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arXiv · 2210.11646

Topological pump of $SU(Q)$ quantum chain and Diophantine equation

Yasuhiro Hatsugai·Yoshihito Kuno
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Abstract

A topological pump of the $SU(Q)$ quantum chain is proposed associated with a current due to a local $[U(1)]^{\otimes Q}$ gauge invariance of colored fermions. The $SU(Q)$ invariant dimer phases are characterized by the $Z_Q$ Berry phases as a topological order parameter with a $d$-dimensional twist space ($d=Q-1$) as a synthetic Brillouin zone. By inclusion of the symmetry breaking perturbation specified by a rational parameter $\Phi=P/Q$, the pump, that encloses around the phase boundary, is characterized by the $Q$ Chern numbers associated with the currents due to uniform infinitesimal twists. The analysis of the systems under the open/periodic/twisted boundary conditions clarifies the bulk-edge correspondence of the pump where the large gauge transformation generated by the center of mass (CoM) plays a central role. An explicit formula for the Chern number is given by using the Diophanine equation. Numerical demonstration by the exact diagonalization and the DMRG for finite systems ($Q=3,4$ and $5$) have been presented to confirm the general discussions for low energy spectra, edge states, CoM's, Chern numbers and the bulk-edge correspondence. A modified Lieb-Schultz-Mattis type argument for the general $SU(Q)$ quantum chain is also mentioned.

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Yasuhiro Hatsugai, Yoshihito Kuno. 2022-10-21. Topological pump of $SU(Q)$ quantum chain and Diophantine equation. https://doi.org/10.1103/physrevb.107.235106

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