Nonequilibrium diagrammatic many-body simulations with quantics tensor trains
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910520858116096 |
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| author | Murray, Matthias Shinaoka, Hiroshi Werner, Philipp |
| author_facet | Murray, Matthias Shinaoka, Hiroshi Werner, Philipp |
| contents | The nonequilibrium Green's function formalism provides a versatile and powerful framework for numerical studies of nonequilibrium phenomena in correlated many-body systems. For calculations starting from an equilibrium initial state, a standard approach consists of discretizing the Kadanoff-Baym contour and implementing a causal time-stepping scheme in which the self-energy of the system plays the role of a memory kernel. This approach becomes computationally expensive at long times, because of the convolution integrals and the large amount of computer memory needed to store the Green's functions. A recent idea for the compression of nonequilibrium Green's functions is the quantics tensor train representation. Here, we explore this approach by implementing equilibrium and nonequilibrium simulations of the two-dimensional Hubbard model with a second-order weak-coupling approximation to the self-energy. We show that calculations with compressed two-time functions are possible without any loss of accuracy, and that the quantics tensor train implementation shows a much improved scaling of the computational effort and memory demand with the length of the time contour. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_03809 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Nonequilibrium diagrammatic many-body simulations with quantics tensor trains Murray, Matthias Shinaoka, Hiroshi Werner, Philipp Strongly Correlated Electrons The nonequilibrium Green's function formalism provides a versatile and powerful framework for numerical studies of nonequilibrium phenomena in correlated many-body systems. For calculations starting from an equilibrium initial state, a standard approach consists of discretizing the Kadanoff-Baym contour and implementing a causal time-stepping scheme in which the self-energy of the system plays the role of a memory kernel. This approach becomes computationally expensive at long times, because of the convolution integrals and the large amount of computer memory needed to store the Green's functions. A recent idea for the compression of nonequilibrium Green's functions is the quantics tensor train representation. Here, we explore this approach by implementing equilibrium and nonequilibrium simulations of the two-dimensional Hubbard model with a second-order weak-coupling approximation to the self-energy. We show that calculations with compressed two-time functions are possible without any loss of accuracy, and that the quantics tensor train implementation shows a much improved scaling of the computational effort and memory demand with the length of the time contour. |
| title | Nonequilibrium diagrammatic many-body simulations with quantics tensor trains |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2312.03809 |