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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 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.
I am also thinking about several mysteries related to the phase diagrams of Onsager-integrable chiral clock models. In particular, what can we say about the structure in the gapless regions?
These two schematic phase diagrams correspond to site-dimension 3 (RSPT) and 4 (SPT). They appear in this paper with Abhishodh Prakash and Paul Fendley.
In this paper with Imogen Camp we found exact tensor network ground states within the gapped regions of these phase diagrams, and beyond.
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