Publications (51)178.35 Total impact
 Comptes Rendus Physique 01/2002; 3(6):685695. · 1.82 Impact Factor
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ABSTRACT: In the weak backscattering limit, point contact tunneling between quantum Hall edges is well described by a Poissonian process where Laughlin quasiparticles tunnel independently, leading to the unambiguous measurement of their fractional charges. In the strong backscattering limit, the tunneling is well described by a Poissonian process again, but this time involving real electrons. In between, interactions create essential correlations, which we untangle exactly in this Letter. Our main result is an exact closed form expression for the probability distribution of the charge $N(t)$ that tunnels in the time interval $t$. Formally, this distribution corresponds to a sum of independent Poisson processes carrying charge $\nu e$, $2\nu e$, etc., or, after resummation, processes carrying charge $e$, $2e$, etc. In the course of the proof, we compare the integrable and Keldysh approaches, and find, as a result of spectacular cancellations between perturbative integrals, the expected agreement. Comment: 4 pagesPhysical review. B, Condensed matter 09/2000; · 3.77 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: These are notes of lectures given at The NATO Advanced Study Institute/EC Summer School on ``New Theoretical Approaches to Strongly Correlated Systems'' (Newton Institute, April 2000). They are a sequel to the notes I wrote two years ago for the Summer School ``Topological Aspects of Low Dimensional Systems'', (Les Houches, July 1998). In this second part, I review the formfactors technique and its extension to massless quantum field theories. I then discuss the calculation of correlators in integrable quantum impurity problems, with special emphasis on point contact tunneling in the fractional quantum Hall effect, and the twostate problem of dissipative quantum mechanics.08/2000;  [Show abstract] [Hide abstract]
ABSTRACT: Nonequilibrium transport properties are determined exactly for an adiabatically contacted singlechannel quantum wire containing one impurity. Employing the Luttinger liquid model with interaction parameter g, for very strong interactions g less, similar0.2, and sufficiently low temperatures, we find an Sshaped currentvoltage relation. The unstable branch with negative differential conductance gives rise to current oscillations and hysteretic effects. These nonperturbative and nonlinear features appear only out of equilibrium.Physical Review Letters 05/2000; 84(16):36825. · 7.73 Impact Factor  [Show abstract] [Hide abstract]
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 nonselfconjugate 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 nondiagonal 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 E6, or two E8) of bound states is necessary to close the bootstrap.Physics Letters B 01/2000; · 4.57 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: I discuss and extend the recent proposal of Leclair and Mussardo for finite temperature correlation functions in integrable QFTs. I give further justification for its validity in the case of onepoint functions of conserved quantities. I also argue that the proposal is not correct for two (and higher) point functions, and give some counterexamples to justify that claim.Nuclear Physics B 01/2000; · 4.33 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: I discuss in this paper the continuum limit of integrable spin chains based on the superalgebras sl(N/K). The general conclusion is that, with the full ``supersymmetry'', none of these models is relativistic. When the supersymmetry is broken by the generator of the sub u(1), Gross Neveu models of various types are obtained. For instance, in the case of sl(N/K) with a typical fermionic representation on every site, the continuum limit is the GN model with N colors and K flavors. In the case of sl(N/1) and atypical representations of spin j, a close cousin of the GN model with N colors, j flavors and flavor anisotropy is obtained. The Dynkin parameter associated with the fermionic root, while providing solutions to the Yang Baxter equation with a continuous parameter, thus does not give rise to any new physics in the field theory limit. These features are generalized to the case where an impurity is embedded in the system.Nuclear Physics B 05/1999; · 4.33 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: These are lectures presented at the Les Houches Summer School ``Topology and Geometry in Physics'', July 1998. They provide