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Motivated by the crystal structures of [(CuCl2tachH)3Cl]Cl2 and Ca3Co2O6, wedevelop a low-energy effective theory using the bosonization technique for aspin-1/2 frustrated three-leg spin tube with trigonal prism units in two limitcases. The features obtained with the effective theory are numericallyelucidated by the density matrix renormalization group method. Three differentquantum phases in the ground state of the system, say, one gapped dimerizedphase and two distinct gapless phases, are identified, where the two gaplessphases are found to have the conformal central charge c=1 and 3/2,respectively. Spin gaps, spin and dimer correlation functions, and theentanglement entropy are obtained. In particular, it is disclosed that thecritical phase with c=3/2 is the consequence of spin frustrations, which mightbelong to the SU(2)k=2 Wess-Zumino-Witten-Novikov universality class, and isinduced by the twist term in the bosonized Hamiltonian density.

Low-energy effective theory and two distinct critical phases in a spin-1/2 frustrated three-leg spin tube