Autoencoder-based analytic continuation method for strongly correlated quantum systems
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866916415047467008 |
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| author | Kliczkowski, Maksymilian Keyes, Lauren Roy, Sayantan Paiva, Thereza Randeria, Mohit Trivedi, Nandini Maska, Maciej M. |
| author_facet | Kliczkowski, Maksymilian Keyes, Lauren Roy, Sayantan Paiva, Thereza Randeria, Mohit Trivedi, Nandini Maska, Maciej M. |
| contents | The single particle Green's function provides valuable information on the momentum and energy-resolved spectral properties for a strongly correlated system. In large-scale numerical calculations using quantum Monte Carlo (QMC), dynamical mean field theory (DMFT), including cluster-DMFT, one usually obtains the Green's function in imaginary-time $G(τ)$. The process of inverting a Laplace transform to obtain the spectral function $A(ω)$ in real-frequency is an ill-posed problem and forms the core of the analytic continuation problem. In this Letter, we propose to use a completely unsupervised autoencoder-type neural network to solve the analytic continuation problem. We introduce an encoder-decoder approach that, together with only minor physical assumptions, can extract a high-quality frequency response from the imaginary time domain. With a deeply tunable architecture, this method can, in principle, locate sharp features of spectral functions that might normally be lost using already well-established methods, such as maximum entropy (MaxEnt) methods. We demonstrate the strength of the autoencoder approach by applying it to QMC results of $G(τ)$ for a single-band Hubbard model. The proposed method is general and can also be applied to other ill-posed inverse problems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_17920 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Autoencoder-based analytic continuation method for strongly correlated quantum systems Kliczkowski, Maksymilian Keyes, Lauren Roy, Sayantan Paiva, Thereza Randeria, Mohit Trivedi, Nandini Maska, Maciej M. Strongly Correlated Electrons Disordered Systems and Neural Networks Computational Physics The single particle Green's function provides valuable information on the momentum and energy-resolved spectral properties for a strongly correlated system. In large-scale numerical calculations using quantum Monte Carlo (QMC), dynamical mean field theory (DMFT), including cluster-DMFT, one usually obtains the Green's function in imaginary-time $G(τ)$. The process of inverting a Laplace transform to obtain the spectral function $A(ω)$ in real-frequency is an ill-posed problem and forms the core of the analytic continuation problem. In this Letter, we propose to use a completely unsupervised autoencoder-type neural network to solve the analytic continuation problem. We introduce an encoder-decoder approach that, together with only minor physical assumptions, can extract a high-quality frequency response from the imaginary time domain. With a deeply tunable architecture, this method can, in principle, locate sharp features of spectral functions that might normally be lost using already well-established methods, such as maximum entropy (MaxEnt) methods. We demonstrate the strength of the autoencoder approach by applying it to QMC results of $G(τ)$ for a single-band Hubbard model. The proposed method is general and can also be applied to other ill-posed inverse problems. |
| title | Autoencoder-based analytic continuation method for strongly correlated quantum systems |
| topic | Strongly Correlated Electrons Disordered Systems and Neural Networks Computational Physics |
| url | https://arxiv.org/abs/2311.17920 |