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The Lieb-Mattis theorem about antiferromagnetic ordering of energy levels onbipartite lattices is generalized to finite-size two-leg spin-1/2 ladder modelfrustrated by diagonal interactions. For reflection-symmetric model withsite-dependent interactions we prove exactly that the lowest energies insectors with fixed total spin and reflection quantum numbers are monotoneincreasing functions of total spin. The nondegeneracy of most levels is provedalso. We also establish the uniqueness and obtain the spin value of thelowest-level multiplet in the whole sector formed by reflection-symmetric(antisymmetric) states. For a wide range of coupling constants, we prove thatthe ground state is a unique spin singlet. For other values of couplings, itmay be also a unique spin triplet or may consist of both multiplets. Similarresults have been obtained for the ladder with arbitrary boundary impurityspin. Some partial results have also been obtained in the case of periodicalboundary conditions.Comment: 17 page

physical review. b, condensed matter and materials physics

Energy-level ordering and ground-state quantum numbers for a frustrated two-leg spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>1</mml:mn><mml:mo>∕</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math>ladder

Energy-level ordering and ground-state quantum numbers for a frustrated two-leg spin-1∕2ladder