arXiv subjects

A. I. Lichtenstein

Publications and source records attributed to A. I. Lichtenstein.

At least 19 recordsLinked to original sources

arXiv2026

A Unified Approach to Strong Local Correlations and Collective Fluctuations: Eliminating Divergence in the Spin Channel

Dynamical mean-field theory (DMFT) provides an optimal local approximation for correlated lattice systems by mapping the lattice onto a self-consistent effective impurity model. To account for the missing long-range correlations, we propose a novel extended approach, which we term fluctuating dynamical mean-field theory (fDMFT). It incorporates collective fluctuations of auxiliary impurity models across different sites via functional integration. Technically, this method involves obtaining a family of DMFT solutions on a grid for a self-consistent auxiliary classical field applied to the lattice. While the result can, in principle, be improved diagrammatically, we find that the minimal version of the theory already yields accurate results, with lowest-order diagrammatic corrections offering only minor improvements. This consistent framework, based on our fluctuating local field concept, demonstrates superior performance for the nearly half-filled Hubbard model compared to other known diagrammatic extensions of DMFT.

cond-mat.str-el↗

arXiv2025

Superconductivity of Bad Fermions: Origin of Two Gaps in HTSC Cuprates

We investigate the spectral properties of the doped ${t-t'}$ Hubbard model with parameters typical for high-temperature cuprate superconductors. Our approach is based on a novel strong-coupling Green's function expansion around a reference system -- the exactly solvable undoped particle-hole symmetric Hubbard lattice -- that possesses a large antiferromagnetic Mott-Hubbard-Slater gap in the electron spectrum. The electron spectral function in the case of a large next-nearest-neighbor hopping ${t'=-0.3t}$, which is characteristic of the ${T_c \approx 100\,\text{K}}$ family of cuprates, reveals a strongly renormalized flat band feature with a pseudogap around the antinodal point. The superconducting response of this system to a small ${d_{x^2-y^2}}$-like external field exhibits a very unusual form. It features a pseudogap at the antinodal point in the normal part of the Nambu Green's function, related to a ``bad-fermion'' behavior in a normal phase, as well as a ${d}$-wave-like structure in the anomalous (Gorkov's) Green's function, with zero response at the nodal point of the Brillouin zone. Remarkably, we find that the anomalous part of the response deviates essentially from the simplest ${(\cos{k_x}-\cos{k_y})}$ form in momentum space. Specifically, its extrema are shifted away from the ${(π,0)}$ and ${(0,π)}$ points due to suppression of the response by the pseudogap. The observed two-gap structure of the electron spectra in a generic strong-coupling model of cuprates can serve as a basis for phenomenological treatment of different physical properties of high-temperature superconductors within two-fluid model.

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↗

arXiv2023

Exchange interactions in iron and nickel: DFT+DMFT study in paramagnetic phase

We analyze possible ways to calculate magnetic exchange interactions within the density functional theory plus dynamical mean-field theory (DFT+DMFT) approach in the paramagnetic phase. Using the susceptibilities obtained within the ladder DMFT approach together with the random phase approximation result for the Heisenberg model, we obtain bilinear exchange interactions. We show that the earlier obtained result of Stepanov et al. [Phys. Rev. Lett. 121, 037204 (2018); Phys. Rev. B 105, 155151 (2022)] corresponds to considering individual magnetic moments in each orbital in the leading-order approximation in the non-local correlations. We consider a more general approach and apply it to evaluate the effective magnetic parameters of iron and nickel. We show that the analysis, based on the inverse orbital-summed susceptibilities, yields reasonable results for both, weak and strong magnets. For iron we find, in the low-temperature limit, the exchange interaction $J_0\simeq 0.20$ eV, while for nickel we obtain $J_0\simeq 1.2$ eV. The considered method also allows one to describe the spin-wave dispersion at temperatures $T\sim T_C$, which is in agreement with the experimental data.

cond-mat.str-el↗

arXiv2023

Extended regime of coexisting metallic and insulating phases in a two-orbital electronic system

We investigate the metal-to-insulator phase transition driven by the density-density electronic interaction in the quarter-filled model on a cubic lattice with two orbitals split by a crystal field. We show that a systematic consideration of the non-local collective electronic fluctuations strongly affects the picture of the phase transition provided by the dynamical mean field theory. Our calculations reveal the appearance of metallic and Mott insulating states characterised by the same density but different values of the chemical potential, which is missing in the local approximation to electronic correlations. We find that the region of concomitant metastability of these two solutions is remarkably broad in terms of the interaction strength. It starts at a critical value of the interaction slightly larger than the bandwidth and extends to more than twice the bandwidth, where the two solutions merge into a Mott insulating phase. Our results illustrate that non-local correlations can have crucial consequences on the electronic properties in the strongly correlated regime of the simplest multi-orbital systems.

