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We study the ground state phase diagram of a frustrated spin-1/2 four-legtube. Using a variety of complementary techniques, namely density matrixrenormalization group, exact diagonalization, Schwinger boson mean fieldtheory, quantum Monte-Carlo and series expansion, we explore the parameterspace of this model in the regime of all-antiferromagnetic exchange. Incontrast to unfrustrated four-leg tubes we uncover a rich phase diagram. Apartfrom the Luttinger liquid fixed point in the limit of decoupled legs, thiscomprises several gapped ground states, namely a plaquette, an incommensurate,and an antiferromagnetic quasi spin-2 chain phase. The transitions betweenthese phases are analyzed in terms of total energy and static structure factorcalculations and are found to be of (weak) first order. Despite the absence oflong range order in the quantum case, remarkable similarities to the classicalphase diagram are uncovered, with the exception of the icommensurate regime,which is strongly renormalized by quantum fluctuations. In the limit of largeleg exchange the tube exhibits a deconfinement cross-over from gapped magnonlike excitations to spinons.

Quantum phases of a frustrated four-leg spin tube