a simple introduction to non perturbative methods of field theory in 1+1 dimensions, and their application to the study of strongly correlated condensed matter problems  in particular quantum impurity problems. The level is moderately advanced, and takes the student all the way to the most recent progress in the field: many exercises and additional references are provided. In the first part, I give a sketchy introduction to conformal field theory. I then explain how boundary conformal invariance can be used to classify and study low energy, strong coupling fixed points in quantum impurity problems. In the second part, I discuss quantum integrability from the point of view of perturbed conformal field theory, with a special emphasis on the recent ideas of massless scattering. I then explain how these ideas allow the computation of (experimentally measurable) transport properties in crossover regimes. The case of edge states tunneling in the fractional quantum Hall effect is used throughout the lectures as an example of application.01/1999;  [Show abstract] [Hide abstract]
ABSTRACT: The solution of the BukhvostovLipatov model is completed by computing the physical excitations and their factorized S matrix. The origin of the paradoxes which led in recent years to the suspicion that the model may not be integrable is also explained.Journal of Physics A General Physics 01/1999; 32(18).  [Show abstract] [Hide abstract]
ABSTRACT: Contents 1 Some notions of conformal field theory 1.1 The free boson via path integrals 1.2 Normal ordering and OPE 1.3 The stress energy tensor 1.4 Conformal in(co)variance 1.5 Some remarks on ward identities in QFT 1.6 The Virasoro algebra: Intuitive introduction 1.7 Cylinders 1.8 The free boson via Hamiltonians 1.9 Modular invariance 2 Conformal invariance analysis of quantum impurity fixed points 2.1 Boundary conformal field theory 2.2 Partition funcitons and boundary states 2.3 Boundary entropy 3 The boundary sineGordon model: General results 3.1 The model and the flow 3.2 Perturbation near the UV fixed point 3.3 Perturbation near the IR fixed point 3.4 An alternative to the instanton expansion: The conformal invariance analysis 4 Search for integrability: Classical analysis 5 Quantum integrability 5.1 Conformal perturbation theory 5.2 Smatrices 5.3 Back to the boundary sineGordon model 6 The thermodynamic Betheansatz: The gas of particles with "YangBaxter statistics" 6.1 Zamolodchikov Fateev algebra 6.2 The TBA 6.3 A standard computation: The central charge 6.4 Thermodynamics of the flow between N and D fixed points 7 Using the TBA to compute static transport properties 7.1 Tunneling in the FQHE 7.2 Conductance without impurity 7.3 Conductance with impurity01/1999;  [Show abstract] [Hide abstract]
ABSTRACT: It is shown that the conformal field theories SU(n)k*SU(n)1/SU(n)k+1 and SU(m)l*SU(m)1/SU(m)1+1 are equivalent, where k+n=n/m, l+m=m/n, for a pair (m, n) of relatively prime positive integers.Journal of Physics A General Physics 12/1998; 23(16):L789.  [Show abstract] [Hide abstract]
ABSTRACT: These lectures provide a simple introduction to non perturbative methods of field theory in 1 + 1 dimensions, and their application to the study of strongly correlated condensed matter problems — in particular quantum impurity problems. The level is moderately advanced, and takes the student all the way to the most recent progress in the field: many exercises and additional references are provided. In the first part, I give a sketchy introduction to conformal field theory. I then explain how boundary conformal invariance can be used to classify and study low energy, strong coupling fixed points in quantum impurity problems. In the second part, I discuss quantum integrability from the point of view of perturbed conformal field theory, with a special emphasis on the recent ideas of massless scattering. I then explain how these ideas allow the computation of (experimentally measurable) transport properties in crossover regimes. The case of edge states tunneling in the fractional quantum Hall effect is used throughout the lectures as an example of application.12/1998: pages 473550;  [Show abstract] [Hide abstract]
ABSTRACT: The author establishes using standard Coulomb gas methods, the values of a new set of geometrical exponents that have been previously conjectured. These exponents give, for any p, the number of configurations of p twodimensional selfavoiding walks of the same length l which are attached by their ends.Journal of Physics A General Physics 12/1998; 19(13):L807.  [Show abstract] [Hide abstract]