cond-mat.str-el↗

arXiv2022

Multi-channel fluctuating field approach to competing instabilities in interacting electronic systems

Systems with strong electronic Coulomb correlations often display rich phase diagrams exhibiting different ordered phases involving spin, charge, or orbital degrees of freedom. The theoretical description of the interplay of the corresponding collective fluctuations giving rise to this phenomenology remains however a tremendous challenge. Here, we introduce a multi-channel extension of the recently developed fluctuating field approach to competing collective fluctuations in correlated electron systems. The method is based on a variational optimization of a trial action that explicitly contains the order parameters of the leading fluctuation channels. It gives direct access to the free energy of the system, facilitating the distinction between stable and meta-stable phases of the system. We apply our approach to the extended Hubbard model in the weak to intermediate coupling regime where we find it to capture the interplay of competing charge density wave and antiferromagnetic fluctuations with qualitative agreement with more computationally expensive methods. The multi-channel fluctuation field approach thus offers a promising new route for a numerically cheap treatment of the interplay between collective fluctuations in large systems.

cond-mat.str-el↗

arXiv2022

Spin-orbit coupling and Kondo resonance in Co adatom on Cu(100) surface: DFT+ED study

We report density functional theory plus exact diagonalization of the multi-orbital Anderson impurity model calculations for the Co adatom on the top of Cu(001) surface. For the Co atom $d$-shell occupation $n_d \approx$ 8, a singlet many-body ground state and Kondo resonance are found, when the spin-orbit coupling is included in the calculations. The differential conductance is evaluated in a good agreement with the scanning tuneling microscopy measurements. The results illustrate the essential role which the spin-orbit coupling is playing in a formation of Kondo singlet for the multi-orbital impurity in low dimensions.

cond-mat.str-el↗

arXiv2022

Spin dynamics of itinerant electrons: local magnetic moment formation and Berry phase

The state-of-the-art theoretical description of magnetic materials relies on solving effective Heisenberg spin problems or their generalizations to relativistic or multi-spin-interaction cases that explicitly assume the presence of local magnetic moments in the system. We start with a general interacting fermionic model that is often obtained in ab initio electronic structure calculations and show that the corresponding spin problem can be introduced even in the paramagnetic regime, which is characterized by a zero average value of the magnetization. Further, we derive a physical criterion for the formation of the local magnetic moment and confirm that the latter exists already at high temperatures well above the transition to the ordered magnetic state. The use of path-integral techniques allows us to disentangle spin and electronic degrees of freedom and to carefully separate rotational dynamics of the local magnetic moment from Higgs fluctuations of its absolute value. It also allows us to accurately derive the topological Berry phase and relate it to a physical bosonic variable that describes dynamics of the spin degrees of freedom. As the result, we demonstrate that the equation of motion in the case of a large magnetic moment takes a conventional Landau-Lifshitz form that explicitly accounts for the Gilbert damping due to itinerant nature of the original electronic model.

cond-mat.str-el↗

arXiv2021

Local Plaquette Physics as Key Ingredient of High-Temperature Superconductivity in Cuprates

A major pathway towards understanding complex systems is given by exactly solvable reference systems that contain the essential physics of the system. For the $t-t'-U$ Hubbard model, the four-site plaquette is known to have a quantum critical point in the $U-μ$ space where states with electron occupations $N=2, 3, 4$ per plaquette are degenerate [Phys. Rev. B {\bf 94}, 125133 (2016)]. We show that such a critical point in the lattice causes an instability in the particle-particle singlet d-wave channel and manifests some of the essential elements of the cuprate superconductivity. For this purpose we design an efficient superperturbation theory -- based on the dual fermion approach -- with the critical plaquette as the reference system. Thus, the perturbation theory already contains the relevant d-wave fluctuations from the beginning via the two-particle correlations of the plaquette. We find that d-wave superconductivity remains a leading instability channel under reasonably broad range of parameters. The next-nearest-neighbour hopping $t'$ is shown to play a crucial role in a formation of strongly bound electronic bipolarons whose coherence at lower temperature results in superconductivity. The physics of the pseudogap within the developed picture is also discussed.

cond-mat.str-el↗

arXiv2021

Coexisting charge density wave and ferromagnetic instabilities in monolayer InSe

Recently fabricated InSe monolayers exhibit remarkable characteristics that indicate the potential of this material to host a number of many-body phenomena. Here, we consistently describe collective electronic effects in hole-doped InSe monolayers using advanced many-body techniques. To this end, we derive a realistic electronic-structure model from first principles that takes into account the most important characteristics of this material, including a flat band with prominent van Hove singularities in the electronic spectrum, strong electron-phonon coupling, and weakly-screened long-ranged Coulomb interactions. We calculate the temperature-dependent phase diagram as a function of band filling and observe that this system is in a regime with coexisting charge density wave and ferromagnetic instabilities that are driven by strong electronic Coulomb correlations. This regime can be achieved at realistic doping levels and high enough temperatures, and can be verified experimentally. We find that the electron-phonon interaction does not play a crucial role in these effects, effectively suppressing the local Coulomb interaction without changing the qualitative physical picture.

