Research

My research focuses on quantum many-body systems and the mathematics that describes them, often utilising integrable or exactly-solvable models. 

I am particularly interested in topological phases of matter, and the role of symmetry in their classification. I consider limits of these classifications, for example, where the Hamiltonian describing the system is gapless, or has long-range (algebraically decaying) couplings. 

Symmetry-protected topological phases often have interesting boundary physics and in a recent paper with Ryan Thorngren and Ruben Verresen we investigated this bulk-boundary correspondence in quantum chains with long-range couplings. This work raises some fascinating mathematical problems in the theory of block-Toeplitz determinants. 

I am interested in tensor networks and their role as ground states of many-body Hamiltonians, as well as their appearance in the theory of integrable models. See here for a case study describing some of my work on quantum chains with exact tensor network ground states.