Stacking and the triviality of invertible phases
Sven Bachmann, Alan Getz, Pieter Naaijkens, Naomi Wray
2025
I am currently a doctoral student in the School of Mathematics at Cardiff University -- I completed my BSc Mathematics and Physics here in 2022 and MSc Mathematics in 2023. As part of my role in the School as a graduate tutor, I teach classes supporting modules in the first and second year of our undergraduate maths course. This has fuelled my interest in maths pedagogy and education research, prompting me to build my knoweldge taking the Associate Fellowship Programme in 2025 (AFHEA).
In my project, I am investigating techniques inspired by Algebraic Quantum Field Theory to model systems with topological order, hosting anyonic excitations: an attractive candidate for quantum computation. My project looks towards generalising the categorical formulation of anyon theories to encompass fractonic states of matter. My research interests lie in Topological Phases, Quantum Spin Systems, and Category Theory.
As a profoundly deaf wearer of Cochlear Implants, I advocate for inclusivity of the D/deaf and hard of hearing in academic meetings and conferences and sit on the EDI Committee for the School of Mathematics.
In my project, I am investigating techniques inspired by Algebraic Quantum Field Theory to model systems with topological order, hosting anyonic excitations: an attractive candidate for quantum computation. My project looks towards generalising the categorical formulation of anyon theories to encompass fractonic states of matter. My research interests lie in Topological Phases, Quantum Spin Systems, and Category Theory.
As a profoundly deaf wearer of Cochlear Implants, I advocate for inclusivity of the D/deaf and hard of hearing in academic meetings and conferences and sit on the EDI Committee for the School of Mathematics.
In this paper, we study the superselection structure of a stack of two 2D quantum systems in the operator algebraic framework. In particular, we find that each irreducible sector stacks to be an irreducible sector in the stacked system, leading to a faithful functor between the corresponding categories. This naturally leads to conclude the triviality of invertible phases. Further, we show the functor is also surjective and in fact an equivalence between the stacked system category and the '(Deligne) product' of the single layer categories.
In 2023, I was awarded the Champion for EDI at Cardiff University's Enriching Student Life Awards. This came after many years of advocating for deaf accessibility, teaching BSL to various groups and within the society, and raising awareness of the struggles deaf students and people experience.
I am a keen runner, cyclist, and hiker -- especially enjoying Cardiff's proximity to the Brecon Beacons. I enjoyed many years at University training with and racing for the Cardiff University Triathlon Club, participating in annual BUCS races. When the timing isn't too early, I really enjoy a sunrise swim in Penarth (best in the winter months when you can't really see the water).
Most favourite activity to do on any given day: an Escape Room.
Topic that I can talk about for over 3 hours: Books. Any genre any era.