Real-space construction and selection rules of center-of-mass momentum eigenstates in two-dimensional many-body lattices

arXiv:2610.32054v1 Announce Type: new 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.