arXiv subjects

Alexander I. Lichtenstein

Publications and source records attributed to Alexander I. Lichtenstein.

At least 37 records · Page 2Linked to original sources

arXiv2020

Dual fermion method as a prototype of generic reference-system approach for correlated fermions

We present a purely diagrammatic derivation of the dual fermion scheme [Phys. Rev. B 77 (2008) 033101]. The derivation makes particularly clear that a similar scheme can be developed for an arbitrary reference system provided it has the same interaction term as the original system. Thereby no restrictions are imposed by the locality of the reference problem or by the nature of the original problem as a lattice one. We present new arguments in favour of keeping the dual denominator in the expression for the lattice self-energy independently of the truncation of the dual interaction. As an example we present the computational results for the half-filled 2D Hubbard model with the choice of a $2\times2$ plaquette with periodic boundary conditions as a reference system. We observe that obtained results are in a good agreement with numerically exact lattice quantum Monte Carlo data.

cond-mat.str-el↗

arXiv2020

Correlated nonequilibrium steady states without energy flux

Floquet engineering of closed quantum systems can lead to the formation of long-lived prethermal states that, in general, eventually thermalize to infinite temperature. Coupling these driven systems to dissipative baths can stabilize such states, establishing a true nonequilibrium steady state. We demonstrate that in a certain strongly interacting lattice model coupled to a bath and driven by an electric field, such steady states can have the remarkable property that the cycle-averaged rate of energy transfer between the lattice and the baths vanishes. Despite this, we show that these states retain a clear nonequilibrium nature.

cond-mat.str-el↗

arXiv2020

Detecting quantum critical points in the $t-t'$ Fermi-Hubbard model via complex network theory

A considerable success in phenomenological description of high-T$_{\rm c}$ superconductors has been achieved within the paradigm of Quantum Critical Point (QCP) - a parental state of a variety of exotic phases that is characterized by dense entanglement and absence of well-defined quasiparticles. However, the microscopic origin of the critical regime in real materials remains an open question. On the other hand, there is a popular view that a single-band $t-t'$ Hubbard model is the minimal model to catch the main relevant physics of superconducting compounds. Here, we suggest that emergence of the QCP is tightly connected with entanglement in real space and identify its location on the phase diagram of the hole-doped $t-t'$ Hubbard model. To detect the QCP we study a weighted graph of inter-site quantum mutual information within a four-by-four plaquette that is solved by exact diagonalization. We demonstrate that some quantitative characteristics of such a graph, viewed as a complex network, exhibit peculiar behavior around a certain submanifold in the parametric space of the model. This method allows us to overcome difficulties caused by finite size effects and to identify the transition point even on a small lattice, where long-range asymptotics of correlation functions cannot be accessed.

cond-mat.str-el↗

arXiv2019

Exact real-time dynamics of single-impurity Anderson model from a single-spin hybridization-expansion

In this work we introduce a modified real-time continuous-time hybridization-expansion quantum Monte Carlo solver for a time-dependent single-orbital Anderson impurity model: CT-1/2-HYB-QMC. In the proposed method the diagrammatic expansion is performed only for one out of the two spin channels, while the resulting effective single-particle problem for the other spin is solved semi-analytically for each expansion diagram. CT-1/2-HYB-QMC alleviates the dynamical sign problem by reducing the order of sampled diagrams and makes it possible to reach twice as long time scales in comparison to the standard CT-HYB method. We illustrate the new solver by calculating an electric current through impurity in paramagnetic and spin-polarized cases.

cond-mat.str-el↗

arXiv2019

Josephson lattice model for phase fluctuations of local pairs in copper-oxide superconductors

