Solving fractional quantum Hall problems with thermodynamic-limit bootstrap
Abstract
Determining correlated ground states directly in the thermodynamic limit remains a central challenge in quantum many-body physics. Here we develop a quantum many-body bootstrap that yields a rigorous and tight lower bound on the thermodynamic ground-state energy of a fractional quantum Hall system together with an optimized reduced density matrix ρW⋆ on a spatial window. For sufficiently tight bounds, we find that ρW⋆ accurately reproduces the ground-state reduced density matrix, as directly tested by its fidelity with known model states. For exactly solvable Laughlin and Moore--Read parent Hamiltonians, the bootstrap also reproduces pair correlations and orbital entanglement spectra (OES). For Landau-level-projected Coulomb interactions across multiple fillings, the energy bounds closely track established thermodynamic estimates, while the window density matrix recovers the familiar ν=1/3 Laughlin and ν=5/2 Moore--Read states and the composite Fermi liquid at ν=1/2. More importantly, the same framework also resolves unsettled regimes. At ν=1/4, the OES and real-space correlations identify a composite Fermi liquid, while at ν=12/5 the combined diagnostics suggest RR̅3 as the ground-state order. Our bootstrap therefore provides direct access to both ground-state energies and many-body structure in the thermodynamic limit.
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BibTeX
@misc{gao2026solving,
title = {{Solving fractional quantum Hall problems with thermodynamic-limit bootstrap}},
author = {Qiang Gao and Taige Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21317},
eprint = {2610.21317},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21317},
}
RIS
TY - UNPB
TI - Solving fractional quantum Hall problems with thermodynamic-limit bootstrap
AU - Qiang Gao
AU - Taige Wang
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.21317
UR - https://arxiv.org/abs/2610.21317
AB - Determining correlated ground states directly in the thermodynamic limit remains a central challenge in quantum many-body physics. Here we develop a quantum many-body bootstrap that yields a rigorous and tight lower bound on the thermodynamic ground-state energy of a fractional quantum Hall system together with an optimized reduced density matrix ρ_W^⋆ on a spatial window. For sufficiently tight bounds, we find that ρ_W^⋆ accurately reproduces the ground-state reduced density matrix, as directly tested by its fidelity with known model states. For exactly solvable Laughlin and Moore--Read parent Hamiltonians, the bootstrap also reproduces pair correlations and orbital entanglement spectra (OES). For Landau-level-projected Coulomb interactions across multiple fillings, the energy bounds closely track established thermodynamic estimates, while the window density matrix recovers the familiar ν=1/3 Laughlin and ν=5/2 Moore--Read states and the composite Fermi liquid at ν=1/2. More importantly, the same framework also resolves unsettled regimes. At ν=1/4, the OES and real-space correlations identify a composite Fermi liquid, while at ν=12/5 the combined diagnostics suggest RR̅_3 as the ground-state order. Our bootstrap therefore provides direct access to both ground-state energies and many-body structure in the thermodynamic limit.
ER -