Quantum Order-By-Disorder in Frustrated Spin Nanotube Models*

Thermally driven order-by-disorder has been extensively studied in two-dimesional frustrated Heisenberg magnets where it gives rise to long-range discrete order. Here we discuss the quantum analogue in frustrated magnets wrapped around one-dimensional nanotubes that we call "wrapped magnets". We show that as a function of the ratio of the frustrated bond couplings, wrapped magnets develop quantum phase transitions into states with nematic spin orders. For the simplest J1-J2 wrapped magnet, the emergent order parameter has Z2 symmetry and thus can undergo a transition from disordered to ordered at T=0 (D = 1+ 1). The quantum critical point is in the Ising universality class, and has gapless Ising excitations. In more complex models, such as the wrapped windmill model, there is the interesting possibility of an intermediate spin Luttinger liquid phase.