We derive an expression for the effective Josephson coupling from the microscopic Hubbard model. It serves as a starting point for the description of phase fluctuations of local Cooper pairs in $d_{x^2-y^2}$-wave superconductors in the framework of an effective $XY$ model of plaquettes, the Josephson lattice. The expression for the effective interaction is derived by means of the local-force theorem, and it depends on local symmetry-broken correlation functions that we obtain using the cluster dynamical mean-field theory. Moreover, we apply the continuum limit to the Josephson lattice to obtain an expression for the gradient term in the Ginzburg-Landau theory and compare predicted London penetration depths and Kosterlitz-Thouless transition temperatures with experimental data for YBa$_2$Cu$_3$O$_{7-x}$.

cond-mat.str-el↗

arXiv2019

Two-particle Fermi liquid parameters at the Mott transition: Vertex divergences, Landau parameters, and incoherent response in dynamical mean-field theory

We consider the interaction-driven Mott transition at zero temperature from the viewpoint of microscopic Fermi liquid theory. To this end, we derive an exact expression for the Landau parameters within the dynamical mean-field theory (DMFT) approximation to the single-band Hubbard model. At the Mott transition the symmetric and the anti-symmetric Landau parameter diverge. The vanishing compressibility at the Mott transition directly implies the divergence of the forward scattering amplitude in the charge sector, which connects the proximity of the Mott phase to a tendency towards phase separation. We verify the expected behavior of the Landau parameters in a DMFT application to the Hubbard model on the triangular lattice at finite temperature. Exact conservation laws and the Ward identity are crucial to capture vertex divergences related to the Mott transition. We furthermore generalize Leggett's formula for the static susceptibility of the Fermi liquid to the static fermion-boson response function. In the charge sector the limits of small transferred momentum and frequency of this response function commute at the Mott transition.

cond-mat.str-el↗

arXiv2019

Exactly solvable model of strongly correlated $d$-wave superconductivity

We present an infinite-dimensional lattice of two-by-two plaquettes, the quadruple Bethe lattice, with Hubbard interaction and solve it exactly by means of the cluster dynamical mean-field theory. It exhibits a $d$-wave superconducting phase that is related to a highly degenerate point in the phase diagram of the isolated plaquette at that the groundstates of the particle number sectors $N=2,3,4$ cross. The superconducting gap is formed by the renormalized lower Slater peak of the correlated, hole-doped Mott insulator. We engineer parts of the interaction and find that pair hoppings between $X/Y$-momenta are the main two-particle correlations of the superconducting phase. The suppression of the superconductivity in the overdoped regime is caused by the diminishing of pair hopping correlations and in the underdoped regime by charge blocking. The optimal doping is $\sim 0.15$ at which the underlying normal state shows a Lifshitz transition. The model allows for different intra- and inter-plaquette hoppings that we use to disentangle superconductivity from antiferromagnetism as the latter requires larger inter-plaquette hoppings.

cond-mat.str-el↗

arXiv2018

Fermion-boson vertex within Dynamical Mean-Field Theory

In the study of strongly interacting systems, correlations on the two-particle level are receiving more and more attention. In this work, we study a particular two-particle correlation function: the fermion-boson vertex. It describes the response of the Green's function when an external field is applied and is an important ingredient of diagrammatic extensions of Dynamical Mean-Field Theory. We provide several perspectives on this object, using Ward identities, sum rules, perturbative analysis and asymptotic relations. We then use these tools to study the vertex across the doping-driven metal-insulator transition and find a divergence in the imaginary part.

cond-mat.str-el↗

arXiv2018

Electronic correlations and competing orders in multiorbital dimers: a cluster DMFT study

We investigate the violation of the first Hund's rule in 4$d$ and 5$d$ transition metal oxides that form solids of dimers. Bonding states within these dimers reduce the magnetization of such materials. We parametrize the dimer formation with realistic hopping parameters and find not only regimes, where the system behaves as a Fermi liquid or as a Peierls insulator, but also strongly correlated regions due to Hund's coupling and its competition with the dimer formation. The electronic structure is investigated using the cluster dynamical mean-field theory for a dimer in the two-plane Bethe lattice with two orbitals per site and $3/8$-filling, that is three electrons per dimer. It reveals dimer-antiferromagnetic order of a high-spin (double exchange) state and a low-spin (molecular orbital) state. At the crossover region we observe the suppression of long-range magnetic order, fluctuation enhancement and renormalization of electron masses. At certain interaction strengths the system becomes an incoherent antiferromagnetic metal with well defined local moments.

