Intertwined Order in Strongly Correlated Quantum Systems
Author(s)
Rakic, Milan
Type
Thesis
Abstract
Supersolids are a fascinating quantum phase of matter that have both superfluid and solid properties, and are in some ways an extension of a superfluid, in that it possesses an additional rich and dynamic set of phenomenological features. Supersolids are an example of strongly correlated intertwined order, which is the notion that systems can form phases of matter that are more than the sum of its parts. Put simply, a supersolid is not a superfluid + solid. This intertwined order generates new and exciting physics which looks a little like its constituent components, but also not at all.
In this thesis we develop a homogenisation technique, which begins with a microscopic theory of a supersolid and ends with a phenomenological Lagrangian. By doing this we marry two opposite ends of supersolid theory, providing the phenomenological toolset to study supersolids, but rooted in the foundation of microscopic theory.
We derive the mathematical framework necessary to employ homogenisation, apply it to the Gross-Pitaevskii Lagrangian, elucidate crucial contributions from the thermodynamic ensemble of a supersolid, and obtain an effective theory of the Goldstone modes. We conduct numerics on a soft-core bosonic system, applying homogenisation to our simulated supersolids, and verify our results with Bogoliubov theory.
We find an unexpected result that the supersolid has two distinct values for bulk compressibility, which takes it outside of the class of materials for which this thermodynamic relation holds. To the best of our knowledge, this is the first such example of this particular physical feature in any material.
We then extend homogenisation to include beyond-meanfield effects, in order to apply it to a dipolar BEC. The dipolar BEC has a considerably richer phase diagram, in which we find several exciting results.
In this thesis we develop a homogenisation technique, which begins with a microscopic theory of a supersolid and ends with a phenomenological Lagrangian. By doing this we marry two opposite ends of supersolid theory, providing the phenomenological toolset to study supersolids, but rooted in the foundation of microscopic theory.
We derive the mathematical framework necessary to employ homogenisation, apply it to the Gross-Pitaevskii Lagrangian, elucidate crucial contributions from the thermodynamic ensemble of a supersolid, and obtain an effective theory of the Goldstone modes. We conduct numerics on a soft-core bosonic system, applying homogenisation to our simulated supersolids, and verify our results with Bogoliubov theory.
We find an unexpected result that the supersolid has two distinct values for bulk compressibility, which takes it outside of the class of materials for which this thermodynamic relation holds. To the best of our knowledge, this is the first such example of this particular physical feature in any material.
We then extend homogenisation to include beyond-meanfield effects, in order to apply it to a dipolar BEC. The dipolar BEC has a considerably richer phase diagram, in which we find several exciting results.
Version
Open Access
Editor(s)
Lee, Derek
Date Issued
2025-02-24
Date Awarded
01/03/2025
Citation
2025
License URL
Advisor
Lee, Derek
Ho, Andrew
Sponsor
Leverhulme Foundation
Publisher Department
Department of Physics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)