Quantum order by disorder in frustrated spin nanotubes

We investigate quantum order by disorder in a frustrated spin nanotube formed by wrapping a J₁-J₂ Heisenberg model at 45^∘ around a cylinder. Using Schwinger boson theory and density matrix renormalization group (DMRG), we have computed the ground-state phase diagram to reveal a Z₂ phase in which collinear spin stripes form a right- or left-handed helix around the nanotube. We have derived an analytic estimate for the critical ηc=J₁/2J₂ of the Z₂-helical phase transition, which is in agreement with the DMRG results. By evaluating the entanglement spectrum and nonlocal string order parameters we discuss the topology of the Z₂-helical phase.