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arXiv · 2201.10209

Heisenberg models and Schur--Weyl duality

Jakob Björnberg·Hjalmar Rosengren·Kieran Ryan
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Abstract

We present a detailed analysis of certain quantum spin systems with inhomogeneous (non-random) mean-field interactions. Examples include, but are not limited to, the interchange- and spin singlet projection interactions on complete bipartite graphs. Using two instances of the representation theoretic framework of Schur--Weyl duality, we can explicitly compute the free energy and other thermodynamic limits in the models we consider. This allows us to describe the phase-transition, the ground-state phase diagram, and the expected structure of extremal states.

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Jakob Björnberg, Hjalmar Rosengren, Kieran Ryan. 2022-01-25. Heisenberg models and Schur--Weyl duality. https://arxiv.org/abs/2201.10209

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