cond-mat.str-el↗

arXiv2018

Magnon-assisted tunnelling in van der Waals heterostructures based on CrBr3

The growing family of two-dimensional (2D) materials that are now available can be used to assemble van der Waals heterostructures with a wide range of properties. Of particular interest are tunnelling heterostructures, which have been used to study the electronic states both in the tunnelling barrier and in the emitter and collector contacts. Recently, 2D ferromagnets have been studied theoretically and experimentally. Here we investigate electron tunnelling through a thin (2-6 layers) ferromagnetic CrBr3 barrier. For devices with non-magnetic barriers, conservation of momentum can be relaxed by phonon-assisted tunnelling or by tunnelling through localised states. In the case of our ferromagnetic barrier the dominant tunnelling mechanisms are the emission of magnons at low temperatures or scattering of electrons on localised magnetic excitations above the Curie temperature. Tunnelling with magnon emission offers the possibility of injecting spin into the collector electrode.

cond-mat.mes-hall↗

arXiv2018

Multiband Dual Fermion Approach to Quantum Criticality in the Hubbard Honeycomb Lattice

We study the Hubbard model on the honeycomb lattice in the vicinity of the quantum critical point by means of a multiband formulation of the Dual Fermion approach. Beyond the strong local correlations of the dynamical mean field, critical fluctuations on all length scales are included by means of a ladder diagram summation. Analysis of the susceptibility yields an estimate of the critical interaction strength of the quantum phase transition from a paramagnetic semimetal to an antiferromagnetic insulator, in good agreement to other numerical methods. We further estimate the crossover temperature to the renormalized classical regime. Our data imply that, at large interaction strengths, the Hubbard model on the honeycomb lattice behaves like a quantum nonlinear sigma model, while being in a non-Fermi liquid state.

cond-mat.str-el↗

arXiv2017

Exact diagonalization solver for the extended dynamical mean-field theory

We present an efficient exact diagonalization scheme for the extended dynamical mean-field theory and apply it to the extended Hubbard model on the square lattice with nonlocal charge-charge interactions. Our solver reproduces the phase diagram of this approximation with good accuracy. Details on the numerical treatment of the large Hilbert space of the auxiliary Holstein-Anderson impurity problem are provided. Benchmarks with a numerically exact strong-coupling continuous-time quantum-Monte Carlo solver show better convergence behavior of the exact diagonalization in the deep insulator. Special attention is given to possible effects due to the discretization of the bosonic bath. We discuss the quality of real axis spectra and address the question of screening in the Mott insulator within extended dynamical mean-field theory.

cond-mat.str-el↗

arXiv2017

Relaxation and decoherence of qubits encoded in collective states of engineered magnetic structures

The quantum nature of a microscopic system can only be revealed when it is sufficiently decoupled from surroundings. Interactions with the environment induce relaxation and decoherence that turn the quantum state into a classical mixture. Here, we study the timescales of these processes for a qubit encoded in the collective state of a set of magnetic atoms deposited on a metallic surface. For that, we provide a generalization of the commonly used definitions of $T_{1}$ and $T_{2}$ characterizing relaxation and decoherence rates. We calculate these quantities for several atomic structures, including a collective spin, a setup implementing a decoherence-free subspace, and two examples of spin chains. Our work contributes to the comprehensive understanding of the relaxation and decoherence processes and shows the advantages of the implementation of a decoherence free subspace in these setups.

cond-mat.mes-hall↗

arXiv2016

Quantum-Many-Body Intermetallics: Phase Stability of Fe$_3$Al and Small-Gap Formation in Fe$_2$VAl

