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arXiv · 2204.03763

A classification of $G$-charge Thouless pumps in 1D invertible states

Sven Bachmann·Wojciech De Roeck·Martin Fraas·Tijl Jappens
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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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Sven Bachmann, Wojciech De Roeck, Martin Fraas, Tijl Jappens. 2022-04-07. A classification of $G$-charge Thouless pumps in 1D invertible states. https://arxiv.org/abs/2204.03763

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