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We develop a real space quantum renormalization group (QRG) to explore afrustrated anisotropic four-leg spin-1/2 nanotube in the thermodynamic limit.We obtain the phase diagram, fixed points, critical points, the scaling ofcoupling constants and magnetization curves. Our investigation points out thatin the case of strong leg coupling the diagonal frustrating interaction ismarginal under QRG transformations and does not affect the universality classof the model. Remarkably, the renormalization equations express that the spinnanotube prepared in the strong leg coupling case goes to the strong plaquettecoupling limit (weakly interacting plaquettes). Subsequently, in the limit ofweakly interacting plaquettes, the model is mapped onto a 1D spin-1/2 XXZ chainin a longitudinal magnetic field under QRG transformation. Furthermore, theeffective Hamiltonian of the spin nanotube inspires both first and second orderphase transitions accompanied by the fractional magnetization plateaus. Ourresults show that the anisotropy changes the magnetization curve and the phasetransition points, significantly. Finally, we report the numerical exactdiagonalization results to compare the ground state phase diagram with ouranalytical visions.

Geometrically Frustrated Anisotropic Four-Leg Spin-$1/2$ Nanotube