Gaussian fixed lines of $S=1/2$ XXZ chain with next-nearest neighbor interaction and $sl_2$ loop algebra

Daiki Yomatsu; Kiyohide Nomura

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arXiv · 2509.10808

Gaussian fixed lines of $S=1/2$ XXZ chain with next-nearest neighbor interaction and $sl_2$ loop algebra

Daiki Yomatsu·Kiyohide Nomura

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Abstract

Spin systems are important to understand various physical properties in quantum many-body systems. We numerically study the Gaussian fixed lines (GFLs) of the $S=1/2$ XXZ chain with next-nearest neighbor (NNN) interaction in the XY phase. The GFLs are the set of points where the coefficient of the umklapp scattering vanishes. We show that the GFLs pass through the ``special points'', which are defined as the points where the $sl_2$ loop algebra symmetry governs in low-energy physics. In addition, we have discussed the Tomonaga-Luttinger parameter K, and the metamagnetism influences the shape of the GFLs.

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Daiki Yomatsu, Kiyohide Nomura. 2025-09-13. Gaussian fixed lines of $S=1/2$ XXZ chain with next-nearest neighbor interaction and $sl_2$ loop algebra. https://arxiv.org/abs/2509.10808

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