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F. Lesage

Publications and source records attributed to F. Lesage.

At least 19 recordsLinked to original sources
arXiv2004

Logarithmic lift of the su(2)_{-1/2} model

This paper carries on the investigation of the non-unitary su(2)_{-1/2} WZW model. An essential tool in our first work on this topic was a free-field representation, based on a c=-2 ηξghost system, and a Lorentzian boson. It turns out that there are several ``versions'' of the ηξsystem, allowing different su(2)_{-1/2} theories. This is explored here in details. In more technical terms, we consider extensions (in the c=-2 language) from the small to the large algebra representation and, in a further step, to the full symplectic fermion theory. In each case, the results are expressed in terms of su(2)_{-1/2} representations. At the first new layer (large algebra), continuous representations appear which are interpreted in terms of relaxed modules. At the second step (symplectic formulation), we recover a logarithmic theory with its characteristic signature, the occurrence of indecomposable representations. To determine whether any of these three versions of the su(2)_{-1/2} WZW is well-defined, one conventionally requires the construction of a modular invariant. This issue, however, is plagued with various difficulties, as we discuss.

hep-th↗
arXiv2003

Scattering amplitudes in non-Fermi liquid systems

By a mix of form-factors and analyticity techniques, we determine some fundamental scattering amplitudes in non-Fermi liquid systems. These include the reflection and transmission amplitudes for Laughlin quasiparticles at a point contact between two g=1/2 Luttinger liquids, and the e->e_{edge} at a point contact between a Fermi liquid and a g=1/3 Luttinger liquid (all liquids chiral or not). These results are obtained in closed form, and give rise to rather simple expressions for the probabilities of the most basic processes of non Fermi liquid physics at these special values of the couplings.

cond-mat.str-el↗
arXiv2002

The su(2)_{-1/2} WZW model and the beta-gamma system

The bosonic beta-gamma ghost system has long been used in formal constructions of conformal field theory. It has become important in its own right in the last few years, as a building block of field theory approaches to disordered systems, and as a simple representative -- due in part to its underlying su(2)_{-1/2} structure -- of non-unitary conformal field theories. We provide in this paper the first complete, physical, analysis of this beta-gamma system, and uncover a number of striking features. We show in particular that the spectrum involves an infinite number of fields with arbitrarily large negative dimensions. These fields have their origin in a twisted sector of the theory, and have a direct relationship with spectrally flowed representations in the underlying su(2)_{-1/2} theory. We discuss the spectral flow in the context of the operator algebra and fusion rules, and provide a re-interpretation of the modular invariant consistent with the spectrum.

hep-th↗
arXiv1999

Conductance of Distorted Carbon Nanotubes

We have calculated the effects of structural distortions of armchair carbon nanotubes on their electrical transport properties. We found that the bending of the nanotubes decreases their transmission function in certain energy ranges and leads to an increased electrical resistance. Electronic structure calculations show that these energy ranges contain localized states with significant $σ$-$π$ hybridization resulting from the increased curvature produced by bending. Our calculations of the contact resistance show that the large contact resistances observed for SWNTs are likely due to the weak coupling of the NT to the metal in side bonded NT-metal configurations.

cond-mat.mes-hall↗
arXiv1998

Perturbation of infra-red fixed points and duality in quantum impurity problems

We explain in this paper how a meaningful irrelevant perturbation theory around the infra-red (strong coupling) fixed point can be carried out for integrable quantum impurity problems. This is illustrated in details for the spin 1/2 Kondo model, where our approach gives rise to the complete low temperature expansion of the resistivity, beyond the well known $T^2$ Fermi liquid behaviour. We also consider the edge states tunneling problem, and demonstrate by Keldysh techniques that the DC current satisfies an exact duality between the UV and IR regimes. This corresponds physically to a duality between the tunneling of Laughlin quasi particles and electrons, and, more formally, to the existence of an exact instantons expansion. The duality is deeply connected with integrability, and could not have been expected a priori.

