Theory Seminar: Symmetries, purifications and the Hubbard model
Jiri Guth-Jarkovsky (MPQ): In this seminar I will talk about the recent progress on my project
Jiri Guth-Jarkovsky (MPQ)
Group seminar (hybrid format: B0.32/zoom)
Wed, 16 February 2022, 10:30 am (MEZ)
In this seminar I will talk about the recent progress on my project. It will be split into two parts.
In the first part I will talk generally about symmetries. It is known that a symmetric Hamiltonian doesn't necessarily have symmetric ground state. However, adding an ancillary subspace and considering the purifications on the whole space, we can force the ground state to have the same symmetries as the Hamiltonian (in a way).
In the second part, I will apply the above insights to solve a specific Hamiltonian - the Hubbard model. The Hubbard Hamiltonian governs the behaviour of two species of fermions on a lattice. It contains two main competing terms - a hopping term allowing the fermions to move around the system and a term representing the interaction between two fermions on a single site. To emphasize the role of symmetries, we study the Hubbard model on a permutationally-invariant system, i.e. the Hamiltonian is symmetric with respect to any permutation of the system sites. Depending on the strength of the two terms of the Hamiltonian, we find the ground state (and present the ground state phase diagram).