Hubbard--Heisenberg Thermodynamic Comparison at Half Filling in a Fixed Staggered Field

@misc{miyao2026hubbardheisenberg,
  title = {{Hubbard--Heisenberg Thermodynamic Comparison at Half Filling in a Fixed Staggered Field}},
  author = {Tadahiro Miyao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2605.30663},
  eprint = {2605.30663},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.30663},
}

TY  - UNPB
TI  - Hubbard--Heisenberg Thermodynamic Comparison at Half Filling in a Fixed Staggered Field
AU  - Tadahiro Miyao
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2605.30663
UR  - https://arxiv.org/abs/2605.30663
AB  - We study the repulsive Hubbard model at half filling in the canonical ensemble and compare its thermodynamics with the spin-1/2 antiferromagnetic Heisenberg model at superexchange coupling J_0(U)=4t^2/U. For fixed hopping t≠0, bounded staggered fields |h|≤ h_0, and inverse temperatures βJ_0(U)≥ℓ_0>0, we establish a volume-uniform pressure comparison with error O(U^−3+|h|U^−2). On the Heisenberg field scale h=J_0(U)x, the error improves to O(U^−3) for bounded x. Using the quantum Lee--Yang theorem of Suzuki and Fisher, we obtain a volume-uniform O(U^−1) comparison of staggered magnetizations on compact positive intervals of the scaled field x. By combining a recent fermionic Lee--Yang theorem with analytic interpolation, we improve this estimate to O(U^−2log U) in the thermodynamic limit. The latter analysis also establishes analyticity of the limiting Hubbard pressure at nonzero real fields. The improved comparison extends to vanishing positive fields satisfying U^−3≪ h(U)≪ U^−1, with error O((1+log(U^3h(U)))/(U^3h(U))). Consequently, sufficiently low-temperature Heisenberg Néel order yields a quantitative positive lower bound on the Hubbard staggered magnetization in this regime. Furthermore, we prove O(U^−2) bounds on the double-occupancy and charge-defect densities and the normalized charge-density-wave second moment. At zero staggered field, this decay rate is optimal for both densities, even in the thermodynamic limit. Our approach uses finite-order Schrieffer--Wolff transformations and does not establish spontaneous Néel order at fixed finite U.
ER  -