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Communications in Theoretical Physics

A Variant form of the Takhtajan Equation for the Heisenberg Isotropic Spin Chain

Nian-Ning Huang

Published Mar 1, 1986• 0 citations
Publisher

Abstract

A variant form of the Takhtajan equation for the continuous Heisenberg isotropic spin chain is given when the asymptotic spin is along the 1-axis.
DOI
10.1088/0253-6102/5/2/149

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Digamma-Function Representation of the Ground-State Energy in Antiferromagnetic Heisenberg XXXs\mathrm{XXX}_sXXXs​ Spin Chains
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.