Персона: Ляхова, Яна Сергеевна
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Институт лазерных и плазменных технологий
Стратегическая цель Института ЛаПлаз – стать ведущей научной школой и ядром развития инноваций по лазерным, плазменным, радиационным и ускорительным технологиям, с уникальными образовательными программами, востребованными на российском и мировом рынке образовательных услуг.
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- ПубликацияТолько метаданныеFluctuating local field approach to the description of lattice models in the strong coupling regime(2022) Rubtsov, A. N.; Lyakhova, Y. S.; Ляхова, Яна Сергеевна© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.We consider 2D Hubbard clusters magnetism in the strong coupling regime. We show that the mean field approach does not provide sufficient results. Acting in assumption that the origin of unphysical predictions is the lack of local moment fluctuations, we develop the recently introduced Fluctuating Local Field scheme in the vicinity of atomic limit. Our numerical calculations show significant qualitative improvement of the results obtained within the mean field approach. We supply the discussion of the results with the perspectives for future quantitative improvements.
- ПубликацияТолько метаданныеFluctuating local field approach to free energy of one-dimensional molecules with strong collective electronic fluctuations(2022) Stepanov, E. A.; Rubtsov, A. N.; Lyakhova, Y. S.; Ляхова, Яна Сергеевна© 2022 American Physical Society.The impact of leading collective electronic fluctuations on a free energy of a prototype 1D model for molecular systems is considered within the recently developed fluctuating local field (FLF) approach. The FLF method is a nonperturbative extension of a mean-field theory, where a self-consistent effective constant field is replaced by a fluctuating one. Integrating the fluctuating field out numerically exactly allows one to account for collective electronic fluctuations mediated by this field without any assumptions on their magnitude, degree of nonlinearity, etc. Using a half-filled Hubbard ring as a benchmark system, we find that the FLF method noticeably improves a mean-field estimation for the free energy, in particular below the mean-field Neél temperature. We further demonstrate that the mean-field result can be even more improved introducing a multimode FLF scheme that additionally takes into account subleading fluctuations. Possible applications for the thermodynamics of real molecules are also discussed.
- ПубликацияТолько метаданныеRestricted Boltzmann machine based on a Fermi sea(2021) Lyakhova, Y. S.; Polyakov, E. A.; Rubtsov, A. N.; Ляхова, Яна СергеевнаIn recent years, there has been an intensive research on how to exploit the quantum laws of nature in the machine learning. Models have been put forward which employ spins, photons, and cold atoms. In this work we study the possibility of using the lattice fermions to learn the classical data. We propose an alternative to the quantum Boltzmann machine, the so-called spin-fermion machine (SFM), in which the spins represent the degrees of freedom of the observable data (to be learned), and the fermions represent the correlations between the data. The coupling is linear in spins and quadratic in fermions. The fermions are allowed to tunnel between the lattice sites. The training of SFM can be efficiently implemented since there are closed expressions for the log-likelihood gradient. We find that SFM is more powerful than the classical restricted Boltzmann machine with the same number of physical degrees of freedom. The reason is that SFM has additional freedom due to the rotation of the Fermi sea. We show examples for several data sets.
- ПубликацияОткрытый доступFluctuating field series: Towards calculations of correlated systems with high accuracy(2024) Lyakhova, Y.S.; Semenov, S. D.; Lichtenstein, A. I.; Rubtsov, A. N.; Ляхова, Яна Сергеевна