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arXiv · 2605.30663

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

Tadahiro Miyao
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Abstract

We study the repulsive Hubbard model at half filling in the strong-coupling regime, with a staggered magnetic field of strength \(h\). The analysis is carried out in the canonical half-filled ensemble, with temperature measured on the Heisenberg scale \(J_0(U)=4t^2/U\). Uniformly for \(|h|\le h_0\) and \(\beta J_0(U)\ge \ell_0\), we prove finite-volume Hubbard--Heisenberg pressure estimates with errors uniform in the system size. These estimates pass to thermodynamic limits whenever the limiting pressures exist. The proof uses a strong-coupling unitary transformation which separates the singly occupied spin sector from sectors containing empty or doubly occupied sites. On the singly occupied sector, the effective Hamiltonian is compared with the Heisenberg reference Hamiltonian; the remaining sectors are controlled through a decomposition of the transformed partition function according to the set of empty or doubly occupied sites. For fixed positive staggered-field windows \(I\Subset(0,h_0]\), the magnetisation comparison is then derived from the pressure comparison by convexity of finite-volume pressures. We also prove charge-sector suppression estimates, uniformly for \(|h|\le h_0\): in the large positive-\(U\) Heisenberg-scale regime, the density of empty or doubly occupied sites and the double-occupancy density are small, and the squared staggered charge divided by \(|\Lambda|^2\) is small. Thus the results give a quantitative Gibbs-state formulation of the strong-coupling picture in which the half-filled repulsive Hubbard model is described, at the Heisenberg scale, by effective antiferromagnetic spin degrees of freedom, while charge fluctuations are suppressed.

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Tadahiro Miyao. 2026-05-28. Hubbard--Heisenberg Thermodynamic Comparison at Half Filling in a Fixed Staggered Field. https://arxiv.org/abs/2605.30663

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