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The Lieb-Mattis theorem is generalized to an antiferromagnetic spin-laddermodel with four-spin cyclic exchange interaction. We prove that for J>2K, theantiferromagnetic ordering of energy levels takes place separately in twosectors, which remain symmetric and antisymmetric under the reflection withrespect to the longitudinal axis of the ladder. We prove also that at theself-dual point J=2K, the Lieb-Mattis rule holds in the sectors with fixednumber of rung singlets. In both cases, it agrees with the similar rule forHaldane chain with appropriate spin number.

Antiferromagnetic ordering of energy levels for spin ladder with four-spin cyclic exchange: Generalization of the Lieb-Mattis theorem