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6 papers
Supersymmetric boundaries of one-dimensional phases of fermions beyond symmetry-protected topological states
Alex Turzillo, Minyoung You
It has recently been demonstrated that protected supersymmetry emerges on the boundaries of one-dimensional intrinsically fermionic symmetry protected trivial (SPT) phases. Here we…
Fermionic quantum cellular automata and generalized matrix product unitaries
Lorenzo Piroli, Alex Turzillo, Sujeet K. Shukla +1
We study matrix product unitary operators (MPUs) for fermionic one-dimensional (1D) chains. In stark contrast with the case of 1D qudit systems, we show that (i) fermionic MPUs do…
Symmetry-Enriched Quantum Spin Liquids in
Po-Shen Hsin, Alex Turzillo
We use the intrinsic one-form and two-form global symmetries of (3+1) bosonic field theories to classify quantum phases enriched by ordinary (-form) global symmetry. Differen…
Diagrammatic State Sums for 2D Pin-Minus TQFTs
Alex Turzillo
The two dimensional state sum models of Barrett and Tavares are extended to unoriented spacetimes. The input to the construction is an algebraic structure dubbed half twist algebra…
Free and Interacting Short-Range Entangled Phases of Fermions: Beyond the Ten-Fold Way
Yu-An Chen, Anton Kapustin, Alex Turzillo +1
We extend the periodic table of phases of free fermions in the ten-fold way symmetry classes to a classification of free fermionic phases protected by an arbitrary on-site unitary…
Equivariant Topological Quantum Field Theory and Symmetry Protected Topological Phases
Anton Kapustin, Alex Turzillo
Short-range entangled topological phases of matter are closely connected to Topological Quantum Field Theory. We use this connection to classify bosonic Symmetry Protected Topologi…