Fracton phases: analytical description and simulations of their thermal behavior

Rossi, Dario (2021) Fracton phases: analytical description and simulations of their thermal behavior. [Laurea magistrale], Università di Bologna, Corso di Studio in Physics [LM-DM270]
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Abstract

Many-body physics studies the collective behavior of systems with a large number of microscopic constituents. The interaction between the fundamental particles creates a common behavior within the system with emergent excitations exhibiting uncommon characteristics. In three spatial dimensions it has recently been found that a new kind of particles can exist characterized by a fractionalized mobility, being either immobile or mobile only along sub-dimensional spaces: fractons. In this thesis I explore fracton phases focusing on their topological and thermal properties. Fractons can be explained as a generalization of usual topological particles with some fundamental differences, which make fracton order a new field on its own. Fracton models are studied first from the point of view of exactly solvable lattice spin models, focusing on the similarities and differences with usual topological models. Fracton phases are also described through the use of symmetric tensor gauge theory. This gives a theoretical background which is used to explore some possible phases at finite densities of fractons, like Fermi liquids and quantum Hall states. The thermal properties of such systems are studied in detail through the use of numerical simulations relying on exact-diagonalization. Various correspondences with systems featuring quantum many-body scars are found, in particular with the PXP model. The non-thermal behavior of the models under study is justified by the fragmentation of the Hilbert space in a large number of separated sub-sectors, not related to symmetries of the model. Further, the range of the local Hamiltonian operators is found to be of fundamental relevance in the thermal properties of the system. For certain ranges it is observed that the models are not able to reach the thermal state at long times. Instead, increasing the length of interactions the system becomes ergodic, with the exception of a small number of special eigenstates which remain non-thermal.

Abstract
Tipologia del documento
Tesi di laurea (Laurea magistrale)
Autore della tesi
Rossi, Dario
Relatore della tesi
Correlatore della tesi
Scuola
Corso di studio
Indirizzo
THEORETICAL PHYSICS
Ordinamento Cds
DM270
Parole chiave
Fractons,Tensor gauge theory,PXP model,Eigenstate thermalization hypothesis,Scalar charge theory,Toric code,X-cube model,Topological phases,Fracton order,Fermi liquid,Quantum Hall effect,Thermalization,Ergodicity breaking,Scar states,Quantum many-body scars,Hilbert space fragmentation,Dipole conserving systems,QuSpin
Data di discussione della Tesi
24 Settembre 2021
URI

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