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Heisenberg models and Schur--Weyl duality

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arxiv 2201.10209 v1 pith:RZXE4WYF submitted 2022-01-25 math-ph math.MPmath.PR

Jakob Björnberg , Hjalmar Rosengren , Kieran Ryan This is my paper · ORCID
classification math-phmath.MPmath.PR
keywords dualityinteractionsmodelsschur--weylspinallowsanalysisbipartite
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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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  1. Algebraic Speedups for Exact Inversion of Hamiltonian Evolutions

    quant-ph 2026-07 conditional novelty 8.0 of 10

    Known generator structure—additive eigenvalue relations and Wedderburn sector multiplicities—determines and often drastically lowers the exact query cost of reversing a Hamiltonian evolution.

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