Various intermetallic compounds harbor subtle electronic correlation effects. To elucidate this fact for the Fe-Al system, we perform a realistic many-body investigation based on the combination of density functional theory with dynamical mean-field theory in a charge self-consistent manner. A better characterization and understanding of the phase stability of bcc-based D0$_3$-Fe$_3$Al through an improved description of the correlated charge density and the magnetic-energy is achevied. Upon replacement of one Fe sublattice by V, the Heusler compound Fe$_2$VAl is realized, known to display bad-metal behavior and increased specific heat. We here document a charge-gap opening at low temperatures in line with previous experimental work. The gap structure does not match conventional band theory and is reminiscent of (pseudo)gap charateristics in correlated oxides.

cond-mat.mtrl-sci↗

arXiv2016

Electronic structure and magnetism of samarium and neodymium adatoms on free-standing graphene

The electronic structure of selected rare-earth atoms adsorbed on a free-standing graphene was investigated using methods beyond the conventional density functional theory (DFT+U, DFT+HIA and DFT+ED). The influence of the electron correlations and the spin-orbit coupling on the magnetic properties has been examined. The DFT+U method predicts both atoms to carry local magnetic moments (spin and orbital) contrary to a nonmagnetic $f^6$ ($J=0$) ground-state configuration of Sm in the gas phase. Application of DFT${}+{}$Hubbard-I (HIA) and DFT${}+{}$exact diagonalization (ED) methods cures this problem, and yields a nonmagnetic ground state with six $f$ electrons and $J=0$ for the Sm adatom. Our calculations show that Nd adatom remains magnetic, with four localized $f$ electrons and $J=4.0$. These conclusions could be verified by STM and XAS experiments.

cond-mat.str-el↗

arXiv2016

Versatile Approach to the Spin Dynamics in Correlated Electron Systems

Time-dependent spin phenomena in condensed matter are most often either described in the weakly correlated limit of metallic Stoner/Slater-like magnetism via band theory or in the strongly correlated limit of Heisenberg-like interacting spins in an insulator. However many experimental studies, e.g. of (de)magnetization processes, focus on itinerant local-moment materials such as transition metals and various of their compounds. We here present a general theoretical framework that is capable of addressing correlated spin dynamics, also in the presence of a vanishing charge gap. A real-space implementation of the time-dependent rotational-invariant slave boson methodology allows to treat non-equilibrium spins numerically fast and efficiently beyond linear response as well as beyond the band-theoretical or Heisenberg limit.

cond-mat.str-el↗

arXiv2016

Valence fluctuations and empty-state resonance for Fe adatom on a surface

We report on the formation of the high-energy empty-state resonance in the electronic spectrum of the iron adatom on the Pt(111) surface. By using the combination of the first-principles methods and the finite-temperature exact diagonalization approach, we show that the resonance is the result of the valence fluctuations between atomic configurations of the impurity. Our theoretical finding is fully confirmed by the results of the scanning tunneling microscopy measurements [M.F. Crommie et al., Phys. Rev. B 48, 2851 (1993)]. In contrast to the previous theoretical results obtained by using local spin density approximation, the paramagnetic state of the impurity in the experiment is naturally reproduced within our approach. This opens a new way for interpretation of STM data collected earlier for metallic surface nanosystems with iron impurities.

cond-mat.str-el↗

arXiv2016

Non-equilibrium itinerant-electron magnetism: a time-dependent mean-field theory

We study the dynamical magnetic susceptibility of a strongly correlated electronic system in the presence of a time-dependent hopping field, deriving a generalized Bethe-Salpeter equation which is valid also out of equilibrium. Focusing on the single-orbital Hubbard model within the time-dependent Hartree-Fock approximation, we solve the equation in the non-equilibrium adiabatic regime, obtaining a closed expression for the transverse magnetic susceptibility. From this, we provide a rigorous definition of non-equilibrium (time-dependent) magnon frequencies and exchange parameters, expressed in terms of non-equilibrium single-electron Green functions and self-energies. In the particular case of equilibrium, we recover previously known results.

cond-mat.str-el↗