Crystallographic Interacting Topological Phases and Equivariant
Cohomology: To assume or not to assume
- URL: http://arxiv.org/abs/2007.06595v3
- Date: Wed, 30 Jun 2021 18:00:01 GMT
- Title: Crystallographic Interacting Topological Phases and Equivariant
Cohomology: To assume or not to assume
- Authors: Daniel Sheinbaum, Omar Antol\'in Camarena
- Abstract summary: For symmorphic crystalline interacting gapped systems we derive a classification under adiabatic evolution.
We do not assume an emergent relativistic field theory nor that phases form a topological spectrum.
We compare our results to bosonic symmorphic crystallographic SPT phases and to non-interacting fermionic crystallographic phases in class A.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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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