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• W3199196622 abstract "The spin- frac{1}{2} <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:math> Heisenberg XXZ chain is a paradigmatic quantum integrable model. Although it can be solved exactly via Bethe ansatz techniques, there are still open issues regarding the spectrum at root of unity values of the anisotropy. We construct Baxter’s Q operator at arbitrary anisotropy from a two-parameter transfer matrix associated to a complex-spin auxiliary space. A decomposition of this transfer matrix provides a simple proof of the transfer matrix fusion and Wronskian relations. At root of unity a truncation allows us to construct the Q operator explicitly in terms of finite-dimensional matrices. From its decomposition we derive truncated fusion and Wronskian relations as well as an interpolation-type formula that has been conjectured previously. We elucidate the Fabricius–McCoy (FM) strings and exponential degeneracies in the spectrum of the six-vertex transfer matrix at root of unity. Using a semicyclic auxiliary representation we give a conjecture for creation and annihilation operators of FM strings for all roots of unity. We connect our findings with the `string-charge duality’ in the thermodynamic limit, leading to a conjecture for the imaginary part of the FM string centres with potential applications to out-of-equilibrium physics." @default.
• W3199196622 created "2021-09-27" @default.
• W3199196622 creator A5033108781 @default.
• W3199196622 creator A5048810777 @default.
• W3199196622 creator A5052322079 @default.
• W3199196622 date "2021-09-22" @default.
• W3199196622 modified "2023-10-03" @default.
• W3199196622 title "On the Q operator and the spectrum of the XXZ model at root of unity" @default.
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• W3199196622 doi "https://doi.org/10.21468/scipostphys.11.3.067" @default.
• W3199196622 hasPublicationYear "2021" @default.
• W3199196622 type Work @default.
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