Ordering of Energy Levels in Heisenberg Models and Applications

摘要: In a recent paper [17] we conjectured that for ferromagnetic Heisenberg models the smallest eigenvalues in invariant subspaces of fixed total spin are monotone decreasing as function and called this property ordering energy levels (FOEL). We have proved conjecture model with arbitrary spins coupling constants on chain [17,20]. give pedagogical introduction to result also discuss some extensions implications. The latter include relaxation time symmetric simple exclusion processes graph which FOEL can be proved, equals random walk same jump rates given by constants, i.e., is independent number particles. Therefore, our results provide proof Aldous' Conjecture one dimension.