Abstract

This chapter discusses possibility of realizing spin-density wave (SDW) in a single-channel one-dimensional quantum wire. It should be noted from the outset that purely one-dimensional system of electrons with spin-rotationally invariant interaction between particles (such as the usual Coulomb interaction) cannot have magnetically ordered ground state. At finite temperature, any such order is destroyed by thermal fluctuations, and the statement is known as the Mermin–Wagner theorem. At zero temperature, Goldstone modes associated with spontaneously broken continuous spin symmetry destroy the putative order parameter, making the original assumption of the broken symmetry incorrect. Thus, SDW states are not possible in one-dimensional wire. (Similarly, even one-dimensional superconductivity is not possible.)