cond-mat.mtrl-sci↗

arXiv2021

A DMI guide to magnets micro-world

Dzyaloshinskii-Moriya interaction, DMI in short, represents an antisymmetric type of magnetic interactions that favour orthogonal orientation of spins and competes with Heisenberg exchange. Being introduced to explain weak ferromagnetism in antiferromagnets without an inversion center between magnetic atoms such an anisotropic interaction can be used to analyze other non-trivial magnetic structures of technological importance including spin spirals and skyrmions. Despite the fact that the corresponding DMI contribution to the magnetic energy of the system has a very compact form of the vector product of spins, the determination of DMI from first-principles electronic structure is a very challenging methodological and technical problem whose solution opens a door into the fascinating microscopic world of complex magnetic materials. In this paper we review a few such methods developed by us for calculating DMI and their applications to study the properties of real materials.

cond-mat.str-el↗

arXiv2021

Impact of partially bosonized collective fluctuations on electronic degrees of freedom

In this work we present a comprehensive analysis of collective electronic fluctuations and their effect on single-particle properties of the Hubbard model. Our approach is based on a standard dual fermion/boson scheme with the interaction truncated at the two-particle level. Within this framework we compare various approximations that differ in the set of diagrams (ladder vs exact diagrammatic Monte Carlo), and/or in the form of the four-point interaction vertex (exact vs partially bosonized). This allows to evaluate the effect of all components of the four-point vertex function on the electronic self-energy. In particular, we observe that contributions that are not accounted for by the partially bosonized approximation for the vertex have only a minor effect on electronic degrees of freedom in a broad range of model parameters. In addition, we find that in the regime, where the ladder dual fermion approximation provides an accurate solution of the problem, the leading contribution to the self-energy is given by the longitudional bosonic modes. This can be explained by the fact that contributions of transverse particle-hole and particle-particle modes partially cancel each other. Our results justify the applicability of the recently introduced dual triply irreducible local expansion (D-TRILEX) method that represents one of the simplest consistent diagrammatic extensions of the dynamical mean-field theory. We find that the self-consistent D-TRILEX approach is reasonably accurate also in challenging regimes of the Hubbard model, even where the dynamical mean-field theory does not provide the optimal local reference point (impurity problem) for the diagrammatic expansion.

cond-mat.str-el↗

arXiv2020

Spectral properties of heterostructures containing half-metallic ferromagnets in the presence of local many-body correlations

In this work, we investigate models for bulk, bi- and multilayers containing half-metallic ferromagnets (HMFs), at zero and at finite temperature, in order to elucidate the effects of strong electronic correlations on the spectral properties (density of states). Our focus is on the evolution of the finite-temperature many-body induced tails in the half-metallic gap. To this end, the dynamical mean-field theory (DMFT) is employed. For the bulk, a Bethe lattice model is solved using a matrix product states based impurity solver at zero temperature and a continuous-time quantum Monte Carlo (CT-QMC) solver at finite temperature. We demonstrate numerically, in agreement with the analytical result, that the tails vanish at the Fermi level at zero temperature. In order to study multilayers, taken to be square lattices within the layers, we use the real-space DMFT extension with the CT-QMC impurity solver. For bilayers formed by the HMF with a band or correlated insulator, we find that charge fluctuations between the layers enhance the finite temperature tails. In addition, in the presence of inter-layer hopping, a coherent quasiparticle peak forms in the otherwise correlated insulator. In the multilayer heterostructure setup, we find that by suitably choosing the model parameters, the tails at the HMF/Mott insulator interface can be reduced significantly, and that a high spin polarization is conceivable, even in the presence of long-ranged electrostatic interactions.

cond-mat.str-el↗

arXiv2020

Dual Boson Diagrammatic Monte Carlo Approach Applied to the Extended Hubbard Model

In this work we introduce the Dual Boson Diagrammatic Monte Carlo technique for strongly interacting electronic systems. This method combines the strength of dynamical mean-filed theory for non-perturbative description of local correlations with the systematic account of non-local corrections in the Dual Boson theory by the diagrammatic Monte Carlo approach. It allows us to get a numerically exact solution of the dual boson theory at the two-particle local vertex level for the extended Hubbard model. We show that it can be efficiently applied to description of single particle observables in a wide range of interaction strengths. We compare our exact results for the self-energy with the ladder Dual Boson approach and determine a physical regime, where description of collective electronic effects requires more accurate consideration beyond the ladder approximation. Additionally, we find that the order-by-order analysis of the perturbative diagrammatic series for the single-particle Green's function allows to estimate the transition point to the charge density wave phase.

