Title: Ferromagnetic transition in a one-dimensional spin-orbit-coupled metal and its mapping to a critical point in smectic liquid crystals,
Abstract: We study the quantum phase transition between a paramagnetic and
ferromagnetic metal in the presence of Rashba spin-orbit coupling in one
dimension. Using bosonization, we analyze the transition by means of
renormalization group, controlled by an $\varepsilon$-expansion around the
upper critical dimension of two. We show that the presence of Rashba spin-orbit
coupling allows for a new nonlinear term in the bosonized action, which
generically leads to a fluctuation driven first-order transition. We further
demonstrate that the Euclidean action of this system maps onto a classical
smectic-A -- C phase transition in a magnetic field in two dimensions. We show
that the smectic transition is second-order and is controlled by a new critical
point.