Public defence in the field of Engineering Physics, MSc Koushik Swaminathan

Title of the thesis: Quasiparticle localization and ergodicity breaking in flat-band lattice models

Thesis defender: Koushik Swaminathan 
Opponent: Professor Sebastian Huber, Institut für theoretische Physik, ETH Zürich, Switzerland 
Custos: Professor Päivi Törmä, Aalto University School of Science

A cup of hot coffee gradually cools until it reaches the temperature of its surroundings. In a similar way, particles in a physical system usually spread energy and information until the system settles into a balanced state and largely forgets how it began. Quantum systems, however, do not always behave this way. Particles can sometimes remain stuck in place, allowing the system to preserve information about its starting point for a long time. 

This thesis studies how interactions between particles affect transport, localization and memory in flat-band lattice systems. In a flat band, the shape of the lattice and quantum interference make it difficult for individual particles to move. These systems therefore provide a useful setting for examining whether interactions overcome this restriction or instead create new forms of collective transport. 

A central part of the research concerns the dice lattice, where individual particle motion is strongly restricted. The results show that interactions allow pairs of particles to move together, while unpaired quasiparticles can remain localized. The system can therefore transport particles while still preserving some memory of how it started. This coexistence is important because transport and localization are often treated as opposite behaviours. The findings show that interactions do not simply make every particle mobile. Instead, they determine which particles can move, allowing collective transport and localized behaviour to exist in the same system. The research also reveals a surprising difference between systems with even and odd numbers of particles. Their energy levels follow clearly different patterns, an unusual result that points to a deeper structure not yet fully understood. 

Together, these findings give a clearer picture of how interactions generate transport in flat-band systems. One motivation for studying such systems is their possible connection to unconventional superconductivity and superfluidity, where interactions in flat bands can allow particles to move collectively without resistance. Related processes can also be studied in quantum simulators, where lattice structures and particle interactions can be carefully controlled. Overall, the results show that particle transport can coexist with localized behaviour and long-lasting memory within the same quantum system.

Keywords: Flat bands, Superconductivity, Lattice models, Many-body localization, Exact diagonalization

Thesis available for public display 7 days prior to the defence at Aalto University's public display page. 

Contact Information: 
koushik.swaminathan@aalto.fi  
https://www.linkedin.com/in/koushikswaminathan/