Spring 2024

Nagaoka ferromagnetism (NF) is a long-predicted example of itinerant ferromagnetism in the Hubbard model and has been studied theoretically for many years. NF occurs when there is one hole in a half-filled band and a large onsite Coulomb repulsion, which does not arise naturally in materials. Quantum dots systems like dopant arrays in Si, can be fabricated with atomically precise complex geometries to create highly controllable systems. This makes them good candidates to study itinerant ferromagnetism in different array geometries.

Dissertation Committee Chair: Mohammad Hafezi and Kartik Srinivasan

Committee: 

Yanne Chemo

Efrain Rodriguez

Edo Waks

Xiyuan Lu

Dissertation Committee Chair: Professor Alicia Kollár

Committee: 

Professor Norbert Linke, Advisor and Co-Chair

Professor Zohreh Davoudi

Professor Ian Spielman

Professor Xiaodi Wu

Theories whose fluctuating degrees of freedom live on extended loops as opposed to points, are abundant in nature. One example is the action obtained upon eliminating the redundant gauge fields in a gauge theory. Formulating a Renormalization Group (RG) procedure for such a theory is an open problem. In this work, we outline a procedure that in principle computes the outcome of coarse-graining and rescaling of such a theory. We make estimates that lead to qualitative agreement with known results of phase transitions in gauge theories and the XY-model.

In gradient descent dynamics of neural networks, the top eigenvalue of the Hessian of the loss (sharpness) displays a variety of robust phenomena throughout training. This includes early time regimes where the sharpness may decrease during early periods of training (sharpness reduction), and later time behavior such as progressive sharpening and edge of stability. We demonstrate that a simple $2$-layer linear network (UV model) trained on a single training example exhibits all of the essential sharpness phenomenology observed in real-world scenarios.

Committee: Steven Rolston (chair)

Ian Spielman (advisor)

Mohammad Hafezi (dean's rep)

William Phillips

Trey Porto

In order to simulate interacting fermionic systems on quantum computers, the first step is to encode the physical Hamiltonian into qubit operators. Existing encoding procedures such as the Jordan-Wigner transformation and Bravyi-Kitaev transformation are not resource efficient because they encode each second-quantized fermionic operator into a Pauli string without incorporating the structure of the Hamiltonian in question.

Light emitters within two-dimensional arrays have been demonstrated to exhibit various cooperative effects, including super- and sub-radiance, collective line-shift and linewidth, and topological features such as Chern bands and edge states. Motivated by these intriguing properties, the realization of emitter arrays has been attempted in cold atom experiments, which nevertheless cannot access the deep subwavelength regime.