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arXiv · 1112.3600

Baxter Operators and Hamiltonians for "nearly all" Integrable Closed gl(n) Spin Chains

Rouven Frassek·Tomasz Lukowski·Carlo Meneghelli·Matthias Staudacher
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Abstract

We continue our systematic construction of Baxter Q-operators for spin chains, which is based on certain degenerate solutions of the Yang-Baxter equation. Here we generalize our approach from the fundamental representation of gl(n) to generic finite-dimensional representations in quantum space. The results equally apply to non-compact representations of highest or lowest weight type. We furthermore fill an apparent gap in the literature, and provide the nearest-neighbor Hamiltonians of the spin chains in question for all cases where the gl(n) representations are described by rectangular Young diagrams, as well as for their infinite-dimensional generalizations. They take the form of digamma functions depending on operator-valued shifted weights.

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Rouven Frassek, Tomasz Lukowski, Carlo Meneghelli, Matthias Staudacher. 2011-12-15. Baxter Operators and Hamiltonians for "nearly all" Integrable Closed gl(n) Spin Chains. https://arxiv.org/abs/1112.3600

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