Non-perturbative renormalization group approach to zero-temperature Bose systems

¹  Laboratoire de Physique Théorique de la Matière Condensée, CNRS - UMR 7600, Université Pierre et Marie Curie 4 Place Jussieu, 75252 Paris Cedex 05, France
²  Laboratoire de Physique des Solides, CNRS - UMR 8502, Université Paris-Sud - 91405 Orsay, France
³  Department of Mathematics, Imperial College - 180 Queen's Gate, London SW7 2AZ, UK
⁴  TCMP Division, Saha Institute of Nuclear Physics - 1/AF Bidhannagar, Kolkata-700064, India

Received: 4 September 2007
Accepted: 8 October 2007

Abstract

We use a non-perturbative renormalization group technique to study interacting bosons at zero temperature. Our approach reveals the instability of the Bogoliubov fixed point when d≤3 and yields the exact infrared behavior in all dimensions d > 1 within a rather simple theoretical framework. It also enables to compute the low-energy properties in terms of the parameters of a microscopic model. In one dimension and for not too strong interactions, it yields a good picture of the Luttinger-liquid behavior of the superfluid phase.