Bosonization of Luttinger liquids: spin flipping interactions and spin-orbit coupling

TL;DR

This thesis applies quantum field theory techniques to condensed matter models, analyzing spin interactions, spin-orbit coupling effects, and their impact on the properties and phase diagram of Luttinger liquids.

Contribution

It introduces a detailed analysis of spin-flipping interactions and spin-orbit coupling in Luttinger liquids using bosonization and effective field theories.

Findings

Spin-orbit interactions alter correlation exponents.

New susceptibilities diverge at low temperatures.

Effective bosonic actions describe separated spin and charge modes.

Abstract

In this thesis we present contributions in the field of the applications of quantum field theories techniques to condensed matter models. In chapter 3 we investigate on the non covariant fermionic determinant and its connection to Luttinger liquids. We address the problem of the regularization of the theory. In chapter 4 we treat spin flipping interactions in the non local Thirring model and we obtain an effective bosonic actions that describe separated spin and charge degrees of freedom. In chapter 4 we apply the self consistent harmonic approximation to previously derived bosonic action and we obtain potential depending equations for the spectrum gap. In chapter 5 we include spin-orbit couplings and compute correlations functions. We show that the spin orbit interactions modify the exponents and the phase diagram of the system and makes new susceptibilities diverge for low temperature. Finally in chapter 6 we summarize the main results and the conclusions.