Real-time Impurity Solver Using Grassmann Time-Evolving Matrix Product Operators
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913296444030976 |
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| author | Chen, Ruofan Xu, Xiansong Guo, Chu |
| author_facet | Chen, Ruofan Xu, Xiansong Guo, Chu |
| contents | An emergent and promising tensor-network-based impurity solver is to represent the path integral as a matrix product state, where the bath is analytically integrated out using Feynman-Vernon influence functional. Here we present an approach to calculate the equilibrium impurity spectral function based on the recently proposed Grassmann time-evolving matrix product operators method. The central idea is to perform a quench from a separable impurity-bath initial state as in the non-equilibrium scenario. The retarded Green's function $G(t+t_0, t'+t_0)$ is then calculated after an equilibration time $t_0$ such that the impurity and bath are approximately in thermal equilibrium. There are two major advantages of this method. First, since we focus on real-time dynamics, we do not need to perform the numerically ill-posed analytic continuation in the continuous-time quantum Monte Carlo case that relies on imaginary-time evolution. Second, the entanglement growth of the matrix product states in real-time calculations is observed to be much slower than that in imaginary-time calculations, leading to a significant improvement in numerical efficiency. The accuracy of this method is demonstrated in the single-orbital Anderson impurity model and benchmarked against the continuous-time quantum Monte Carlo method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04880 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Real-time Impurity Solver Using Grassmann Time-Evolving Matrix Product Operators Chen, Ruofan Xu, Xiansong Guo, Chu Strongly Correlated Electrons Quantum Physics An emergent and promising tensor-network-based impurity solver is to represent the path integral as a matrix product state, where the bath is analytically integrated out using Feynman-Vernon influence functional. Here we present an approach to calculate the equilibrium impurity spectral function based on the recently proposed Grassmann time-evolving matrix product operators method. The central idea is to perform a quench from a separable impurity-bath initial state as in the non-equilibrium scenario. The retarded Green's function $G(t+t_0, t'+t_0)$ is then calculated after an equilibration time $t_0$ such that the impurity and bath are approximately in thermal equilibrium. There are two major advantages of this method. First, since we focus on real-time dynamics, we do not need to perform the numerically ill-posed analytic continuation in the continuous-time quantum Monte Carlo case that relies on imaginary-time evolution. Second, the entanglement growth of the matrix product states in real-time calculations is observed to be much slower than that in imaginary-time calculations, leading to a significant improvement in numerical efficiency. The accuracy of this method is demonstrated in the single-orbital Anderson impurity model and benchmarked against the continuous-time quantum Monte Carlo method. |
| title | Real-time Impurity Solver Using Grassmann Time-Evolving Matrix Product Operators |
| topic | Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2401.04880 |