Nagaoka ferromagnetism of SU(N) fermions
The development of quantum gas microscopy for two-dimensional optical lattices has provided an unparalleled tool to study condensed matter physics models with ultracold atoms. In particular, access to spin-resolved projective measurements, have played a significant role in quantifying correlation functions and uncovering of underlying physical phenomena such as magnetic phases of matter. When 173Yb or 87Sr atoms are used in optical lattices, experiments have access to a wider range of models that can be studied in their platform. One of these models (the SU(N) Fermi Hubbard model) has attracted interest due to its predicted exciting magnetic phases when the particle density is varied and the strength of the interaction between two particles increases.
In this project we will numerically explore the SU(3) Fermi Hubbard on a triangular lattice and explore what occurs when a single dopant is introduced into the model, which is predicted to support ferromagnetism. We will perform Numerical Linked Cluster Expansions, which require diagonalizing extremely large matrices and performing weighted sums to compute their thermodynamic and magnetic properties in the thermodynamic limit. In this project we will explore the formation of ferromagnetic Nagaoka polarons as a function of doping and temperature and characterize their phase diagram.
Essay prompt: Please write a short essay stating:
- Why you are interested in the project and relevant course work you have taken.
- Your programming experience with Python/Julia.
- How many credits you want to do.
- Include reference I can contact.
Depending on performance during the semester, there is a possibility of extending the research position into the summer (paid position).
The QMBSG is composed of motivated students to work on projects in the field of computational physics to solve Classical and Quantum Many-Body (MB) Physics problems. MB physics aims to understand the collective behavior of a large number of interacting particles. These interactions can create entirely new kinds of matter and display behaviors that you’d never see with just one particle. Our work spans a wide range of areas of research in Physics, such as quantum simulation with utlracold atoms, quantum sensing with optically pumped magnetometers, statistical mechanics of aerogel mixtures, magnetic and superconducting behavior in condensed matter systems.