In this thesis we will investigate some properties of one-dimensional quantum
systems. From a theoretical point of view quantum models in one dimension are
particularly interesting because they are strongly interacting, since particles
cannot avoid each other in their motion, and you we can never ignore collisions.
Yet, integrable models often generate new and non-trivial solutions, which
could not be found perturbatively.
In this dissertation we shall focus on two important aspects of integrable one-
dimensional models: Their entanglement properties at equilibrium and their
dynamical correlators after a quantum quench. The first part of the thesis will
be therefore devoted to the study of the entanglement entropy in one-
dimensional integrable systems, with a special focus on the XYZ spin-1/2
chain, which, in addition to being integrable, is also an interacting model. We
will derive its Renyi entropies in the thermodynamic limit and its behaviour in
different phases and for different values of the mass-gap will be analysed.
In the second part of the thesis we will instead study the dynamics of correlators
after a quantum quench , which represent a powerful tool to measure how
perturbations and signals propagate through a quantum chain. The emphasis
will be on the Transverse Field Ising Chain and the O(3) non-linear sigma
model, which will be both studied by means of a semi-classical approach.
Moreover in the last chapter we will demonstrate a general result about the
dynamics of correlation functions of local observables after a quantum quench
in integrable systems. In particular we will show that if there are not long-range
interactions in the final Hamiltonian, then the dynamics of the model (non
equal- time correlations) is described by the same statistical ensemble that
describes its statical properties (equal-time correlations).
| Identifer | oai:union.ndltd.org:unibo.it/oai:amsdottorato.cib.unibo.it:5161 |
| Date | 22 February 2013 |
| Creators | Evangelisti, Stefano <1983> |
| Contributors | Ravanini, Francesco |
| Publisher | Alma Mater Studiorum - Università di Bologna |
| Source Sets | Università di Bologna |
| Language | English |
| Detected Language | English |
| Type | Doctoral Thesis, PeerReviewed |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
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