Free to Interacting Map for Crystalline SPT Phases: Equivariance vs Crystalline Equivalence
Daniel Sheinbaum, Omar Antolín-Camarena
Abstract
Freed and Hopkins developed an ansatz for classifying interacting SPT phases using invertible field theories with a natural Free to Interacting (FTI) map from free fermion phases. This ansatz has been generalized to include crystalline phases and a crystalline equivalence principle (CEP). However, motivated by failure of the CEP for weak free fermions and the FTI, here we generalize the original Freed and Hopkins ansatz to a fully equivariant version for symmorphic crystallographic symmetries and show there is a natural equivariant FTI map from symmorphic crystalline weak free fermions. We further discuss why this equivariant ansatz is both mathematically and physically more natural than the spatial symmetry extension by Freed and Hopkins and why full equivariance should hold over the CEP.
Create a lesson
Related papers
2-Morita Theory of E2-Algebras and Module Categories
Rongge Xu, Holiverse Yang
Multiscale Loop Vertex Expansion for Cumulants, the ϕ42 Model
Vincent Rivasseau
Quasi-polynomiality and N-point functions of single connected leaky completed Hurwitz numbers
Chongyu Wang, Chenglang Yang
Coupled stochastic variational principles for multiscale surface gravity waves -- Part I: theoretical framework
Etienne Mémin, Arnaud Debussche
The Sharp Spectral Transition for Almost Mathieu Operators via Alternating Resonances
Jiawei He, Xueyin Wang
Dynamical classical-field limit of Bosonic Gibbs states: Renormalized Hartree NLS correlations in 2D and 3D
Phan Thành Nam, Rongchan Zhu, Xiangchan Zhu