Real-space construction and selection rules of center-of-mass momentum eigenstates in two-dimensional many-body lattices
Abstract
We present a comprehensive framework for the real-space construction of center-of-mass (c.m.) momentum eigenstates in two-dimensional (2D) quantum many-body systems. Unlike standard momentum-space approaches, our real-space formalism explicitly captures the non-uniformity of cyclic subspace dimensions, which are fundamentally governed by the spatial symmetries of the many-body configurations and particle statistics. We demonstrate that performing 2D real-space translations on multi-particle states naturally induces non-trivial translation phase factors associated with the characters of these stabilizer subgroups, leading to a renormalization of permissible momentum values. Notably, we identify an anomalous cross-dimensional momentum coupling in highly symmetric particle distributions, where the permissible momentum values in one direction are strictly constrained by those in the perpendicular direction. We emphasize the algorithmic necessity of this coupling, as neglecting it leads to missing or duplicated basis states in numerical implementations. Concrete examples are provided to demonstrate the practical implementation and physical consequences of this framework.
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BibTeX
@misc{lin2026realspace,
title = {{Real-space construction and selection rules of center-of-mass momentum eigenstates in two-dimensional many-body lattices}},
author = {Ling Lin and Yongguan Ke and Chaohong Lee},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32054},
eprint = {2610.32054},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32054},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Real-space construction and selection rules of center-of-mass momentum eigenstates in two-dimensional many-body lattices
AU - Ling Lin
AU - Yongguan Ke
AU - Chaohong Lee
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32054
UR - https://arxiv.org/abs/2610.32054
AB - We present a comprehensive framework for the real-space construction of center-of-mass (c.m.) momentum eigenstates in two-dimensional (2D) quantum many-body systems. Unlike standard momentum-space approaches, our real-space formalism explicitly captures the non-uniformity of cyclic subspace dimensions, which are fundamentally governed by the spatial symmetries of the many-body configurations and particle statistics. We demonstrate that performing 2D real-space translations on multi-particle states naturally induces non-trivial translation phase factors associated with the characters of these stabilizer subgroups, leading to a renormalization of permissible momentum values. Notably, we identify an anomalous cross-dimensional momentum coupling in highly symmetric particle distributions, where the permissible momentum values in one direction are strictly constrained by those in the perpendicular direction. We emphasize the algorithmic necessity of this coupling, as neglecting it leads to missing or duplicated basis states in numerical implementations. Concrete examples are provided to demonstrate the practical implementation and physical consequences of this framework.
ER -