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arXiv · 2007.06595

Crystallographic Interacting Topological Phases and Equivariant Cohomology: To assume or not to assume

Daniel Sheinbaum·Omar Antolín Camarena
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Abstract

For symmorphic crystalline interacting gapped systems we derive a classification under adiabatic evolution. This classification is complete for non-degenerate ground states. For the degenerate case we discuss some invariants given by equivariant characteristic classes. We do not assume an emergent relativistic field theory nor that phases form a topological spectrum. We also do not restrict to systems with short-range entanglement, stability against stacking with trivial systems nor assume the existence of quasi-particles as is done in SPT and SET classifications respectively. Using a slightly generalized Bloch decomposition and Grassmanians made out of ground state spaces, we show that the $P$-equivariant cohomology of a $d$-dimensional torus gives rise to different interacting phases, where $P$ denotes the point group of the crystalline structure. We compare our results to bosonic symmorphic crystallographic SPT phases and to non-interacting fermionic crystallographic phases in class A. Finally we discuss the relation of our assumptions to those made for crystallographic SPT and SET phases.

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Daniel Sheinbaum, Omar Antolín Camarena. 2020-07-13. Crystallographic Interacting Topological Phases and Equivariant Cohomology: To assume or not to assume. https://doi.org/10.1007/jhep07(2021)139

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