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J. -S. Caux

Publications and source records attributed to J. -S. Caux.

41 records · Page 3Linked to original sources
arXiv2001

Disordered Dirac Fermions: the Marriage of Three Different Approaches

We compare the critical multipoint correlation functions for two-dimensional (massless) Dirac fermions in the presence of a random su(N) (non-Abelian) gauge potential, obtained by three different methods. We critically reexamine previous results obtained using the replica approach and in the limit of infinite disorder strength and compare them to new results (presented here) obtained using the supersymmetric approach to the N=2 case. We demonstrate that this menage a trois of different approaches leads to identical results. Remarkable relations between apparently different conformal field theories (CFTs) are thereby obtained. We further establish a connection between the random Dirac fermion problem and the c=-2 theory of dense polymers. The presence of the c=-2 theory may be seen in all three different treatments of the disorder.

cond-mat.mes-hall↗
arXiv1998

Disordered Dirac Fermions: Multifractality Termination and Logarithmic Conformal Field Theories

We reexamine in detail the problem of fermions interacting with a non-Abelian random vector potential. Without resorting to the replica or supersymmetry approaches, we show that in the limit of infinite disorder strength the theory possesses an exact solution which takes the form of a logarithmic conformal field theory. We show that the proper treatment of the locality conditions in the SU(2) theory leads to the termination of the multifractal spectrum, or in other words to the termination of the infinite hierarchies of negative-dimensional operators that were thought to occur. Based on arguments of logarithmic degeneracies, we conjecture that such a termination mechanism should be present for general SU(N). Moreover, our results lead to the conclusion that the previous replica solution of this problem yields incorrect results.

cond-mat.mes-hall↗
arXiv1997

Termination of Multifractal Behaviour for Critical Disordered Dirac Fermions

We consider Dirac fermions interacting with a disordered non-Abelian vector potential. The exact solution is obtained through a special type of conformal field theory including logarithmic correlators, without resorting to the replica or supersymmetry approaches. It is shown that the proper treatment of the conformal theory leads to a different multifractal scaling behaviour than initially expected. Moreover, the previous replica solution is found to be incorrect at the level of higher correlation functions.

cond-mat.mes-hall↗
arXiv1995

Logarithmic Operators and Hidden Continuous Symmetry in Critical Disordered Models

We study the model of (2 + 1)-dimensional relativistic fermions in a random non-Abelian gauge potential at criticality. The exact solution shows that the operator expansion contains a conserved current - a generator of a continuous symmetry. The presence of this operator changes the operator product expansion and gives rise to logarithmic contributions to the correlation functions at the critical point. We calculate the distribution function of the local density of states in this model and find that it follows the famous log-normal law.

hep-th↗