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We investigate the phase diagram of a generalized spin-1/2 quantumantiferromagnet on a ladder with rung, leg, diagonal, and ring-exchangeinteractions. We consider the exactly soluble models associated with theproblem, obtain the exact ground states which exist for certain parameterregimes, and apply a variety of perturbative techniques in the regime of strongring-exchange coupling. By combining these approaches with considerationsrelated to the discrete Z_4 symmetry of the model, we present the completephase diagram.Comment: 17 pages, 10 figure

Phase diagram of the Heisenberg spin ladder with ring exchange