标题： 非平衡量子杂质问题的无限格拉斯曼时间演化矩阵乘积算子 显示英文标题

标题： Infinite Grassmann time-evolving matrix product operators for non-equilibrium quantum impurity problems

摘要： 一种解决量子杂质问题的新兴数值方法是将杂质路径积分编码为矩阵乘积态。 对于时间依赖的问题，此方法的成本通常随演化时间而变化。 在这里，我们考虑一个常见的非平衡情形，其中杂质最初与热浴处于平衡状态，然后通过一个时间依赖的力项被驱动出平衡。 尽管该问题中没有时间平移不变性，但我们证明仍然可以充分利用无限矩阵乘积态技术，从而得到一种成本几乎与演化时间无关的方法。 我们在可积情况下通过精确对角化验证了该方法的有效性，并在一般情况下通过L形Kadanoff-Baym轮廓的现有计算进行了验证。 我们的方法可能是一种研究长时间非平衡量子动力学的非常有竞争力的方法，并且可能作为非平衡动态平均场理论中的高效杂质求解器使用。 显示英文摘要

摘要： An emergent numerical approach to solve quantum impurity problems is to encode the impurity path integral as a matrix product state. For time-dependent problems, the cost of this approach generally scales with the evolution time. Here we consider a common non-equilibrium scenario where an impurity, initially in equilibrium with a thermal bath, is driven out of equilibrium by a time-dependent force term. Despite that there is no time-translational invariance in the problem, we show that we could still make full use of the infinite matrix product state technique, resulting in a method whose cost is essentially independent of the evolution time. We demonstrate the effectiveness of this method in the integrable case against exact diagonalization, and against existing calculations on the L-shaped Kadanoff-Baym contour in the general case. Our method could be a very competitive method for studying long-time non-equilibrium quantum dynamics, and be potentially used as an efficient impurity solver in the non-equilibrium dynamical mean field theory.