Compactness of quantics tensor train representations of local imaginary-time propagators
Space-time dependence of imaginary-time propagators, vital for ab initio and many-body calculations based on quantum field theories, has been revealed to be compressible using Quantum Tensor Trains (QTTs) [Phys. Rev. X 13, 021015 (2023)]. However, the impact of system parameters, like temperature, o...
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2025-01-01
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| author | Haruto Takahashi, Rihito Sakurai, Hiroshi Shinaoka |
| author_facet | Haruto Takahashi, Rihito Sakurai, Hiroshi Shinaoka |
| author_sort | Haruto Takahashi, Rihito Sakurai, Hiroshi Shinaoka |
| collection | DOAJ |
| description | Space-time dependence of imaginary-time propagators, vital for ab initio and many-body calculations based on quantum field theories, has been revealed to be compressible using Quantum Tensor Trains (QTTs) [Phys. Rev. X 13, 021015 (2023)]. However, the impact of system parameters, like temperature, on data size remains underexplored. This paper provides a comprehensive numerical analysis of the compactness of local imaginary-time propagators in QTT for one-time/-frequency objects and two-time/-frequency objects, considering truncation in terms of the Frobenius and maximum norms. To study worst-case scenarios, we employ random pole models, where the number of poles grows logarithmically with the inverse temperature and coefficients are random. The Green's functions generated by these models are expected to be more difficult to compress than those from physical systems. The numerical analysis reveals that these propagators are highly compressible in QTT, outperforming the state-of-the-art approaches such as intermediate representation and discrete Lehmann reprensentation. For one-time/-frequency objects and two-time/-frequency objects, the bond dimensions saturate at low temperatures, especially for truncation in terms of the Frobenius norm. We provide counting-number arguments for the saturation of bond dimensions for the one-time/-frequency objects, while the origin of this saturation for two-time/-frequency objects remains to be clarified. This paper's findings highlight the critical need for further research on the selection of truncation methods, tolerance levels, and the choice between imaginary-time and imaginary-frequency representations in practical applications. |
| format | Article |
| id | doaj-art-b8bb75bb328048d8a4ab004c0d71755d |
| institution | Kabale University |
| issn | 2542-4653 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SciPost |
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| spelling | doaj-art-b8bb75bb328048d8a4ab004c0d71755d2025-01-08T14:00:46ZengSciPostSciPost Physics2542-46532025-01-0118100710.21468/SciPostPhys.18.1.007Compactness of quantics tensor train representations of local imaginary-time propagatorsHaruto Takahashi, Rihito Sakurai, Hiroshi ShinaokaSpace-time dependence of imaginary-time propagators, vital for ab initio and many-body calculations based on quantum field theories, has been revealed to be compressible using Quantum Tensor Trains (QTTs) [Phys. Rev. X 13, 021015 (2023)]. However, the impact of system parameters, like temperature, on data size remains underexplored. This paper provides a comprehensive numerical analysis of the compactness of local imaginary-time propagators in QTT for one-time/-frequency objects and two-time/-frequency objects, considering truncation in terms of the Frobenius and maximum norms. To study worst-case scenarios, we employ random pole models, where the number of poles grows logarithmically with the inverse temperature and coefficients are random. The Green's functions generated by these models are expected to be more difficult to compress than those from physical systems. The numerical analysis reveals that these propagators are highly compressible in QTT, outperforming the state-of-the-art approaches such as intermediate representation and discrete Lehmann reprensentation. For one-time/-frequency objects and two-time/-frequency objects, the bond dimensions saturate at low temperatures, especially for truncation in terms of the Frobenius norm. We provide counting-number arguments for the saturation of bond dimensions for the one-time/-frequency objects, while the origin of this saturation for two-time/-frequency objects remains to be clarified. This paper's findings highlight the critical need for further research on the selection of truncation methods, tolerance levels, and the choice between imaginary-time and imaginary-frequency representations in practical applications.https://scipost.org/SciPostPhys.18.1.007 |
| spellingShingle | Haruto Takahashi, Rihito Sakurai, Hiroshi Shinaoka Compactness of quantics tensor train representations of local imaginary-time propagators SciPost Physics |
| title | Compactness of quantics tensor train representations of local imaginary-time propagators |
| title_full | Compactness of quantics tensor train representations of local imaginary-time propagators |
| title_fullStr | Compactness of quantics tensor train representations of local imaginary-time propagators |
| title_full_unstemmed | Compactness of quantics tensor train representations of local imaginary-time propagators |
| title_short | Compactness of quantics tensor train representations of local imaginary-time propagators |
| title_sort | compactness of quantics tensor train representations of local imaginary time propagators |
| url | https://scipost.org/SciPostPhys.18.1.007 |
| work_keys_str_mv | AT harutotakahashirihitosakuraihiroshishinaoka compactnessofquanticstensortrainrepresentationsoflocalimaginarytimepropagators |