



@article {2930,
	title = {Classification of (2+1)D invertible fermionic topological phases with symmetry},
	journal = {Phys. Rev. B},
	volume = {105},
	year = {2022},
	month = {5/30/2022},
	abstract = {<p>We provide a classification of invertible topological phases of interacting fermions with symmetry in two spatial dimensions for general fermionic symmetry groups Gf and general values of the chiral central charge c\&minus;. Here Gf is a central extension of a bosonic symmetry group Gb by fermion parity, (\&minus;1)F, specified by a second cohomology class [ω2]\&isin;H2(Gb,Z2). Our approach proceeds by gauging fermion parity and classifying the resulting Gb symmetry-enriched topological orders while keeping track of certain additional data and constraints. We perform this analysis through two perspectives, using G-crossed braided tensor categories and Spin(2c\&minus;)1 Chern-Simons theory coupled to a background G gauge field. These results give a way to characterize and classify invertible fermionic topological phases in terms of a concrete set of data and consistency equations, which is more physically transparent and computationally simpler than the more abstract methods using cobordism theory and spectral sequences. Our results also generalize and provide a different approach to the recent classification of fermionic symmetry-protected topological phases by Wang and Gu, which have chiral central charge c\&minus;=0. We show how the 10-fold way classification of topological insulators and superconductors fits into our scheme, along with general non-perturbative constraints due to certain choices of c\&minus; and Gf. Mathematically, our results also suggest an explicit general parameterization of deformation classes of (2+1)D invertible topological quantum field theories with Gf symmetry.\&nbsp;</p>},
	doi = {https://doi.org/10.1103/PhysRevB.105.235143},
	url = {https://arxiv.org/abs/2109.11039},
	author = {Maissam Barkeshli and Yu-An Chen and Po-Shen Hsin and Naren Manjunath}
}
@article {2928,
	title = {Exactly Solvable Lattice Hamiltonians and Gravitational Anomalies},
	year = {2021},
	month = {10/27/2021},
	abstract = {<p>We construct infinitely many new exactly solvable local commuting projector lattice Hamiltonian models for general bosonic beyond group cohomology invertible topological phases of order two and four in any spacetime dimensions, whose boundaries are characterized by gravitational anomalies. Examples include the beyond group cohomology invertible phase without symmetry in (4+1)D that has an anomalous boundary Z2 topological order with fermionic particle and fermionic loop excitations that have mutual π statistics. We argue that this construction gives a new non-trivial quantum cellular automaton (QCA) in (4+1)D of order two. We also present an explicit construction of gapped symmetric boundary state for the bosonic beyond group cohomology invertible phase with unitary Z2 symmetry in (4+1)D. We discuss new quantum phase transitions protected by different invertible phases across the transitions.</p>},
	url = {https://arxiv.org/abs/2110.14644},
	author = {Yu-An Chen and Po-Shen Hsin}
}
