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.

中文翻译：

---

一维自旋轨道耦合金属中的铁磁跃迁及其到近晶液晶临界点的映射

我们研究了一维Rashba自旋轨道耦合存在下顺磁性和铁磁性金属之间的量子相变。使用玻色化，我们通过归一化组（由$\varepsilon$围绕两个上限的上限展开。我们表明，Rashba自旋轨道耦合的存在允许在玻化作用中使用新的非线性项，这通常会导致波动驱动的一阶跃迁。我们进一步证明了该系统的欧几里得作用映射到二维磁场中经典的近晶A–C相变。我们表明近晶相转变是二阶的，并且受新的临界点控制。