Abstract
Quantum mechanical lattice models, such as the famous Hubbard model, were originally intended as simplified descriptions of the behavior of electrons in real solids. Today it is clear that even such simple models can present remarkably rich physics. At the same time, obtaining reliable solutions for correlated quantum systems is difficult and requires the development of both computing resources and new algorithms and approximations. Parallel with the theoretical developments, applications of lattice models have also expanded to the study of ultracold atoms in optical lattices. The hallmark of these experiments is the possibility to design different kinds of lattices and to tune the interactions between the atoms, making it possible to do real experiments on theoretical "toy models". In this thesis we have used dynamical meanfield theory (DMFT) and its cluster extensions to study superfluidity and topological phenomena in lattice models. The DMFT combines the exact solution of a small reference system with a selfconsistent meanfield treatment of the rest of the lattice. After a short introduction to the physical background of the lattice models, we review the formal definition and practical aspects of the DMFT method. We discuss the BaymKadanoffLuttingerWard functional formalism that can be used to derive the DMFT equations, and review the numerical exact diagonalization and continuoustime quantum MonteCarlo algorithms that were used in the implementation of the method. Publications I and VI discuss superfluid states induced by correlation effects that cannot easily be treated within a static meanfield theory. In Publication I we study a bilayer system where two different types of superfluids can be found depending on the densities of particles in the layers. Publication VI has a focus in the dwave superconductivity and nonuniform, striped magnetism of the twodimensional Hubbard model, which are thought to be connected with the highTc superconductivity in cuprate materials. The stripe state along with nonFermiliquid properties visible only in a beyondmeanfield treatment were observed also in the study of the Hubbard model on the Lieb lattice in Publication V. Topological and geometric properties of lattice systems, such as the Berry curvature and Chern numbers, play a central role in Publications II, III and IV. In Publication II we used exact diagonalization, DMFT and meanfield theory to study the topological phase diagram of an interacting Haldane model. The methods consistently predict a phase diagram with an intermediate topological phase not found in the wellknown noninteracting case. In Publications III and IV meanfield theory is used to study the connection between Berry curvature and the superfluid weight in lattice models, and DMFT calculations were used to support the meanfield results. Topological lattice systems have recently been realized in ultracold gas experiments and it is hoped that the calculations presented here inspire this line of research.
Original language  English 

Qualification  Doctor's degree 
Awarding Institution 

Supervisors/Advisors 

Publisher  
Print ISBNs  9789526080024 
Electronic ISBNs  9789526080031 
Publication status  Published  2018 
MoE publication type  G5 Doctoral dissertation (article) 
Keywords
 DMFT
 Hubbard model
 superfluidity
 stripe phase
 Chern number
 lattice
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Vanhala, T. (2018). Dynamical meanfield theory studies of superfluidity and topological phases in lattice models. Aalto University.