Emergent low-energy many-body Hilbert spaces in Chern bands
Abstract
We show that in Landau levels and more generic Chern bands, the most relevant many-body subspace selected by realistic two-body interactions alone (e.g., in the limit of vanishing bandwidth and band gap) depends strongly on the particle density and can be constructed systematically. Using the well-defined hierarchical structure of conformal Hilbert spaces (CHS), each with a highest-density vacuum state, we compute, for both fermionic and bosonic systems, the many-body quantum metric that quantifies the interaction energy scales of these subspaces. For a large family of short-range, Coulomb-based interactions, particles preferentially occupy the many-body states in the smallest accommodating CHS. This allows us to describe the low-energy physics of the interacting system in terms of the appropriate anyonic degrees of freedom. Our results also explain why, in any Chern band (in lattice or continuum systems), band mixing tends to be suppressed even in the limit of strong interaction; this suppression is stronger when the band deviates less from the ideal trace condition and when the two-body interaction is shorter-ranged.
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BibTeX
@misc{jiang2026emergent,
title = {{Emergent low-energy many-body Hilbert spaces in Chern bands}},
author = {Chen-Xin Jiang and Zi-Xiang Hu and Bo Yang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31831},
eprint = {2609.31831},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31831},
}
RIS
TY - UNPB
TI - Emergent low-energy many-body Hilbert spaces in Chern bands
AU - Chen-Xin Jiang
AU - Zi-Xiang Hu
AU - Bo Yang
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31831
UR - https://arxiv.org/abs/2609.31831
AB - We show that in Landau levels and more generic Chern bands, the most relevant many-body subspace selected by realistic two-body interactions alone (e.g., in the limit of vanishing bandwidth and band gap) depends strongly on the particle density and can be constructed systematically. Using the well-defined hierarchical structure of conformal Hilbert spaces (CHS), each with a highest-density vacuum state, we compute, for both fermionic and bosonic systems, the many-body quantum metric that quantifies the interaction energy scales of these subspaces. For a large family of short-range, Coulomb-based interactions, particles preferentially occupy the many-body states in the smallest accommodating CHS. This allows us to describe the low-energy physics of the interacting system in terms of the appropriate anyonic degrees of freedom. Our results also explain why, in any Chern band (in lattice or continuum systems), band mixing tends to be suppressed even in the limit of strong interaction; this suppression is stronger when the band deviates less from the ideal trace condition and when the two-body interaction is shorter-ranged.
ER -