Infinite Grassmann time-evolving matrix product operators for quantum impurity problems after a quench
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866914047802212352 |
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| author | Sun, Zhijie Chen, Ruofan Li, Zhenyu Guo, Chu |
| author_facet | Sun, Zhijie Chen, Ruofan Li, Zhenyu Guo, Chu |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_04702 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Infinite Grassmann time-evolving matrix product operators for quantum impurity problems after a quench Sun, Zhijie Chen, Ruofan Li, Zhenyu Guo, Chu Strongly Correlated Electrons Quantum Physics 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. |
| title | Infinite Grassmann time-evolving matrix product operators for quantum impurity problems after a quench |
| topic | Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2412.04702 |