Groupe de travail en matière condensée

The motion of strings on (semi)symmetric space target spaces underlies the integrability of the AdS/CFT correspondence. Although the relevant theories, whose excitations are giant magnons, are non-relativistic they are equivalent, via the Polhmeyer reduction, to a family of 2-d relativistic integrable field theories known as (semi)symmetric space sine-Gordon (SSSG) theories. I will review their main features, including the semiclassical quantization of their soliton spectrum, which has been recently sorted out and leads to a natural conjecture for their S-matrix formulation.

The subject of this talk are the XYZ spin chain and the eight-vertex model at the combinatorial point, an off-critical extension of the well-known Razumov-Stroganov point for the XXZ chain which is related to enumerative combinatorics. I will show that these models possess a hidden supersymmetry that changes number of sites. The derivation of this symmetry from Baxter’s Bethe ansatz reveals some new characterisations of the XYZ ground states. Finally, I will discuss a mapping to staggered fermion models with nearest-neighbour exclusion and lattice supersymmetry.

Graphene is a two dimensional honeycomb lattice made of carbon atoms. It is conducting and its charge carriers are massless Dirac fermions. In this talk, I will start by providing an introduction to graphene’s electronic properties. Then I will turn more specifically to its neutral collective excitations in the quantum Hall regime (strong perpendicular magnetic field). The particle-hole excitation spectrum for graphene can be calculated from the dynamical polarizability. The effects of electron-electron interaction are included within the random phase approximation. From the obtained polarizability, the collective excitations are studied (such as magneto-plasmons) and compared to that of the usual two-dimensional electron gases (such as those produced in semiconductor heterojunctions).

In this talk, I will review recent developments in the emerging field of electron quantum optics, stressing analogies and differences with the case of quantum optics with photons. Electron quantum optics aims at preparing, manipulating and measuring coherent single electron excitations propagating in ballistic conductors such as the edge channels of a 2DEG in the integer quantum Hall regime. Because of the Fermi statistics and the presence of strong interactions, electron quantum optics exhibits new features compared to the well known case of quantum optics involving photons. In particular, it provides a natural playground to understand decoherence and relaxation effects in quantum transport.

Non-local field theories as a method to describe the scaling limit of the long-range interacting systems are well-known for many years and they are much studied in statistical physics. The long-range spin systems and rough surfaces are just two examples from many that could be included. We show for a particular non-local free field theory that it has conformal symmetry in arbitrary dimensions. Using the local field theory counterparts of these field theories we find the Noether currents and the Ward identities of the translation, rotation and scale symmetries. The operator product expansion of the introduced energy-momentum tensor with quasi-primary fields is also investigated. We will have a close look to the rough surfeces as a physical example for our model.

A polytope is a bounded intersection of finitely-many closed halfspaces in Euclidean space.  An alternating sign matrix is a square matrix with entries 0, 1 and -1 in which along each row and column the nonzero entries alternate in sign, starting and ending with a 1.  In this talk, a certain polytope which is closely associated with alternating sign matrices will be discussed.  Some properties of this polytope will be obtained using general results for so-called fractional perfect b-matching polytopes of graphs.  It will also be shown that this polytope is related to configurations of higher spin statistical mechanical vertex models with domain-wall boundary conditions.  Some of this work is joint with Vincent Knight.

We consider the quasihole wavefunctions of the non-abelian Read-Rezayi quantum Hall states which are given by the conformal blocks of the minimal model of the WA_{k-1} algebra. By studying the degenerate representations of this conformal field theories, we derive a second order differential equation satisfied by a general many-quasihole wavefunction. We find a surprising duality between the differential equations fixing the electron and quasihole wavefunctions: they both satisfy a Calogero-Sutherland type equation. We use this equation to obtain an analytic expression for the generic wavefunction with one excess flux. This analysis also applies to the more general models WA_{k-1}(k + 1, k + r) corresponding to the recently introduced Jack states.

These results hints at some novel structure about non polynomial solutions of Calogero-Sutherland Hamiltonian.

Invariants of topological manifolds that are based on the representation theory of quantum groups play an important role in mathematical physics. In particular, they are of interest to quantum gravity, where they are known under the name of spin foam models. Compared to the `classical´ models which are based on the representation theory of Lie groups, the q-deformed models constructed upon the representation categories of quantum groups offer several advantages, the most important one being the improvement of the convergence properties. In this talk, I will discuss q-deformations of spin foam models in three and four space-time dimensions. I will firstly review the derivation of the Ponzano-Regge model of 3d quantum gravity from a physical perspective and present the Turaev-Viro invariant as a natural regulator of its divergences. I will then discuss analogue constructions in four dimensions and present recent results concerning the q-deformation of a certain constrained topological model.

Entanglement is probably the most fundamental and intriguing feature  of quantum theory. A well-known measure of entanglement between two parts of a system is the Von Neumann entropy (or more generally the Renyi entropy) of either subsystem, which is the quantum version of the classical Shannon entropy. In a large system where the Hamiltonian is not known precisely, the wavefunction can be modelled as a random superposition of the basis states: a random state. I will show how one can compute analytically (using a Coulomb gas method) the probability distribution of the Renyi entropy for a random pure state of a large bipartite quantum system. In particular, we find
that this distribution changes shape twice, at two critical values. This is the consequence of two phase transitions in the corresponding charge density of the Coulomb gas.