ABSTRACT: The authors calculate numerically the transfer matrix spectrum of the 2D Ising model at T=Tc and in a magnetic field h not=0. In the limit h to 0, their results reproduce the mass spectrum conjectured by Zamolodchikov (1988). Scaling functions are also studied.Journal of Physics A General Physics 12/1998; 22(11):L513. 
Article: Collapse of twodimensional linear polymers: a transfer matrix calculation of the exponent νt
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ABSTRACT: Using a transfer matrix technique and finite size scaling, the authors calculate the exponent nu t of twodimensional polymers at the theta point. They find nu t=0.55+or0.01 by two slightly different calculations on the square lattice. This value is compared with those which had been previously proposed in the literature.Journal of Physics A General Physics 12/1998; 18(17):L1075.  [Show abstract] [Hide abstract]
ABSTRACT: By using a quantitative version of the ctheorem in conformal theories, the authors determine some universal geometrical features of twodimensional critical systems, with emphasis on the ratios of mean square distances for polymers.Journal of Physics A General Physics 12/1998; 22(13):L601.  [Show abstract] [Hide abstract]
ABSTRACT: The author calculates the order parameters (local height probabilities) in the ordered phase of integrable SU(n) vertex models. The author shows that they have formally the same expression as the partition functions of the associated critical theory in a finite box with appropriate boundary conditions, once the distance to criticality in the former case is properly identified with the modular parameter in the latter. This points out a relation between offcritical integrable models and conformal theories in a finite geometry.Journal of Physics A General Physics 12/1998; 22(1):L41.  [Show abstract] [Hide abstract]
ABSTRACT: The authors discuss how coset lattice models perturbed in the appropriate direction should still be obtained by projections of noncritical integrable vertex models. The latter are described in the continuum limit by Toda field theories. By studying the mass spectrum of these theories and the projection mechanism, they conjecture without explicit construction of the S matrix the mass spectrum of the simplest coset models. Among cases considered are the unitary series perturbed in Phi 13 direction, the zn models, the tricritical Ising and tricritical threestate Potts models perturbed by the thermal operator. The latter exhibit an E7 and E6 structure respectively. Some numerical checks are presented.Journal of Physics A General Physics 12/1998; 23(5):791.  [Show abstract] [Hide abstract]
ABSTRACT: The author performs a transfer matrix study of the F model and the Flory model of polymer melting. For the F model, which can be reformulated in terms of polymers, he calculates numerically the exponent eta (T) of the massless phase and the results are in good agreement with recent conjectures. For the Flory model the author finds a very similar behaviour suggesting that these two models have the same kind of transition. The discrepancy with Monte Carlo calculations where a firstorder phase transition has been found is discussed.Journal of Physics A General Physics 12/1998; 19(12):2409.  [Show abstract] [Hide abstract]
ABSTRACT: A single impurity in the onedimensional 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 {ital g}=1/2 (the equivalent of the Toulouse point) at any temperature {ital T} and impurity coupling, expressing the charge density in terms of a hypergeometric function. We find in particular that at {ital T}=0 the oscillatory part of the density goes as ln{ital x} at small distance and {ital x}{sup {minus}1/2} at large distance. {copyright} {ital 1996 The American Physical Society.}Physical review. B, Condensed matter 12/1996; 54(19):1359713603. · 3.77 Impact Factor
Publication Stats
2k  Citations  
178.35  Total Impact Points  
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Institutions

1993–2000

University of Southern California
 • Department of Physics and Astronomy
 • Department of Mathematics
Los Angeles, California, United States


1991–1998

University of California, Santa Barbara
 • Department of Physics
 • Kavli Institute for Theoretical Physics
Santa Barbara, CA, United States 
University of Chicago
 Enrico Fermi Institute
Chicago, Illinois, United States


1996

University of California, Los Angeles
 Department of Mathematics
Los Angeles, California, United States


1991–1993

Yale University
 Department of Physics
New Haven, CT, United States
