De Angelis, Damiano
(2023)

*Frustrated XYZ spin-1/2 chain and its continuum limit.*
[Laurea magistrale], Università di Bologna, Corso di Studio in

Physics [LM-DM270]

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## Abstract

The XYZ spin-1/2 model describes a completely anisotropic spin chain, which is the most generic nearest neighbor quantum magnet in one dimension. It describes a truly interacting many-body system, but it is also known to be integrable in the Bethe ansatz framework, which, despite its complexity, allows to extract most of the thermodynamic properties. This is done by obtaining the solution for a finite chain and then taking the thermodynamic limit to describe a macroscopic system. Peculiarly, all techniques proposed in the second half of the 20th century for this system are valid only for chains with an even number of sites. Although in general such boundary conditions are not expected to affect the thermodynamic properties of a system, recent literature has shown that an odd number of sites, by inducing frustration, can expose a different sector of the model. In this project, we retrieve and analyze the very convoluted recent literature dealing with the extension of the solution of the model to the case of odd-numbered sites. The analysis then moves to the study of its thermodynamic limit. In the continuum limit, the XYZ chain maps in the famous sine-Gordon model, but, once again, this mapping is non-trivial. Applying frustrated boundary conditions to the chain grants access to the sector of the sine-Gordon model with an odd number of topological excitations. In particular, the chain's ground state corresponds to a single soliton, whose dispersion relation allows us a match between the two models.

Abstract

The XYZ spin-1/2 model describes a completely anisotropic spin chain, which is the most generic nearest neighbor quantum magnet in one dimension. It describes a truly interacting many-body system, but it is also known to be integrable in the Bethe ansatz framework, which, despite its complexity, allows to extract most of the thermodynamic properties. This is done by obtaining the solution for a finite chain and then taking the thermodynamic limit to describe a macroscopic system. Peculiarly, all techniques proposed in the second half of the 20th century for this system are valid only for chains with an even number of sites. Although in general such boundary conditions are not expected to affect the thermodynamic properties of a system, recent literature has shown that an odd number of sites, by inducing frustration, can expose a different sector of the model. In this project, we retrieve and analyze the very convoluted recent literature dealing with the extension of the solution of the model to the case of odd-numbered sites. The analysis then moves to the study of its thermodynamic limit. In the continuum limit, the XYZ chain maps in the famous sine-Gordon model, but, once again, this mapping is non-trivial. Applying frustrated boundary conditions to the chain grants access to the sector of the sine-Gordon model with an odd number of topological excitations. In particular, the chain's ground state corresponds to a single soliton, whose dispersion relation allows us a match between the two models.

Tipologia del documento

Tesi di laurea
(Laurea magistrale)

Autore della tesi

De Angelis, Damiano

Relatore della tesi

Correlatore della tesi

Scuola

Corso di studio

Indirizzo

THEORETICAL PHYSICS

Ordinamento Cds

DM270

Parole chiave

spin-chain,XYZ,Bethe ansatz,eight-vertex,frustration,thermodynamic limit,continuum limit,sine-Gordon,soliton

Data di discussione della Tesi

15 Dicembre 2023

URI

## Altri metadati

Tipologia del documento

Tesi di laurea
(NON SPECIFICATO)

Autore della tesi

De Angelis, Damiano

Relatore della tesi

Correlatore della tesi

Scuola

Corso di studio

Indirizzo

THEORETICAL PHYSICS

Ordinamento Cds

DM270

Parole chiave

spin-chain,XYZ,Bethe ansatz,eight-vertex,frustration,thermodynamic limit,continuum limit,sine-Gordon,soliton

Data di discussione della Tesi

15 Dicembre 2023

URI

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