arXiv subjects

Alexander I. Lichtenstein

Publications and source records attributed to Alexander I. Lichtenstein.

At least 55 records · Page 3Linked to original sources

arXiv2016

Double occupancy in DMFT and the Dual Boson approach

We discuss the calculation of the double occupancy using Dynamical Mean-Field Theory (DMFT) in finite dimensions. The double occupancy can be determined from the susceptibility of the auxiliary impurity model or from the lattice susceptibility. The former method underestimates, whereas the latter overestimates the double occupancy. We illustrate this for the square-lattice Hubbard model. We propose an approach for which both methods lead to identical results by construction and which resolves this ambiguity. This self-consistent dual boson scheme results in a double occupancy that is numerically close to benchmarks available in the literature.

cond-mat.str-el↗

arXiv2015

Hidden spin-orbital hexagonal ordering induced by strong correlations in LiVS$_2$

We present a first-principles many-body analysis of multi-orbital lattice susceptibilities in the metallic phase of the quasi-twodimensional compound LiVS$_2$. We base this on advanced correlated electronic structure methods for the $t_{2g}$-shell to reveal a highly entangled spin-orbital hexagonal ordering (SOHO) bringing about an inherently intersite order parameter for the trimerization transition, which eventually leads to an intriguing insulating phase at low temperature.

cond-mat.mtrl-sci↗

arXiv2015

Mechanisms of finite temperature magnetism in the three-dimensional Hubbard model

We examine the nature of the transition to the antiferromagnetically ordered state in the half-filled three-dimensional Hubbard model using the dual-fermion multiscale approach. Consistent with analytics, in the weak-coupling regime we find that spin-flip excitations across the Fermi surface are important, and that the strong coupling regime is described by Heisenberg physics. In the intermediate interaction, strong correlation regime we find aspects of both local and non-local correlations. We analyze the critical exponents of the transition in the strong coupling regime and find them to be consistent with Heisenberg physics down to an interaction of $U/t=10$.

cond-mat.str-el↗

arXiv2015

Thermodynamic consistency of the charge response in dynamical mean-field based approaches

We consider the thermodynamic consistency of the charge response function in the (extended) Hubbard model. In DMFT, thermodynamic consistency is preserved. We prove that the static, homogeneous DMFT susceptibility is consistent as long as vertex corrections obtained from the two-particle impurity correlation function are included. In presence of a nonlocal interaction, the problem may be treated within extended DMFT (EDMFT), or its diagrammatic extension, the dual boson approach. We show that here, maintaining thermodynamic consistency requires knowledge of three- and four-particle impurity correlation functions, which are typically neglected. Nevertheless, the dual boson approximation to the response is remarkably close to consistency. This holds even when two-particle vertex corrections are neglected. EDMFT is consistent only in the strongly correlated regime and near half-filling, where the physics is predominantly local.

cond-mat.str-el↗

arXiv2015

Spin and orbital exchange interactions from Dynamical Mean Field Theory

We derive a set of equations expressing the parameters of the magnetic interactions characterizing a strongly correlated electronic system in terms of single-electron Green's functions and self-energies. This allows to establish a mapping between the initial electronic system and a spin model including up to quadratic interactions between the effective spins, with a general interaction (exchange) tensor that accounts for anisotropic exchange, Dzyaloshinskii-Moriya interaction and other symmetric terms such as dipole-dipole interaction. We present the formulas in a format that can be used for computations via Dynamical Mean Field Theory algorithms.

cond-mat.str-el↗

arXiv2015

Shifting the Voltage Drop in Electron Transport through a Single Molecule

A Mn-porphyrin was contacted on Au(111) in a low-temperature scanning tunneling microscope (STM). Differential conductance spectra show a zero-bias resonance that is due to an underscreened Kondo effect according to many-body calculations. When the Mn center is contacted by the STM tip, the spectrum appears to invert along the voltage axis. A drastic change in the electrostatic potential of the molecule involving a small geometric relaxation is found to cause this observation.

cond-mat.mes-hall↗

arXiv2015

Electronic structure and core-level spectra of light actinide dioxides in the dynamical mean-field theory

The local-density approximation combined with the dynamical mean-field theory (LDA+DMFT) is applied to the paramagnetic phase of light actinide dioxides: UO2, NpO2, and PuO2. The calculated band gaps and the valence-band electronic structure are in a very good agreement with the optical absorption experiments as well as with the photoemission spectra. The hybridization of the actinide 5f shell with the 2p states of oxygen is found to be relatively large, it increases the filling of the 5f orbitals from the nominal ionic configurations with two, three, and four electrons to nearly half-integer values 2.5, 3.4 and 4.4. The large hybridization leaves an imprint also on the core-level photoemission spectra in the form of satellite peaks. It is demonstrated that these satellites are accurately reproduced by the LDA+DMFT calculations.

