Publications (10)37.05 Total impact
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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. · 7.94 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: 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 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: 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: 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.  [show abstract] [hide abstract]
ABSTRACT: We develop in this letter an analytical approach using form factors to compute time dependent correlations in integrable quantum impurity problems. As an example, we obtain for the first time the frequency dependent conductivity $G(\omega)$ for the tunneling between the edges in the $\nu=1/3$ fractional quantum Hall effect, and the spectrum $S(w)$ of the spinspin correlation in the anisotropic Kondo model and equivalently in the double well system of dissipative quantum mechanics, both at vanishing temperature. Comment: 4 pages, Revtex and 2 figuresPhysical Review Letters 05/1996; 76(18):33883391. · 7.94 Impact Factor  [show abstract] [hide abstract]
ABSTRACT: We explicitly evaluate the infinite series of integrals that appears in the "AndersonYuval" reformulation of the anisotropic Kondo problem in terms of a onedimensional Coulomb gas. We do this by developing a general approach relating the anisotropic Kondo problem of arbitrary spin with the boundary sineGordon model, which describes impurity tunneling in a Luttinger liquid and in the fractional quantum Hall effect. The Kondo solution then follows from the exact perturbative solution of the latter model in terms of Jack polynomials. Comment: 4 pages in revtex twocolumnPhysical Review Letters 01/1996; 75(24):44924495. · 7.94 Impact Factor
Publication Stats
141  Citations  
37.05  Total Impact Points  
Top Journals
Institutions

1996–2000

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