Studies in Strongly Correlated Systems: From Ultracold Superfluids to Strange Metals

Abstract

Almost all the technology that we use today depends on our ability to control and exploit the properties of many electron phases. These phases are primarily made up of non-interacting fermions embodied in a metal or a simple band-insulator like silicon, and the physics of which have been understood for over 50 years now. The next generation of technology will have to overcome new obstacles, which are becoming more and more apparent, as we move forward. Most of these obstacles originate from fundamental limitations that are imposed by the laws of quantum mechanics. A way forward is to use strongly interacting electronic phases to tackle said obstacles. In this thesis, four new works that deal with such strongly interacting systems, are presented.

The first work tackles the entropy problem in cold atomic experiments. The field of cold atoms has emerged as a promising platform for simulating many-body quantum phenomena that would otherwise be difficult to study via traditional methods. However, the presence of excess entropy in fermion based simulations has hindered the field's progress. In chapter 2 of the thesis, we present our solution for addressing the said ``entropy problem" and demonstrate the effectiveness of our proposal by showing that the conditions necessary, for obtaining a fermionic superfluid, are optimal.

The second and the third work deals with the subject of non-Fermi liquids, which are electronic states of matter devoid of particle-like excitations of the kind usually found in metals. This makes a non-Fermi liquid (NFL) behave distinctly from a usual metal (a Fermi liquid) and hence NFLs are also called strange metals. In particular, this part of the thesis introduces the reader to a recent model of a zero-dimensional strange metal, called the SYK model, which is analytically solvable and has interesting connections to black hole physics. We show in chapter 3 that new electronic phases like strange half-metals (SHM) and Mott Insulators (MI) can be obtained from the SYK non-Fermi liquid. Additionally, in chapter 4 we discuss the construction of a higher-dimensional generalization of the SYK model and show that a new class of lattice non-Fermi liquids, different from the SYK model, emerge from our construction