arXiv subjects

Ya. S. Lyakhova

Publications and source records attributed to Ya. S. Lyakhova.

5 recordsLinked to original sources

arXiv2026

Quantized Collective Fluctuations in Correlated Fermion Systems

Collective excitations in fermionic systems play a crucial role in determining their physical properties. An important challenge is to develop efficient theoretical approaches for describing these excitations and their coupling to fermionic degrees of freedom. In this work, we revisit the problem of quantifying the contributions of individual bosonic modes of collective fluctuations to observable properties of correlated fermion systems within the framework of the Fluctuating Local Field (FLF) method. Whereas the auxiliary field in this method was previously considered only classically, we formulate its systematic extension termed Quantum FLF (Q-FLF) that incorporates selected bosonic Matsubara modes, thus tailoring it to description of quantum collective fluctuations. As a testbed, we apply the approach to a half-filled one-dimensional Hubbard chain and compute the Green's function, the total energy, and the antiferromagnetic susceptibility. Our results demonstrate that the proposed scheme enables an efficient and selective characterization of the contributions of individual bosonic modes. In particular, low Matsubara frequencies are found to have a quantitative impact on integrated observables such as total energy and antiferromagnetic susceptibility. At the same time, an accurate description of single-particle properties requires inclusion of higher-frequency bosonic modes.

cond-mat.str-el↗

arXiv2026

Time-dependent fluctuating local field approach for description of the correlated fermions dynamics

We formulate a time-dependent Fluctuating Local Field (TD-FLF) method for correlated fermion dynamics, extending the stationary FLF approach. The wavefunction is approximated as an ensemble of non-interacting states subject to a classical fluctuating field, with dynamics encoded in the field's time-dependent distribution. This reduces the time-dependent Schrödinger equation to a generalized eigenvalue problem in a significantly reduced basis. Applied to half-filled 2D Hubbard lattices, TD-FLF yields highly accurate results, outperforming mean-field theory and capturing oscillation frequencies and amplitudes in good agreement with exact diagonalization. Its low computational cost and flexibility make TD-FLF a promising tool for simulating driven correlated systems.

cond-mat.str-el↗

arXiv2024

Fluctuating field series: towards calculations of correlated systems with high accuracy

We introduce regular series expansion for weakly- and moderately-correlated fermionic systems, based on Fluctuating Local Field approach. The method relies on the explicit account of leading fluctuating mode(s) and is therefore suitable for medium-sized lattices. It can be also used as a solver for the cluster approximations for infinite-size lattices. We introduce classical fluctuating field coupled to fermionic collective mode(s). This way, fluctuations in selected modes are treated in a non-perturbative way. Other degrees of freedom are accounted for the diagram expansion performed at each value of the fluctuating field. The method is benchmarked for the $U/t=1$ and $U/t=2$ Hubbard lattices at half-filling. Results for susceptibility in the antiferromagnetic channel along with the single particle density of states are compared with the numerically exact quantum Monte Carlo data. Calculations up to the third order of the series expansion are performed and show a uniform convergence to the reference result for the susceptibility. This convergence is observed well below the DMFT Neél temperature and makes our practically simple method applicable in a much wider temperature range than DMFT-based diagrammatic schemes.

cond-mat.str-el↗

arXiv2021

Effectively Trainable Semi-Quantum Restricted Boltzmann Machine

We propose a novel quantum model for the restricted Boltzmann machine (RBM), in which the visible units remain classical whereas the hidden units are quantized as noninteracting fermions. The free motion of the fermions is parametrically coupled to the classical signal of the visible units. This model possesses a quantum behaviour such as coherences between the hidden units. Numerical experiments show that this fact makes it more powerful than the classical RBM with the same number of hidden units. At the same time, a significant advantage of the proposed model over the other approaches to the Quantum Boltzmann Machine (QBM) is that it is exactly solvable and efficiently trainable on a classical computer: there is a closed expression for the log-likelihood gradient with respect to its parameters. This fact makes it interesting not only as a model of a hypothetical quantum simulator, but also as a quantum-inspired classical machine-learning algorithm.

cond-mat.dis-nn↗

arXiv2016

Properties of magneto-dipole X-ray lines in different radiation models

We compare polarization properties of the cyclotron, and relativistic dipole radiation of electrons moving in the magnetic field on a helix with ultra-relativistic longitudinal and non-relativistic transverse velocity components. The applicability of these models in the case of accretion onto a neutron star is discussed. The test, based on polarization observations is suggested, to distinguish between the cyclotron, and relativistic dipole origin of features, observed in X-ray spectra of some X-ray sources, among which the Her X-1 is the most famous.

astro-ph.HE↗