Intrinsic Zak Phase of Solitons: A Geometric Correspondence with the Center-of-Mass Position
Abstract
The center-of-mass position of a nonlinear soliton in a lattice is commonly attributed to the interplay between nonlinearity and lattice confinement. Here, we reveal its geometric origin by establishing an exact relation between the soliton position and an intrinsic Zak phase. Unlike the Zak phase of a linear Bloch band, this intrinsic Zak phase arises from the nonlinear self-consistent band of the lattice reconstructed by the soliton density. We construct a composite periodic function to define this phase and demonstrate that its topological winding during nonlinear Thouless pumping dictates the quantized soliton displacement. Our results establish band geometry as a fundamental descriptor of nonlinear soliton position in a lattice and provide a geometric framework for their topological transport.
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BibTeX
@misc{hu2026intrinsic,
title = {{Intrinsic Zak Phase of Solitons: A Geometric Correspondence with the Center-of-Mass Position}},
author = {Xiao-Xiao Hu and Chen Cheng and Hong-Gang Luo},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02918},
eprint = {2611.02918},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02918},
}
RIS
TY - UNPB
TI - Intrinsic Zak Phase of Solitons: A Geometric Correspondence with the Center-of-Mass Position
AU - Xiao-Xiao Hu
AU - Chen Cheng
AU - Hong-Gang Luo
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.02918
UR - https://arxiv.org/abs/2611.02918
AB - The center-of-mass position of a nonlinear soliton in a lattice is commonly attributed to the interplay between nonlinearity and lattice confinement. Here, we reveal its geometric origin by establishing an exact relation between the soliton position and an intrinsic Zak phase. Unlike the Zak phase of a linear Bloch band, this intrinsic Zak phase arises from the nonlinear self-consistent band of the lattice reconstructed by the soliton density. We construct a composite periodic function to define this phase and demonstrate that its topological winding during nonlinear Thouless pumping dictates the quantized soliton displacement. Our results establish band geometry as a fundamental descriptor of nonlinear soliton position in a lattice and provide a geometric framework for their topological transport.
ER -