Ferromagnetism in the Hubbard Model: Squares, Rings and More

Submitted by mbritton on

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.

Towards a Renormalization Group scheme for field theories on loops

Submitted by mbritton on

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.

Bullseye! New Method Accurately Centers Quantum Dots Within Photonic Chips

Submitted by bedfordb on

Researchers at JQI and the National Institute of Standards and Technology (NIST) have developed standards and calibrations for optical microscopes that allow quantum dots to be aligned with the center of a photonic component to within an error of 10 to 20 nanometers (about one-thousandth the thickness of a sheet of paper). Such alignment is critical for chip-scale devices that employ the radiation emitted by quantum dots to store and transmit quantum information.

Universal Sharpness Dynamics in Neural Network Training: Fixed Point Analysis, Edge of Stability, and Route to Chaos

Submitted by mbritton on

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.

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