Strong correlations in low dimensional systems

TL;DR

This paper explores the unique physics of one-dimensional interacting quantum particles, focusing on bosons in optical lattices, and discusses phenomena like superfluid-insulator transitions and Bose glass formation using bosonization.

Contribution

It provides a detailed analysis of one-dimensional quantum systems, emphasizing bosonization techniques and their application to fundamental phase transition problems.

Findings

Superfluid to Mott insulator transition in 1D systems

Disorder induces Bose glass phase in 1D bosonic systems

Bosonization effectively solves complex 1D quantum problems

Abstract

I describe in these notes the physical properties of one dimensional interacting quantum particles. In one dimension the combined effects of interactions and quantum fluctuations lead to a radically new physics quite different from the one existing in the higher dimensional world. Although the general physics and concepts are presented, I focuss in these notes on the properties of interacting bosons, with a special emphasis on cold atomic physics in optical lattices. The method of bosonization used to tackle such problems is presented. It is then used to solve two fundamental problems. The first one is the action of a periodic potential, leading to a superfluid to (Mott)-Insulator transition. The second is the action of a random potential that transforms the superfluid in phase localized by disorder, the Bose glass. Some discussion of other interesting extensions of these studies is given.