cond-mat↗
arXiv1998

Strong coupling resistivity in the Kondo model

By applying methods of integrable quantum field theory to the Kondo problem, we develop a systematic perturbation expansion near the IR (strong coupling) fixed point. This requires the knowledge of an infinity of irrelevant operators and their couplings, which we all determine exactly. A low temperature expansion (ie all the corrections to Fermi liquid theory) of the resistivity then follows, extending for instance the well known Nozieres $T^2$ result in the exactly screened case to arbitrary order. The example of the ordinary Kondo model is worked out in details: we determine $ρ$ up to order $T^6$, and compare the result with available numerical data.

cond-mat↗
arXiv1998

Two-Leg Ladders and Carbon Nanotubes: Exact Properties at Finite Doping

Recently Lin, Balents, and Fisher have demonstrated that two-leg Hubbard ladders and armchair carbon nanotubes renormalize onto the integrable SO(8) Gross-Neveu model. We exploit this integrability to examine these systems in their doped phase. Using thermodynamic Bethe ansatz, we compute exactly both the spin and single particle gaps and the Luttinger parameter describing low energy excitations. We show both the spin and particle gap do not vanish at finite doping, while the Luttinger parameter remains close to its free fermionic value of 1. A similar set of conclusions is drawn for the undoped systems' behaviour in a finite magnetic field. We also comment on the exisitence in these systems of the $π$-resonance, a hallmark of Zhang's SO(5) theory of high $T_c$ superconductivity.

cond-mat.str-el↗
arXiv1998

Boundary flows in minimal models

We discuss in this paper the behaviour of minimal models of conformal theory perturbed by the operator $Φ_{13}$ at the boundary. Using the RSOS restriction of the sine-Gordon model, adapted to the boundary problem, a series of boundary flows between different set of conformally invariant boundary conditions are described. Generalizing the "staircase" phenomenon discovered by Al. Zamolodchikov, we find that an analytic continuation of the boundary sinh-Gordon model provides a flow interpolation not only between all minimal models in the bulk, but also between their possible conformal boundary conditions. In the particular case where the bulk sinh-Gordon coupling is turned to zero, we obtain a boundary roaming trajectory in the $c=1$ theory that interpolates between all the possible spin $S$ Kondo models.

hep-th↗
arXiv1998

Boundary conditions changing operators in non conformal theories

Boundary conditions changing operators have played an important role in conformal field theory. Here, we study their equivalent in the case where a mass scale is introduced, in an integrable way, either in the bulk or at the boundary. More precisely, we propose an axiomatic approach to determine the general scalar products ${}_b<θ_1, ... ,θ_m||θ'_1, ... ,θ'_{n}>_a$ between asymptotic states in the Hilbert spaces with $a$ and $b$ boundary conditions respectively, and compute these scalar products explicitely in the case of the Ising and sinh-Gordon models with a mass and a boundary interaction. These quantities can be used to study statistical systems with inhomogeneous boundary conditions, and, more interestingly maybe, dynamical problems in quantum impurity problems. As an example, we obtain a series of new exact results for the transition probability in the double well problem of dissipative quantum mechanics.

hep-th↗
arXiv1997

Boundary interactions changing operators and dynamical correlations in quantum impurity problems

Recent developments have made possible the computation of equilibrium dynamical correlators in quantum impurity problems. In many situations however, one is rather interested in correlators subject to a non equilibrium initial preparation; this is the case for instance for the occupation probability $P(t)$ in the double well problem of dissipative quantum mechanics (DQM). We show in this paper how to handle this situation in the framework of integrable quantum field theories by introducing ``boundary interactions changing operators''. We determine the properties of these operators by using an axiomatic approach similar in spirit to what is done for form-factors. This allows us to obtain new exact results for $P(t)$; for instance, we find that that at large times (or small $g$), the leading behaviour for $g < 1/2}$ is $P(t)\propto e^{-Γt}\cosΩt$, with the universal ratio. $Ω/Γ= \cot {πg}/{2(1-g)}$.

cond-mat↗
arXiv1997

Tunneling in quantum wires II: A new line of IR fixed points

In a previous paper, we showed that the problem of tunneling in quantum wires was integrable in the isotropic case $g_σ=2$. In the present work, we continue the exploration of the general phase diagram by looking for other integrable cases. Specifically, we discuss in details the manifold $g_ρ+g_σ=2$, where the associated ``double sine-Gordon'' model is integrable. Transport properties are exactly computed. Surprisingly, the IR fixed points, while having complete reflection of charge and spin currents, do not correspond to two separate leads. Their main characteristic is that they are approached along irrelevant operators of dimension $1+{1\over g_ρ}$ and $1+{1\over g_σ}$, corresponding to transfer of one electron charge but no spin, or one spin 1/2 but no charge.

