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arXiv · 2412.04702

Infinite Grassmann time-evolving matrix product operators for quantum impurity problems after a quench

Zhijie Sun·Ruofan Chen·Zhenyu Li·Chu Guo
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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 sudden quench of the impurity Hamiltonian. 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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Zhijie Sun, Ruofan Chen, Zhenyu Li, Chu Guo. 2024-12-06. Infinite Grassmann time-evolving matrix product operators for quantum impurity problems after a quench. https://doi.org/10.1103/g5y8-jfb2

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