AI 中文总结
研究低维受限系统中声子的非互易性，通过将位移场映射到自旋自由度引入该特征，用一维谐振链验证，引入短程相互作用发现能导致非互易态相变，可通过测量电感变化探测非互易性，此模型有特殊$U(1)$对称性。
AI 中文摘要
低维固态或冷原子系统的一个重要特征是在受限方向上离子/原子自由度的振荡受限，传统规范量子化的声子并非理想描述。本文提出通过将位移场映射到自旋自由度，把此特征引入到原本不受限的系统中。通过一维谐振链验证了该方法的有效性，结果表明长距离处出现大量狄拉克费米子，且无声学模式，这是整个链受限平面外运动的标志。接着引入短程相互作用，发现略高于能隙的能量尺度会导致向具有$\hat{T}^2 = +1$型自发时间反演对称性破缺（TRSB）的非互易态的（量子）相变。尽管总粒子数不守恒，但该模型具有未被充分认识的具有守恒“极化电荷”的$U(1)$对称性，因此可以通过测量有序相内外人工规范场的电感变化来探测非互易性。
英文摘要
An important feature of solid-state or cold atom systems in low dimensions is the restricted oscillations of ionic/atomic degrees of freedom in the confining directions, for which the conventional phonon from canonical quantization is not an ideal description. In this work we propose a general recipe to introduce this feature to otherwise unrestricted systems by mapping displacement fields to spin degrees of freedom. We demonstrate the validity of the approach with a 1D harmonic chain, and the results lead to massive Dirac fermions at long distances, showing the absence of acoustic modes as the signature of confined out-of-plane motion of the entire chain. We then introduce a short-range interaction via anharmonicities and show that for energy scale slightly above the gap, it gives rise to a (quantum) phase transition to a nonreciprocal state with spontaneous time reversal symmetry breaking (TRSB) of the type $\hat{T}^2=+1$. Despite the non-conserved total particle number, the model holds an under-appreciated $U(1)$ symmetry with conserved "polarization charge", so that the nonreciprocity can be probed by measuring the change of inductivity to artificial gauge fields in and out of the ordered phase.