cond-mat.str-el↗
arXiv1997

Tunneling in quantum wires I: Exact solution of the spin isotropic case

We show that the problem of impurity tunneling in a Luttinger liquid of electrons with spin is solvable in the spin isotropic case ($g_σ=2$, $g_ρ$ arbitrary). The resulting integrable model is similar to a two channel anisotropic Kondo model, but with the impurity spin in a "cyclic representation" of the quantum algebra $su(2)_q$ associated with the anisotropy. Using exact, non-perturbative techniques we study the RG flow, and compute the DC conductance. As expected from the analysis of Kane and Fisher we find that the IR fixed point corresponds to two separate leads. We also prove an exact duality between the UV and IR expansions of the current at vanishing temperature.

cond-mat.str-el↗
arXiv1997

The Maxwell-Bloch Theory in Quantum Optics and the Kondo Model

In this letter, the problem of radiation in a fiber geometry interacting with a two level atom is mapped onto the anisotropic Kondo model. Thermodynamical and dynamical properties are then computed exploiting the integrability of this latter system. We compute some correlation functions, decay rates and Lamb shifts. In turn this leads to an analysis of the classical limit of the anisotropic Kondo model.

hep-th↗
arXiv1996

Correlations in one dimensional quantum impurity problems with an external field or a temperature

We discuss in more details the theory of low energy excitations in quantum impurity problems with an external field at vanishing temperature, giving further support to results of the previous paper. We then extend these results to the next order at low frequency, obtaining in particular the exact expression, as a function of the bias, of the first two derivatives of the response function $χ''(ω)$ at $ω=0$ in the double well problem of dissipative quantum mechanics. We also extend our approach to the case of non vanishing temperature and no external field. Fendley et al. had obtained in that case an expression for the Hall conductance with a single impurity using a Landauer-Büttiker type approach. We recover their result in the framework of linear response theory using renormalized form-factors. We also obtain, as a function of the temperature, the first derivative of the response function $χ''(ω)$ at $ω=0$ in the double well problem of dissipative quantum mechanics.

cond-mat↗
arXiv1996

Correlations in one dimensional quantum impurity problems with an external field

We study response functions of integrable quantum impurity problems with an external field at $T=0$ using non perturbative techniques derived from the Bethe ansatz. We develop the first steps of the theory of excitations over the new, field dependent ground state, leading to renormalized (or ``dressed'') form-factors. We obtain exactly the low frequency behaviour of the dynamical susceptibility $χ''(ω)$ in the double well problem of dissipative quantum mechanics (or equivalently the anisotropic Kondo problem),and the low frequency behaviour of the AC noise $S_t(ω)$ for tunneling between edges in fractional quantum Hall devices. We also obtain exactly the structure of singularities in $χ''(ω)$ and $S_t(ω)$. Our results differ significantly from previous perturbative approaches.

cond-mat↗
arXiv1996

Finite temperature correlations in the one-dimensional quantum Ising model

We extend the form-factors approach to the quantum Ising model at finite temperature. The two point function of the energy is obtained in closed form, while the two point function of the spin is written as a Fredholm determinant. Using the approach of \Korbook, we obtain, starting directly from the continuum formulation, a set of six differential equations satisfied by this two point function. Four of these equations involve only spacetime derivatives, of which three are equivalent to the equations obtained earlier in \mccoy,\perk. In addition, we obtain two new equations involving a temperature derivative. Some of these results are generalized to the Ising model on the half line with a magnetic field at the origin.

cond-mat↗
arXiv1996

Exact Friedel oscillations in the g=1/2 Luttinger liquid

A single impurity in the 1D Luttinger model creates a local modification of the charge density analogous to the Friedel oscillations. In this paper, we present an exact solution of the case $g={1\over 2}$ (the equivalent of the Toulouse point) at any temperature $T$ and impurity coupling, expressing the charge density in terms of a hypergeometric function. We find in particular that at $T=0$, the oscillatory part of the density goes as $\ln x$ at small distance and $x^{-1/2}$ at large distance.

cond-mat↗