I shall describe  recent work with J-S Caux, H Konno  and M Sorrell in which we consider  the XXZ model in the  massless regime. This quantum spin  chain  is happily  both  quantum  integrable and  experimentally realisable.  I  shall  describe  how  the  vertex  operator  approach, developed originally  for the massive antiferromagnetic  model, may be used to  find exact  lattice form-factors for  the massless  regime. I will show how these form-factors  may be used to compute contributions to  the  longitudinal  structure  factor.  I  shall  give  an  explicit expression   the   exact   two-particle   contribution   and   present quantitative  evidence for  the dominance  of this  contribution. This structure  factor  is   directly  measurable  via  neutron  scattering experiments.

I will present results of our recent work [3] on equilibration of quantum Hall edge states at integer filling factors which was motivated by experiments involving point contacts at finite bias [1,2]. Idealizing the experimental situation and extending the notion of a quantum quench, I will discuss the time evolution of a non-equilibrium state in a translationally invariant system. It will be shown that electron interactions bring the system into a steady state at long times, which is, strikingly, not a thermal one.  For filling factor \nu=1 I will consider relaxation arising from finite-range and Coulomb interactions between electrons in the same channel, and for filling factor \nu=2  due to contact interactions between electrons in different channels. Comparison of the results with experiments [1,2] will be presented.

[1] “Energy Relaxation in the Integer Quantum Hall Regime” H. le Sueur,
C. Altimiras, U. Gennser, A. Cavanna, D. Mailly, F. Pierre, Phys. Rev. Lett. 105, 056803 (2010).

[2] “Non-equilibrium edge-channel spectroscopy in the integer quantum Hall regime”,
C. Altimiras, H. le Sueur, U. Gennser, A. Cavanna,  D. Mailly and F. Pierre, Nature Physics 6, 34 (2009).

[3] “Equilibration of integer quantum Hall edge states”,
D.L. Kovrizhin, J.T. Chalker, arXiv:1009.4555

The Ashkin-Teller (AT) model is a 2D statistical model, consisting of two coupled Ising models. It has a critical line  with constant central charge c=1 and varying critical exponents, containing in particular the Z_4 spin model of Fateev-Zamolodchikov. We construct a discretely holomorphic parafermion existing for the whole critical line, identify the corresponding interface in terms of the cluster representation of the AT model, and find that this interface has a constant fractal dimension d_f=3/2 along the critical line. In this talk, I will explain this construction and discuss attempts to relate the Z_N and AT interfaces to SLE. I will also compare our results to recent works by M. Picco, R. Santachiara and A. Sicilia (LPTHE/LPTMS).

I will give an overview of the recent developments in respect to the computation, starting from the first principles, of the long-distance (and/or long-time) asymptotics behavior of the two-point functions in integrable models that are away from their free-fermion point. In particular, I will discuss the cases of zero and non-zero temperature. I will argue that, generically speaking, the two-point functions of integrable models can be represented in terms of series of multiple integrals that have a natural interpretation as a multidimensional deformations of the Fredholm series for the Fredholm determinant  of an integrable integral operator. Such representations can be obtained from the so-called form-factor expansion of two-point functions. I will then explain how the interpretation in terms of multidimensional deformations of Fredholm determinants allows one to build on Riemann–Hilbert problem based techniques so as to construct new types of series representations (the so-called multidimensional Natte series) that  allow to read-off the asymptotic behavior of the correlator. Part of these results stem from a joint work with Kitanine, Maillet, Slavnov and Terras.

Linear statistics on ensembles of random matrices occur frequently in many applications. We present a general method to compute probability distributions of linear statistics for large matrix size N. This is applied to the calculation of full probability distribution of conductance and shot noise for ballistic scattering in chaotic cavities, in the limit of large number of open electronic channels. The method is based on a mapping to a Coulomb gas problem in Laplace space, displaying phase transitions as the Laplace parameter is varied. As a consequence, the sought distributions generally display a central Gaussian region flanked on both sides by non-Gaussian tails, and weak non-analytical points at the junction of the two regimes.

References:
Phys. Rev. B 81, 104202 (2010)
Phys. Rev. Lett. 101, 216809 (2008)

Quantum wires are networks of one-dimensional wires connected at nodes. Focusing our attention on star graphs made of n edges and one junction (also seen as a defect), a quantum field theoretical framework is developed and applied to the computation of physical quantities such as the conductance. The one-body scattering matrix corresponding to the boundary conditions at the junction is studied in some detail and different situations: at criticality where the boundary conditions are scale invariant, and away from criticality. In this last case, the presence/absence of bound states determines the existence of two different regimes with inequivalent physical properties, bound states driving the system out of equilibrium. Considering the Tomonago-Luttinger model on a star graph, the electromagnetic conductance is derived in both regimes and in explicit form, and the impact of the bound and antibound states pointed out.