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

• URL: http://arxiv.org/abs/2412.04702v1
• Date: Fri, 06 Dec 2024 01:28:30 GMT
• Title: Infinite Grassmann time-evolving matrix product operators for non-equilibrium quantum impurity problems
• Authors: Zhijie Sun, Ruofan Chen, Zhenyu Li, Chu Guo,
• Abstract summary: 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. 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.
• Score: 2.4775350526606355
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• Abstract: 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.

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