Machine learning many-body non-Hermitian correlated models
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School of Science |
Master's thesis
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en
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51
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Abstract
In this thesis, the properties of the interacting non-Hermitian Aubry–André–Harper (AAH) model are investigated using a many-body tight binding method. The non-Hermitian AAH model possesses a localization transition and exceptional points, both of which are inherited in the interacting model Correlation entropy is a powerful tool for characterizing fermionic many-body interactions, and for the AAH model, the exceptional points appear as peaks in the correlation entropy-- a result which is shown to be distinct from the behavior of the interacting Hermitian AAH model. However, measuring the correlation entropy is experimentally challenging as it requires knowledge of all particle--particle correlators, a task that becomes impractical in the thermodynamic limit. In addition, these correlators are complex-valued and cannot be directly measured. Nevertheless, machine learning can be used to extract the correlation entropy from a reduced set of inputs using the related and real-valued local density--density correlators. This study elucidates the relationship between exceptional points and correlation entropy, extends the applicability of correlation entropy to non-Hermitian systems, and provides a machine learning algorithm to predict the correlation entropy using only real-valued quantities.Description
Supervisor
Lado, JoseThesis advisor
Pereira, ElizabethAikebaier, Faluke