Symmetry-protected many-body Aharonov-Bohm effect

Abstract

It is known as a purely quantum effect that a magnetic flux affects the real physics of a particle, such as the energy spectrum, even if the flux does not interfere with the particle's path - the Aharonov-Bohm effect. Here we examine an Aharonov-Bohm effect on a many-body wavefunction. Specifically, we study this many-body effect on the gapless edge states of a bulk gapped phase protected by a global symmetry (such as ${\mathbb{Z}}_N$) - the symmetry-protected topological (SPT) states. The many-body analogue of spectral shifts, the twisted wavefunction and the twisted boundary realization are identified in this SPT state. An explicit lattice construction of SPT edge states is derived, and a challenge of gauging its non-onsite symmetry is overcome. Agreement is found in the twisted spectrum between a numerical lattice calculation and a conformal field theory prediction.

5 pages main text + 8 pages appendix, 3 figures. v2: nearly PRB version

References in corpus (2)

• Symmetry-protected topological phases and orbifolds: Generalized Laughlin's argument
• Symmetry-protected topological phases with charge and spin symmetries: response theory and dynamical gauge theory in 2D, 3D and the surface of 3D

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