Physics

The importance of the tenfold way in physics was only recognized in this century. Simply put, it implies that there are ten fundamentally different kinds of matter. But it goes back to 1964, when the topologist C. T. C. Wall classified the associative real super division algebras and found ten of them. The three 'purely even' examples were already familiar: the real numbers, complex numbers and quaternions. The rest become important when we classify representations of groups on Z/2-graded Hilbert spaces. We explain this classification, its connection to Clifford algebras, and some of its implications.

Zoom Link: https://pitp.zoom.us/j/96451287888?pwd=dlp2eVhKVTU0L2hqN2UxMy95V21SQT09

We investigate the ground states of spin-S Kitaev ladders using exact analytical solutions (for S=1/2), perturbation theory, and the density matrix renormalization group (DMRG) method. We find an even-odd effect: in the case of half-integer S, we find phases with spontaneous symmetry breaking (SSB) and symmetry-protected topological (SPT) order; for integer S, we find SSB and trivial paramagnetic phases. We also study the transitions between the various phases; notably, for half-integer S we find a transition between two distinct SPT orders, and for integer S we find unnecessary first order phase transitions within a trivial phase

Zoom link:  https://pitp.zoom.us/j/96692976298?pwd=d3dieERwTHJ2MEh5NFF2bFpnS3hOUT09

I will introduce asymptotically safe quantum gravity, which is based on the quantum realization of scale invariance, as one candidate theory to describe nature at all scales. I will discuss the concept of an asymptotically safe fixed point, and how the realization of scale invariance at high energies might provide a predictive and UV-complete description of nature. In particular, I will focus on the interplay of gravity and matter, and highlight mechanisms how this interplay might lead to constraints and predictions of asymptotically safe gravity-matter systems.

Zoom Link: https://pitp.zoom.us/j/99056179498?pwd=SzlXK1R5dExNckFMM1pMS3IvS1VyQT09

Quantum algorithms have been found which are able to solve important problems exponentially faster than any known classical algorithm. The most well known example is Shor's algorithm which would be able to break all RSA encryption if fault tolerant quantum computers existed for it to be run on. It is currently not believed that quantum computers will be able to efficiently solve NP-Complete problems, but the answer is still unknown. I present a novel quantum algorithm which is able to solve 3-SAT along with numerical simulations to see how it performs on small instances, but new methods of analyzing the complexity of quantum algorithms will need to be developed before we can say exactly how it performs. This will be the goal of my PSI essay.

Zoom Link: https://pitp.zoom.us/j/95795655548?pwd=aU5jNFhFZHEzUWpLK1FvWjd2Q1c2Zz09