Ömer Mert Aksoy Massachusetts Institute of Technology
“Symmetry-Topological-Order Correspondence and Its Applications”
Abstract
Symmetry is one of the most powerful tools in physics. On the one hand, the presence of symmetries can constraint the spectral properties in the form of conservation laws or anomalies. On the one hand, the phases of matter can be characterized and organized by their corresponding (spontaneous) symmetry breaking patterns. Recently a deep connection between the symmetry structure of quantum matter in d-dimensional space and topological orders in (d+1)-dimensional space, the so-called Symmetry-topological-order (SymTO) correspondence, has been uncovered. In this talk, I will give a pedagogical review of the SymTO construction for the simplest paradigmatic examples of spontaneous symmetry breaking and topological orders, namely the transverse field Ising model in one dimension and Kitaev’s toric code in two dimension, respectively. I will then provide an example where SymTO construction can be used to understand the symmetry breaking patterns in spin chains with non-invertible symmetries, i.e., unusual symmetry transformations that do not have an inverse and, hence, are not implemented by unitary operators. If time permits, I will discuss, as a second application, our upcoming work on organizing gapped phases of matter using certain algebraic structures of the SymTO construction. No prior knowledge on topological orders or SymTO correspondence will be needed.
Ömer Aksoy graduated from Bilkent University in 2017 with a B.Sc. in Electrical and Electronics Engineering and a minor in Physics. He received his M.Sc. and Ph.D. degrees from ETH Zurich in 2019 and 2023, respectively. He currently works as a postdoctoral associate in the Condensed Matter Theory Group at MIT, focusing on generalized symmetries and their applications to quantum matter.
Date: December 25, 2024 Wednesday
Time: 15:30
Place: SA-240
All interested are cordially invited.