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As The T-Shirt Slogan Says, “The Physics May Be Theoretical, But The Fun Is Real!”

A mug with phrases, I am donut on it.
Graphic by Dr. Peterson

Mathematicians joke about a topologist mistakenly biting her coffee mug while pouring coffee into her donut. Topologists study the geometric properties of objects that are unchanged after bending, twisting, or pulling, however, cutting and tearing are not allowed. Thus to a topologist, donuts and coffee mugs are identical since they both have one handle, or one hole, each. It turns out topology is playing an increasingly important role in physics, specifically condensed matter physics, and this is why I am working with my research group to intensively investigate it at Cal State Long Beach.

Condensed matter physicists study solids and liquids, such as, conductors, insulators, semiconductors, and superconductors. All these phases of matter require large numbers of interacting constituent particles; after all, a crystal cannot even be defined with only one atom. In our familiar three-dimensional world it is relatively easy to tell a crystal from a liquid since one has atoms in a regularly ordered array while the other is featureless like a still pond. However, when the constituent particles are made to strongly interact, or when quantum effects begin to dominate, things can get more interesting.

Beginning around the 1970s, condensed matter physicists, largely from the semiconductor industry, began creating materials where the constituent particles (usually electrons) could be confined to two, or even one, spatial dimension and quantum mechanical effects reign. At very low temperatures, a myriad of unexpected and exotic quantum phases of matter were subsequently, and continue to be, discovered. Many of these phases host bizarre emergent quantum quasiparticles with fractional charge and/or strange quantum entanglement properties. Unlike common liquids or crystals, these newly discovered phases are not so easily understood. After years of research, physicists are realizing that topology provides the proper framework. These so-called topological phases have specific global properties analogous to the number of holes in a donut that can be used to mathematically classify them. My group has been intensely studying these phases theoretically using high-performance computer clusters and advanced theoretical techniques. In particular, we focus on manifestations of these topological phases in actual experimentally realizable systems. Besides generating significant scientific attention (the 2016 Nobel prize was awarded for the study of topological phases of matter), some of these phases are being proposed as platforms from which to construct quantum computers that promise to transform society!

Former CSULB students David Ronquillo and Michael Arciniaga (Master’s graduates in 2015 and now PhD students in physics at Ohio State University and University of California Santa Cruz, respectively), along with me, have had research recently published in Physical Review B studying topological phases in systems consisting of magnetic spins and electrons, respectively. Our group was also recently awarded a research grant from the National Science Foundation.

Dr. Peterson standing with students in a classroom before a whiteboard filled with information

(L-R): Students Matthew Acosta, David Ronquillo, Dan Silva, Ryan Hashi, Michael Arciniaga, and Dr. Peterson.

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