturbed by the adjoint. Graded parafermions are also discussed. A pattern peculiar to supergroups is the emergence of another class of models, whose simplest representative is the OSP(1/2)/OSP(0/2) sigma model, where the (non unitary) orthosymplectic symmetry is realized non-linearly (and can be spontaneously broken). For most models, we provide an integrable lattice realization. We show in particular that integrable osp(1/2) spin chains with integer spin flow to UOSP(1/2) WZW models in the continuum limit, hence providing what is to our knowledge the first physical realization of a super WZW model.

Notes on topological insulators

This paper is a survey of the ℤ2-valued invariant of topological insulators used in condensed matter physics. The ℤ-valued topological invariant, which was originally called the TKNN invariant in physics, has now been fully understood as the first Chern number. The ℤ2 invariant is more mysterious; we will explain its equivalent descriptions from different points of view and provide the relations between them. These invariants provide the classification of topological insulators with different symmetries in which K-theory plays an important role. Moreover, we establish that both invariants are realizations of index theorems which can also be understood in terms of condensed matter physics.

The geometry of the double gyroid wire network: quantum and classical

Quantum wire networks have recently become of great interest. Here we deal with a novel nano material structure of a Double Gyroid wire network. We use methods of commutative and non-commutative geometry to describe this wire network. Its non--commutative geometry is closely related to non-commutative 3-tori as we discuss in detail.

The noncommutative geometry of wire networks from triply periodic sufaces

We study wire networks that are the complements of triply periodic minimal surfaces. Here we consider the P, D, G surfaces which are exactly the cases in which the corresponding graphs are symmetric and self-dual. Our approach is using the Harper Hamiltonian in a constant magnetic field as set forth in [1–3]. We treat this system with the methods of noncommutative geometry and obtain a classification for all the C* geometries that appear.

Dynamical Critical Exponent for Two-Species Totally Asymmetric Diffusion on a Ring ?

We present a study of the two species totally asymmetric diffusion model using the Bethe ansatz. The Hamiltonian has Uq(SU(3)) symmetry. We derive the nested Bethe ansatz equations and obtain the dynamical critical exponent from the finite-size scaling properties of the eigenvalue with the smallest real part. The dynamical critical exponent is 3 which is the exponent corresponding to KPZ growth in the single species asymmetric diffusion model.

Clifford representations in integrable systems

In this paper we analyze integrable systems from a Clifford algebra point of view. This approach allows us to give a clear representation theoretic exposition of techniques used in spin systems, thereby showing their naturality. We then extend this approach to the analysis of the XX-model with nondiagonal boundaries which is among others related to growing and fluctuating interfaces and stochastic reaction-diffusion systems. With this rationale, it is possible to diagonalize the system and find new hidden conservation laws.

Theoretical Properties of Materials Formed as Wire Network Graphs from Triply Periodic CMC Surfaces, Especially the Gyroid

We report on our recent results from a mathematical study of wire network graphs that are complements to triply periodic CMC surfaces and can be synthesized in the lab on the nanoscale. Here, we studied all three cases in which the graphs corresponding to the networks are symmetric and self-dual. These are the cubic, diamond and gyroid surfaces. The gyroid is the most interesting case in its geometry and properties as it exhibits Dirac points (in 3d). It can be seen as a generalization of the honeycomb lattice in 2d that models graphene. Indeed, our theory works in more general cases, such as periodic networks in any dimension and even more abstract settings. After presenting our theoretical results, we aim to invite an experimental study of these Dirac points and a possible quantum Hall effect. The general theory also allows to find local symmetry groups which force degeneracies aka level crossings from a finite graph encoding the elementary cell structure. Vice-versa one could hope to start with graphs and then construct matching materials that will then exhibit the properties dictated by such graphs.

Avalanches in the raise and peel model in the presence of a wall

We investigate a non-equilibrium one-dimensional model known as the raise and peel model describing a growing surface which grows locally and has non-local desorption. For specific values of adsorption (ua) and desorption (ud) rates, the model shows interesting features. At ua = ud, the model is described by a conformal field theory (with conformal charge c = 0) and its stationary probability can be mapped onto the ground state of the XXZ quantum chain. Moreover, for the regime ua ud, the model shows a phase in which the avalanche distribution is scale-invariant. In this work, we study the surface dynamics by looking at avalanche distributions using a finite-sized scaling formalism and explore the effect of adding a wall to the model. The model shows the same universality for the cases with and without a wall for an odd number of tiles removed, but we find a new exponent in the presence of a wall for an even number of tiles released in an avalanche. New insights into the effect of parity on avalanche distributions are discussed and we provide a new conjecture for the probability distribution of avalanches with a wall obtained by using an exact diagonalization of small lattices and Monte Carlo simulations.