A classification of $G$-charge Thouless pumps in 1D invertible states
- URL: http://arxiv.org/abs/2204.03763v2
- Date: Fri, 8 Dec 2023 16:28:53 GMT
- Title: A classification of $G$-charge Thouless pumps in 1D invertible states
- Authors: Sven Bachmann, Wojciech De Roeck, Martin Fraas and Tijl Jappens
- Abstract summary: For the case of spin chains, i.e. one-dimensional bosonic SPT's, this theory implies that cyclic processes are classified by zero-dimensional SPT's.
We provide a proof for the completeness of the proposed classification for compact symmetry groups $G$.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Recently, a theory has been proposed that classifies cyclic processes of
symmetry protected topological (SPT) quantum states. For the case of spin
chains, i.e.\ one-dimensional bosonic SPT's, this theory implies that cyclic
processes are classified by zero-dimensional SPT's. This is often described as
a generalization of Thouless pumps, with the original Thouless pump
corresponding to the case where the symmetry group is $U(1)$ and pumps are
classified by an integer that corresponds to the charge pumped per cycle. In
this paper, we review this one-dimensional theory in an explicit and rigorous
setting and we provide a proof for the completeness of the proposed
classification for compact symmetry groups $G$.
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