标题： 分子几何相位来自精确的电子-核分解 显示英文标题

标题： Molecular geometric phase from the exact electron-nuclear factorization

摘要： Born-Oppenheimer 电子波函数$\Phi_R^{BO}(r)$在围绕两个绝热势能面在$R$空间的锥形交叉运输时，会拾取拓扑相位因子$\pm 1$，这是Berry相位的一个特例。 我们证明，如果几何相位$\gamma = \oint \mathrm{Im} \langle \Phi_R |\nabla_{\mu} \Phi_R\rangle \cdot d\mathbf{R}_{\mu}$用精确电子-核分解$\Phi_R(r)\chi(R)$中的条件电子波函数$\Phi_R(r)$来计算而不是用绝热函数$\Phi_R^{BO}(r)$来计算，那么这个拓扑量就会还原为一个几何量$e^{i\gamma}$。伪旋转分子的一个模型，同样适用于块状晶体中的动力学Jahn-Teller离子，提供了由精确分解产生的诱导矢势和分子几何相的第一个例子。诱导矢势对循环核电流的贡献不能通过规范变换来消除。计算了精确势能面并发现它包含一个依赖于条件电子波函数的Fubini-Study度规的项。 显示英文摘要

摘要： The Born-Oppenheimer electronic wavefunction $\Phi_R^{BO}(r)$ picks up a topological phase factor $\pm 1$, a special case of Berry phase, when it is transported around a conical intersection of two adiabatic potential energy surfaces in $R$-space. We show that this topological quantity reverts to a geometric quantity $e^{i\gamma}$ if the geometric phase $\gamma = \oint \mathrm{Im} \langle \Phi_R |\nabla_{\mu} \Phi_R\rangle \cdot d\mathbf{R}_{\mu}$ is evaluated with the conditional electronic wavefunction $\Phi_R(r)$ from the exact electron-nuclear factorization $\Phi_R(r)\chi(R)$ instead of the adiabatic function $\Phi_R^{BO}(r)$. A model of a pseudorotating molecule, also applicable to dynamical Jahn-Teller ions in bulk crystals, provides the first examples of induced vector potentials and molecular geometric phase from the exact factorization. The induced vector potential gives a contribution to the circulating nuclear current which cannot be removed by a gauge transformation. The exact potential energy surface is calculated and found to contain a term depending on the Fubini-Study metric for the conditional electronic wavefunction.