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

TL;DR

This paper introduces a non-perturbative renormalization-group method to analyze zero-temperature interacting bosons, revealing fixed point instabilities and exact infrared behaviors across dimensions, and connecting microscopic parameters to low-energy properties.

Contribution

It presents a novel non-perturbative RG approach that uncovers fixed point instabilities and provides exact infrared behavior for bosonic systems in various dimensions.

Findings

Reveals instability of the Bogoliubov fixed point for d ≤ 3.

Provides exact infrared behavior in all dimensions d > 1.

Accurately describes Luttinger-liquid behavior in 1D for moderate interactions.

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 $d\leq 3$ 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.