AI 中文总结
研究具有附加手性项的自旋\(1/2\)海森堡链零温性质，结合解析与计算方法，证明转变点是有特定指数的里夫希茨转变，手性相有特殊性质，推导场论并确定其普适性质，数值计算验证结论。
AI 中文摘要
我们研究了具有强度为\(g\)的附加三格点手性项的自旋\(1/2\)海森堡链的零温性质。该模型已知是可积的，先前使用贝塞耳假设的工作已确定对于\(g < g_c = 2/\pi\)从通常的临界态到\(g > g_c\)时到手性相的相变。在此，我们结合解析和计算方法证明，转变点包含一个具有动力学临界指数\(z = 3\)的非同寻常的里夫希茨转变，手性相是一个自发破缺\(SU(2)\)对称性的部分自旋极化相。我们为临界点推导了一个强相互作用手性玻色子场论，并表明即使其小动量、低能量响应也是不平凡的。我们还确定了手性相的普适性质，具体表明它具有一个二次色散的铁磁“磁振子”模式，与卢廷格液体典型的幂律奇点和线性色散激发共存。我们的结论通过基于矩阵乘积态方法和精确对角化的数值计算得到验证。
英文摘要
We study the zero-temperature properties of a spin-$1/2$ Heisenberg chain with an additional three-site chiral term of strength $g$. The model is known to be integrable and previous work using Bethe ansatz has identified a phase transition from the usual critical state for $g< g_c = 2/π$ to a chiral phase for $g>g_c$. Here we combine analytical and computational approaches to demonstrate that the transition point comprises an unusual Lifshitz transition with dynamical critical exponent $z=3$, and the chiral phase is a partially spin-polarized phase which spontaneously breaks SU(2) symmetry. We derive a strongly interacting chiral boson field theory for the critical point, and show that even its small-momentum, low-energy response is non-trivial. We also determine the universal properties of the chiral phase, and specifically show that it has a simultaneous quadratically dispersing ferromagnetic "magnon" mode coexisting with the power-law singularities and linearly dispersing excitations typical of a Luttinger liquid. Our conclusions are validated using numerics based on matrix product state methods and exact diagonalization.
Comments28 pages, 11 figures
