arXiv subjects

Aleksey Alekseev

Publications and source records attributed to Aleksey Alekseev.

6 recordsLinked to original sources

arXiv2026

Charge-Ordered States and the Phase Diagram of the Extended Hubbard Model on the Bethe lattice

We study the extended Hubbard model (EHM) with both onsite Hubbard interaction and the intersite density-density interaction between nearest-neighbors using the standard Hartree mean-field approximation (MFA) on the Bethe lattice. We found that, at the ground state, the system can be in a charge-ordered band-insulating (COI), a charge-order metallic (COM) or a non-charge-ordered (NO) state. Moreover, the finite-temperature phase diagrams are presented. Several observables like a charge-order parameter, a spectral function, and particularly at finite temperatures, a thermally-excited charge carrier concentration (to visualize the degree of metallicity) are analyzed. The results show that increasing onsite repulsion suppresses charge order and change the properties of the system from insulating to metallic. Worth noting, that a number of phenomena can be found within the MFA, where their analysis is much simpler than in more advanced approaches. The method used for the EHM on the Bethe lattice also allows for a series of analytical derivations and simplifications to see general geometry-independent features and analytical results, avoiding the numerical inaccuracies and other issues that appear with a purely numerical solution.

cond-mat.str-el↗

arXiv2026

Phase structure of the one-dimensional $\mathbb{Z}_2$ lattice gauge theory with second nearest-neighbor interactions

We investigate the ground-state phase diagram of a one-dimensional $\mathbb{Z}_2$ lattice gauge theory (LGT) model with hard-core bosons at half-filling, extending previous studies by including second nearest-neighbor (2NN) interactions. Using matrix product state techniques within the density matrix renormalization group, we compute charge gap, static structure factor, pair-pair correlation functions, and entanglement entropy for various interaction strengths and field parameters. We analyze two representative neatest-neighbor interaction strengths ($V_1$) that correspond to the Luttinger liquid (LL) and Mott insulator (MI) phases in the absence of the 2NN interactions. We introduce the 2NN coupling $V_2$ and investigate its impact on the system. Our results reveal very rich behavior. As the 2NN repulsion increases, in the case of small $V_1$, we observe a direct transition from the LL phase to a charge-ordered insulator (COI) phase with four-site ordering pattern, whereas for large $V_1$, we observe a transition from the MI phase with two-site ordering pattern (previously found with only $V_1$ included), going through an intermediate LL region, and finally reaching the COI regime. Additionally, the inclusion of 2NN interactions enhances charge order and suppresses pair coherence, evidenced by sharp peaks in the structure factor and rapid decay in pair-pair correlators. Our work extends the well-studied phase structure of 1D $\mathbb{Z}_2$ LGT models and demonstrates the interplay between gauge fields, confinement, and extended interactions.

cond-mat.str-el↗

arXiv2026

Charge order on a triangular lattice with Mott physics and arbitrary charge density

Triangular-lattice systems attract a lot of attention due to various frustration-induced and strongly correlated effects. Here, we focus on the charge-ordering phenomenon by means of investigation of the extended Hubbard model with dynamical mean-field theory (DMFT). By considering the intersite nearest-neighbor interaction we have found a very rich phase diagram that contains large number of features, phases, and phase transitions. Among them are pinball-liquid (PL) phases where we distinguish charge-transfer-driven and Mott-localization-driven PLs; phase transitions that change their order as model parameters evolve (from discontinuous to continuous); very strong particle-hole asymmetry. Various features of the phase diagram are found to be better understood by means of the simple mean-field approximation (MFA). Moreover, besides helping with interpretation of the phase diagram, the MFA results together with results for the atomic-limit model are found to be able to set rather good expectations on how the DMFT phase diagram should look like. Nevertheless, a few features were not expected and are found within the DMFT, such as a small-region intermediate metallic phase on an electron-doped side of the phase diagram.

cond-mat.str-el↗

arXiv2025

Particle-Hole Asymmetry and Pinball Liquid in a Triangular-Lattice Extended Hubbard Model within Mean-Field Approximation

Recently, triangular lattice models have received a lot of attention since they can describe a number of strongly-correlated materials that exhibit superconductivity and various magnetic and charge orders. In this research we present an extensive analysis of the charge-ordering phenomenon of the triangular-lattice extended Hubbard model with repulsive onsite and nearest-neighbor interaction, arbitrary charge concentration, and $\sqrt{3}\times\sqrt{3}$ supercell (3-sublattice assumption). The model is solved in the ground state with the mean-field approximation which allowed to identify $8$ charge-ordered phases and a large variety of phase transitions. An exotic pinball-liquid phase was found and described. Moreover, strong particle-hole asymmetry of the phase diagram is found to play an important role for triangular lattices. The detailed analysis of band structures, unavailable for more advanced methods, such as dynamical mean-field theory, allowed us to interpret the found triangular-lattice phases and provided a great insight into the mechanisms behind the phase transitions that can also be met when correlation effects are taken into account. The complexity of the mean-field phase diagram showed the importance and usefulness of the results for the further research with correlation effects included. Together with atomic-limit approximation it can serve them as both a starting point, and a tool to interpret results.

cond-mat.str-el↗

arXiv2021

The Estimation of Approximation Error using the Inverse Problem and the Set of Numerical Solutions

The Inverse Problem for the estimation of a point-wise approximation error occurring at the discretization and solving of the system of partial differential equations is addressed. The set of the differences between the numerical solutions is used as the input data. The analyzed solutions are obtained by the numerical algorithms of the distinct inner structure on the same grid. The approximation error is estimated by the Inverse Problem, which is posed in the variational statement with the zero order Tikhonov regularization. The numerical tests, performed for the two dimensional inviscid compressible flows corresponding to Edney-I and Edney-VI shock wave interference modes, are provided. The analyzed flowfields are computed using ten different numerical algorithms. The comparison of the estimated approximation error and the true error, obtained by subtraction of numerical and analytic solutions, is presented.

math.NA↗

arXiv2016

On Relationship of Koopman Eigenvalues and Frequencies in Dynamic Mode Decomposition

The frequency estimation from the Koopman eigenvalues (phase angles) obtained via Dynamic Mode Decomposition (DMD) is addressed. Since the calculations of the frequencies from the phase angles are nonunique, the modifications of DMD for uniqueness restoration are considered. The nonlinear oscillating mode of supersonic jet, impinging the flat plate, is used as a toy problem.

physics.flu-dyn↗