cond-mat.str-el↗

arXiv2015

Magnetic interactions in strongly correlated systems: spin and orbital contributions

We present a technique to map an electronic model with local interactions (a generalized multi-orbital Hubbard model) onto an effective model of interacting classical spins, by requiring that the thermodynamic potentials associated to spin rotations in the two systems are equivalent up to second order in the rotation angles. This allows to determine the parameters of relativistic and non-relativistic magnetic interactions in the effective spin model in terms of equilibrium Green's functions of the electronic model. The Hamiltonian of the electronic system includes, in addition to the non-relativistic part, relativistic single-particle terms such as the Zeeman coupling to an external magnetic fields, spin-orbit coupling, and arbitrary magnetic anisotropies; the orbital degrees of freedom of the electrons are explicitly taken into account. We determine the complete relativistic exchange tensors, accounting for anisotropic exchange, Dzyaloshinskii-Moriya interactions, as well as additional non-diagonal symmetric terms (which may include dipole-dipole interaction). Our procedure provides the complete exchange tensors in a unified framework, including previously disregarded features such as the vertices of two-particle Green's functions and non-local self-energies. We do not assume any smallness in spin-orbit coupling, so our treatment is in this sense exact. Finally, we show how to distinguish and address separately the spin, orbital and spin-orbital contributions to magnetism.

cond-mat.str-el↗

arXiv2014

Beyond extended dynamical mean-field theory: Dual boson approach to the two-dimensional extended Hubbard model

The dual boson approach [Ann. Phys. 327, 1320 (2012)] provides a means to construct a diagrammatic expansion around the extended dynamical mean-field theory (EDMFT). In this paper, we present the numerical implementation of the approach and apply it to the extended Hubbard model with nearest-neighbor interaction $V$. We calculate the EDMFT phase diagram and study the effect of diagrams beyond EDMFT on the transition to the charge-ordered phase. Including diagrammatic corrections to the EDMFT polarization shifts the EDMFT phase boundary to lower values of $V$. The approach interpolates between the random phase approximation in the weak coupling limit and EDMFT for strong coupling. Neglecting vertex corrections leads to results reminiscent of the EDMFT+$GW$ approximation. We however find significant deviations from the dual boson results already for small values of the interaction, emphasizing the crucial importance of fermion-boson vertex corrections.

cond-mat.str-el↗

arXiv2014

Superconductivity, antiferromagnetism and phase separation in the two-dimensional Hubbard model: A dual-fermion approach

The dual-fermion approach offers a way to perform diagrammatic expansion around the dynamical mean-field theory. Using this formalism, the influence of antiferromagnetic fluctuations on the self-energy is taken into account through ladder-type diagrams in the particle-hole channel. The resulting phase diagram for the (quasi-)two-dimensional Hubbard model exhibits antiferromagnetism and d-wave superconductivity. Furthermore, a uniform charge instability, i.e., phase separation, is obtained in the low doping regime around the Mott insulator. We also examine spin/charge density wave fluctuations including d-wave symmetry. The model exhibits a tendency towards an unconventional charge density-wave, but no divergence of the susceptibility is found.

cond-mat.str-el↗

arXiv2014

Collective Charge Excitations of Strongly Correlated Electrons, Vertex Corrections and Gauge Invariance

We consider the collective, long-wavelength charge excitations in correlated media in presence of short- and long-range forces. As an example for the case of a short-range interaction, we examine the two-dimensional Hubbard model within dynamical mean-field theory (DMFT). It is shown explicitly that the DMFT susceptibility including vertex corrections respects the Ward identity and yields a manifestly gauge-invariant response in finite dimensions. For computing the susceptibility, we use a different expression and establish its formal equivalence to the standard DMFT formula. It allows for a more stable analytical continuation. We find a zero-sound mode expected for short-range forces. The relation between the vertex corrections, gauge invariance, and the appearance of the collective modes is discussed. Long-range forces are treated within extended dynamical mean-field theory. In order to obtain a gauge-invariant response, it is necessary to additionally incorporate some non local vertex corrections into the polarization. In doing so, we obtain plasmons in the three-dimensional Hubbard model. The plasma frequency is determined by the (single-particle) density distribution as a consequence of gauge invariance. We compare this result with the plasma frequency extracted from the analytical continuation of the susceptibility. It is in good agreement with the prediction from the gauge-invariance condition.

cond-mat.str-el↗

arXiv2014

From Hubbard bands to spin-polaron excitations in the doped Mott material Na$_x$CoO$_2$

We investigate the excitation spectrum of strongly correlated sodium cobaltate within a realistic many-body description beyond dynamical mean-field theory (DMFT). At lower doping around $x$=0.3, rather close to Mott-critical half-filling, the single-particle spectral function of Na$_x$CoO$_2$ displays an upper Hubbard band which is captured within DMFT. Momentum-dependent self-energy effects beyond DMFT become dominant at higher doping. Around a doping level of $x\sim 0.67$, the incoherent excitations give way to finite-energy spin-polaron excitations in close agreement with optics experiments. These excitations are a direct consequence of the formation of bound states between quasiparticles and paramagnons in the proximity to in-plane ferromagnetic ordering.

