Microscopic origin of the $c=1$ universality class

K.K. Kozlowski

Lab. de Physique, ENS de Lyon, UMR 5672 CNRS, Lyon

Mon, Nov. 28th 2016, 14:15

Salle Claude Itzykson, Bât. 774, Orme des Merisiers

I will explain how, starting from certain quite general hypothesis on the finite-volume form factors of local operators, one can derive the emergence of a $c=1$ free boson model as an effective theory governing the large-distance regime of multi-point correlation functions. The approach is applicable to the one-dimensional massless quantum Hamiltonians belonging to the Luttinger liquid universality class. I will argue that, in the large-distance regime, the local operators of the model can be represented by well-suited vertex operators associated to the free boson model. This leads to an effective field theoretic description of the large distance behaviour of correlation functions in 1D quantum critical models. The fundamental part of this work is that such an effective description is obtained starting from the first principles, directly at the microscopic level, and that the mapping is constructive. Furthermore, the work gives a clear picture of the mechanism which leads to the emergence of the Luttinger liquid universality class. \\ \\ This is a joint work with J.-M. Maillet (ENS-Lyon, Lyon, France).

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