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Higher-dimensional generalizations of the Thouless charge pump

Kapustin, Anton and Spodyneiko, Lev (2020) Higher-dimensional generalizations of the Thouless charge pump. . (Unpublished)

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We define and study analogs of the Thouless charge pump for many-body gapped systems in dimension D. We show how to attach a topological invariant to a D-dimensional family of such systems, provided all of them have an on-site U(1) symmetry. For a large class of families we argue that this topological invariant is an integer. In the case of gapped systems of free fermions in two dimensions, the invariant can be expressed in terms of the curvature of the Bloch-Berry connection. We also obtain a new formula for the Thouless charge pump in 1d which involves only static linear response and is analogous to the Streda formula for Hall conductivity.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Kapustin, Anton0000-0003-3903-5158
Spodyneiko, Lev0000-0002-6099-7717
Record Number:CaltechAUTHORS:20200518-151948447
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:103290
Deposited By: Tony Diaz
Deposited On:18 May 2020 23:12
Last Modified:18 May 2020 23:12

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