cond-mat.str-el↗

arXiv2014

Fermi Condensation Near van Hove Singularities Within the Hubbard Model on the Triangular Lattice

The proximity of the Fermi surface to van Hove singularities drastically enhances interaction effects and leads to essentially new physics. In this work we address the formation of flat bands ("Fermi condensation") within the Hubbard model on the triangular lattice and provide a detailed analysis from an analytical and numerical perspective. To describe the effect we consider both weak-coupling and strong-coupling approaches, namely the renormalization group and dual fermion methods. It is shown that the band flattening is driven by correlations and is well pronounced even at sufficiently high temperatures, of the order of 0.1-0.2 of the hopping parameter. The effect can therefore be probed in experiments with ultracold fermions in optical lattices.

cond-mat.str-el↗

arXiv2014

Long-lived nonequilibrium states in the Hubbard model with an electric field

We study the single-band Hubbard model in the presence of a large spatially uniform electric field out of equilibrium. Using the Keldysh nonequilibrium formalism, we solve the problem using perturbation theory in the Coulomb interaction U. We present numerical results for the charge current, the total energy of the system and the double occupancy on an infinite-dimensional hypercubic lattice with nearest-neighbor hopping. The system is isolated from an external bath and is in the paramagnetic state. We show that an electric field pulse can drive the system to a steady nonequilibrium state, which does not evolve into a thermal state. We compare results obtained within second-order perturbation theory (SOPT), self-consistent second-order perturbation theory (SCSOPT) and iterated perturbation theory (IPT). We also discuss the importance of initial conditions for a system which is not coupled to an external bath.

cond-mat.str-el↗

arXiv2012

Non-equilibrium magnetic interactions in strongly correlated systems

We formulate a low-energy theory for the magnetic interactions between electrons in the multi-band Hubbard model under non-equilibrium conditions determined by an external time-dependent electric field which simulates laser-induced spin dynamics. We derive expressions for dynamical exchange parameters in terms of non-equilibrium electronic Green functions and self-energies, which can be computed, e.g., with the methods of time-dependent dynamical mean-field theory. Moreover, we find that a correct description of the system requires, in addition to exchange, a new kind of magnetic interaction, that we name "twist exchange", which formally resembles Dzyaloshinskii-Moriya coupling, but is not due to spin-orbit, and is actually due to an effective three-spin interaction. Our theory allows the evaluation of the related time-dependent parameters as well.

cond-mat.str-el↗

arXiv2012

Valence-band satellite in the ferromagnetic nickel: LDA+DMFT study with exact diagonalization

The valence-band spectrum of the ferromagnetic nickel is calculated using the LDA+DMFT method. The auxiliary impurity model emerging in the course of the calculations is discretized and solved with the exact diagonalization, or, more precisely, with the Lanczos method. Particular emphasis is given to spin dependence of the valence-band satellite that is observed around 6 eV below the Fermi level. The calculated satellite is strongly spin polarized in accord with experimental findings.

cond-mat.mtrl-sci↗

arXiv2011

Multi-orbital Kondo physics of Co in Cu hosts

We investigate the electronic structure of cobalt atoms on a copper surface and in a copper host by combining density functional calculations with a numerically exact continuous-time quantum Monte Carlo treatment of the five-orbital impurity problem. In both cases we find low energy resonances in the density of states of all five Co $d$-orbitals. The corresponding self-energies indicate the formation of a Fermi liquid state at low temperatures. Our calculations yield the characteristic energy scale -- the Kondo temperature -- for both systems in good agreement with experiments. We quantify the charge fluctuations in both geometries and suggest that Co in Cu must be described by an Anderson impurity model rather than by a model assuming frozen impurity valency at low energies. We show that fluctuations of the orbital degrees of freedom are crucial for explaining the Kondo temperatures obtained in our calculations and measured in experiments.

cond-mat.str-el↗

arXiv2011

Continuous-time Monte Carlo methods for quantum impurity models

Quantum impurity models describe an atom or molecule embedded in a host material with which it can exchange electrons. They are basic to nanoscience as representations of quantum dots and molecular conductors and play an increasingly important role in the theory of "correlated electron" materials as auxiliary problems whose solution gives the "dynamical mean field" approximation to the self energy and local correlation functions. These applications require a method of solution which provides access to both high and low energy scales and is effective for wide classes of physically realistic models. The continuous-time quantum Monte Carlo algorithms reviewed in this article meet this challenge. We present derivations and descriptions of the algorithms in enough detail to allow other workers to write their own implementations, discuss the strengths and weaknesses of the methods, summarize the problems to which the new methods have been successfully applied and outline prospects for future applications.

cond-mat.str-el↗