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arXiv · 2512.01869

Digamma-Function Representation of the Ground-State Energy in Antiferromagnetic Heisenberg $\mathrm{XXX}_s$ Spin Chains

Reaz Shafqat
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Abstract

The antiferromagnetic Heisenberg spin chain remains a central framework for exploring exactly solvable models within quantum integrable systems. For the isotropic XXX chain, the ground-state energy per site of the spin-1/2 system is famously given by ln2. Extending the classic formulations to arbitrary spin-s, Takhtajan and Babujian derived two separate finite-series expressions for integer and half-integer spin representations. Current work introduces a unified analytical expression for the ground-state energy density in terms of the digamma function. This compact formulation reproduces both Takhtajan Babujian series.

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Reaz Shafqat. 2025-12-01. Digamma-Function Representation of the Ground-State Energy in Antiferromagnetic Heisenberg $\mathrm{XXX}_s$ Spin Chains. https://arxiv.org/abs/2512.01869

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