Quantum

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

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Briefings

A new framework for real-space construction of center-of-mass momentum eigenstates in 2D many-body lattices is presented. The study shows that 2D real-space translations induce non-trivial translation phase factors based on stabilizer subgroup characters, which renormalize permissible momentum values. An anomalous cross-dimensional momentum coupling is identified, where one direction's permissible values are strictly constrained by the perpendicular direction, a coupling deemed algorithmically necessary for numerical implementations.

Key points

• The study presents a real-space formalism for 2D quantum many-body systems that explicitly captures non-uniform cyclic subspace dimensions governed by spatial symmetries.
• Performing 2D real-space translations on multi-particle states naturally induces non-trivial translation phase factors associated with the characters of stabilizer subgroups, leading to momentum value renormalization.

Context

This research addresses a gap in numerical implementations of many-body quantum systems by providing a method to construct center-of-mass momentum eigenstates in real space. The framework is essential for accurately simulating 2D lattice systems where standard momentum-space approaches fail due to non-uniform subspace dimensions.

Limitations

The evidence is limited to the arXiv preprint v1, which may not reflect final experimental validation or peer-reviewed results. The study focuses on theoretical frameworks and algorithmic necessity rather than providing definitive experimental data or long-term physical predictions.

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