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

Reaz Shafqat

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.

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

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.

Paper Structure

This paper contains 5 sections, 53 equations.

Table of Contents

  1. IntroductionThis work is based on the master's thesis of Reaz Shfqat submitted to the Department of Theoretical Physics of the University of Dhaka, Session: 21-22.
  2. Babujian’s thermodynamic Bethe ansatz for $\mathrm{XXX}_s$ chain
  3. Proposed Expression
  4. Conclusion
  5. Acknowledgements