Lorenzo Gotta
Pairing and topological phases in cold atoms with long range interactions.
Rel. Fabrizio Dolcini, Guillaume Roux. Politecnico di Torino, Corso di laurea magistrale in Physics Of Complex Systems (Fisica Dei Sistemi Complessi), 2019

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Abstract: 
Pairing and topological phases in cold atoms with long range interactions Chapter 1 Introduction The systematic study and classiﬁcation of phase transitions has become a popular research area in physics over the past decades. The most familiar phenomena associated to the concept of phase transition are the ones giving rise to macroscopic changes in the properties of strongly correlated manybody systems due to thermal ﬂuctuations. The most prominent examples of this kind of behaviour are the ferromagneticparamagnetic transition in lattice spin models and the liquidgas transition. On the other hand, when dealing with quantummechanical systems changes of matter from one state to another can arise as the result of the variation of parameters other than temperature. In particular, when a given manybody quantum problem is studied at zero temperature, thereby suppressing thermal ﬂuctuations, it is the interplay between kinetic energy and interactions that can cause the system to jump into diﬀerent phases as the model parameters are varied. Phase transitions occurring at zero temperature are widely known as quantum phase transitions. In the framework of the physics of phase transitions, the role of dimensionality is a noticeable one. The major challenge in this perspective is the treatment of low dimensional systems, where standard meanﬁeld treatments and ordinary perturbation theory are known to fail due to the enhancement of ﬂuctuations. The goal of describing collective behaviours in reduced dimensionality is usually pursued in onedimensional (1D) systems, which turn out to be simple enough to be studied in an eﬀective way through both numerical and analytical techniques, while exhibiting a rich and deeply fascinating phenomenology. As a matter of fact, since particles conﬁned to one dimension cannot avoid interactions with each other, the typical low energy excitations of the system are represented by collective density waves, which substitute nearly free quasiparticle excitations characterizing the behaviour of threedimensional Fermi liquids in the description of the eﬀects of the interplay between kinetic ﬂuctuations and interactions. On the other hand, the tools employed in the activity of tackling 1D manybody problems are eﬃcient and well developed. The analytical techniques aremainly based on the bosonization technique, which allows for the reformulation of strongly correlated 1D systems onto free bosonic theories, which can then be analyzed by means of standard path integral techniques. Meanwhile, the density matrix renormalization group (DMRG) algorithm represents the stateoftheart numerical machinery in the study of 1D physics, since it allows to eﬃciently extract the low energy properties of the model Hamiltonian and consequently characterize the corresponding phase diagram by means of the behaviour of properly chosen order parameters. As a ﬁnal remark pointing out the relevance of the research eﬀort in the direction of a better understanding of 1D manybody quantum systems, it is worth noticing that 1D systems do not represent only a playground for theorists, but have been experimentally realized by means of setups with cold atoms trapped in optical lattices, where the experimentalist is able to tune the model parameters by varying the characteristic features of the trapping laser beams and meanwhile has a comfortable access to the most relevant observables. 

Relators:  Fabrizio Dolcini, Guillaume Roux 
Academic year:  2018/19 
Publication type:  Electronic 
Number of Pages:  86 
Subjects:  
Corso di laurea:  Corso di laurea magistrale in Physics Of Complex Systems (Fisica Dei Sistemi Complessi) 
Classe di laurea:  New organization > Master science > LM44  MATHEMATICAL MODELLING FOR ENGINEERING 
Ente in cotutela:  Université de ParisSud (Paris XI) (FRANCIA) 
Aziende collaboratrici:  CNRS LPTMS 
URI:  http://webthesis.biblio.polito.it/id/eprint/11717 
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