Nikita Sopenko

My research interests: mathematical physics, quantum statistical mechanics, quantum field theory, operator algebra.

I am a Research Associate at the Center of Mathematical Sciences and Applications at Harvard University. Previously, I was a member of the Institute for Advanced Study in Princeton. I graduated from California Institute of Technology in 2023, my advisor was Anton Kapustin.

e-mail: sopenko [at] cmsa [dot] fas [dot] harvard [dot] edu, niksopenko [at] gmail [dot] com

My CV. You can find my publications on Google Scholar and arXiv.

I co-organize the Geometry and Quantum Theory seminar with Dan Freed.

Selected papers and preprints

(with Corey Jones and Ryan Thorngren) Quantum cellular automata and invertible phases of matter, pdf, arXiv:2608.26456.
Reflection positivity and a refined index for 2d invertible phases, pdf, arXiv:2509.01711.
(with Jonah Kudler-Flam and Vladimir Narovlansky) Optimal bound on long-range distillable entanglement, pdf, arXiv:2504.02926, journal.
An index for invertible phases of two-dimensional quantum spin systems, pdf, arXiv:2410.02059.
(with Anton Kapustin) Anomalous symmetries of quantum spin chains and a generalization of the Lieb-Schultz-Mattis theorem, pdf, arXiv:2401.02533, journal.
(with Anton Kapustin and Adam Artymowicz) Quantization of the higher Berry curvature and the higher Thouless pump, pdf, arXiv:2305.06399, journal.
Chiral topologically ordered states on a lattice from vertex operator algebras, pdf, arXiv:2301.08697, journal.
(with Anton Kapustin) Local Noether theorem for quantum lattice systems and topological invariants of gapped states, pdf, arXiv:2201.01327, journal.
An index for two-dimensional SPT states, pdf, arXiv:2101.00801, journal.
(with Anton Kapustin and Bowen Yang) A classification of phases of bosonic quantum lattice systems in one dimension, pdf, arXiv:2012.15491, journal.
(with Anton Kapustin) Hall conductance and the statistics of flux insertions in gapped interacting lattice systems, pdf, arXiv:2006.14151, journal.