cond-mat.str-el↗

arXiv2020

Dynamically induced doublon repulsion in the Fermi-Hubbard model probed by a single-particle density of states

We investigate the possibility to control dynamically the interactions between repulsively bound pairs of fermions (doublons) in correlated systems with off-resonant ac fields. We introduce an effective Hamiltonian that describes the physics of doublons up to the second-order in the high-frequency limit. It unveils that the doublon interaction, which is attractive in equilibrium, can be completely suppressed and then switched to repulsive by varying the power of the ac field. We show that the signature of the dynamical repulsion between doublons can be found in the single-fermion density of states averaged in time. Our results are further supported by nonequilibrium dynamical mean-field theory simulations for the half-filled Fermi-Hubbard model.

cond-mat.str-el↗

arXiv2020

Relativistic exchange interactions in CrX$_3$ (X=Cl, Br, I) monolayers

It has been predicted theoretically and indirectly confirmed experimentally that single-layer CrX$_3$ (X=Cl, Br, I) might be the prototypes of topological magnetic insulators (TMI). In this work, by using first-principles calculations combined with atomistic spin dynamics we provide a complete picture of the magnetic interactions and magnetic excitations in CrX$_3$. The focus is here on the two most important aspects for the actual realization of TMI, namely the relativistic magnetic interactions and the finite-size (edge) effects. We compute the full interaction tensor, which includes both Kitaev and Dzyaloshinskii-Moriya terms, which are considered as the most likely mechanisms for stabilizing topological magnons. First, we instigate the properties of bulk CrI$_3$ and compare the simulated magnon spectrum with the experimental data [Phys. Rev. X 8, 041028 (2018)]. Our results suggest that a large size of topological gap, seen in experiment ($\approx$ 4 meV), can not be explained by considering pair-wise spin interactions only. We identify several possible reasons for this disagreement and suggest that a pronounced magneto-elastic coupling should be expected in this class of materials. The magnetic interactions in the monolayers of CrX$_3$ are also investigated. The strength of the anisotropic interactions is shown to scale with the position of halide atom in the Periodic Table, the heavier the element the larger is the anisotropy. Comparing the magnons for the bulk and single-layer CrI$_3$, we find that the size of the topological gap becomes smaller in the latter case. Finally, we investigate finite-size effects in monolayers and demonstrate that the anisotropic couplings between Cr atoms close to the edges are much stronger than those in ideal periodic structure. This should have impact on the dynamics of the magnon edge modes in this class of materials.

cond-mat.mtrl-sci↗

arXiv2020

From local to non-local correlations: the Dual Boson perspective

Extended dynamical mean-field theory (EDMFT) is insufficient to describe non-local effects in strongly correlated systems, since corrections to the mean-field solution are generally large. We present an efficient scheme for the construction of diagrammatic extensions of EDMFT that avoids usual double counting problem by using an exact change of variables (the dual boson formalism) to distinguish the correlations included in the mean-field solution and those beyond. With a computational efficiency comparable to EDMFT+GW approach, our scheme significantly improves on the charge order transition phase boundary in the extended Hubbard model.

cond-mat.str-el↗

arXiv2019

Investigation of the Yu-Shiba-Rusinov states of a multi-impurity Kondo system

Recent studies of mutually interacting magnetic atoms coupled to a superconductor have gained enormous interest due to the potential realization of topological superconductivity. The Kondo exchange coupling J_K of such atoms with the electrons in the superconductor has a pair-breaking effect which produces so-called Yu-Shiba-Rusinov (YSR) states within the superconducting energy gap, whose energetic positions are intimately connected with the requirements for topological superconductivity. Here, using the tip of a scanning tunneling microscope, we artificially craft a multi-impurity Kondo system coupled to a superconducting host consisting of an Fe adatom interacting with an assembly of interstitial Fe atoms on an oxygen-reconstructed Ta(100) surface and we experimentally investigate the signatures of Kondo screening and the YSR states. With the help of numerical renormalization group (NRG) calculations, we show that the observed behavior can be qualitatively reproduced by a two-impurity Kondo system whose inter-impurity antiferromagnetic interaction J is adjusted by the number of interstitial Fe atoms in the assembly. When driving the system from the regime of two decoupled Kondo singlets (small J) to that of an antiferromagnetic dimer (large J), the YSR state shows a characteristic cross-over in its energetic position and particle-hole asymmetry.

cond-mat.supr-con↗