26 citations · 100 across the 11 of their papers we have counts for
11 papers
Quantum cellular automata and invertible phases of matter
Corey Jones, Nikita Sopenko, Ryan Thorngren
We introduce and study (fermionic and bosonic) invertible quasi-local algebras over uniformly locally finite metric spaces with infinite-dimensional local von Neumann algebras.…
Reflection positivity and a refined index for 2d invertible phases
Nikita Sopenko
We analyze the validity of reflection positivity in the classification of invertible phases of quantum spin systems. We provide a mathematical model in which every 2d invertible st…
Optimal bound on long-range distillable entanglement
Jonah Kudler-Flam, Vladimir Narovlansky, Nikita Sopenko
We prove an upper bound on long-range distillable entanglement in spatial dimensions. Namely, it must decay faster than , where is the distance between entangled regio…
An index for invertible phases of two-dimensional quantum spin systems
Nikita Sopenko
We define an index for invertible phases of two-dimensional fermionic and bosonic quantum spin systems without any additional symmetry. Conjecturally, it provides a microscopic def…
Anomalous symmetries of quantum spin chains and a generalization of the Lieb-Schultz-Mattis theorem
Anton Kapustin, Nikita Sopenko
For any locality-preserving action of a group on a quantum spin chain one can define an anomaly index taking values in the group cohomology of . The anomaly index is a kinem…
Quantization of the higher Berry curvature and the higher Thouless pump
Adam Artymowicz, Anton Kapustin, Nikita Sopenko
We show that for families of 1d lattice systems in an invertible phase, the cohomology class of the higher Berry curvature can be refined to an integral degree-3 class on the param…
Chiral topologically ordered states on a lattice from vertex operator algebras
Nikita Sopenko
We propose a class of pure states of two-dimensional lattice systems realizing topological order associated with unitary rational vertex operator algebras. We show that the states…
Local Noether theorem for quantum lattice systems and topological invariants of gapped states
Anton Kapustin, Nikita Sopenko
We study generalizations of the Berry phase for quantum lattice systems in arbitrary dimensions. For a smooth family of gapped ground states in d dimensions, we define a closed (d+…
An index for two-dimensional SPT states
Nikita Sopenko
We define an index for 2d -invariant invertible states of bosonic lattice systems in the thermodynamic limit for a finite symmetry group . We show that this index is an invar…
A classification of phases of bosonic quantum lattice systems in one dimension
Anton Kapustin, Nikita Sopenko, Bowen Yang
We study invertible states of 1d bosonic quantum lattice systems. We show that every invertible 1d state is in a trivial phase: after tensoring with some unentangled ancillas it ca…
Hall conductance and the statistics of flux insertions in gapped interacting lattice systems
Anton Kapustin, Nikita Sopenko
We study charge transport for zero-temperature infinite-volume gapped lattice systems in two dimensions with short-range interactions. We show that the Hall conductance is locally…