arXiv subjects

Jörg Bünemann

Publications and source records attributed to Jörg Bünemann.

18 recordsLinked to original sources

arXiv2017

Charge and pairing dynamics in the attractive Hubbard model: mode coupling and the validity of linear-response theory

Pump-probe experiments have turned out as a powerful tool in order to study the dynamics of competing orders in a large variety of materials. The corresponding analysis of the data often relies on standard linear-response theory generalized to non-equilibrium situations. Here we examine the validity of such an approach within the attractive Hubbard model for which the dynamics of pairing and charge-density wave orders is computed using the time-dependent Hartree-Fock approximation (TDHF). Our calculations reveal that the `linear-response assumption' is justified for small to moderate non-equilibrium situations (i.e., pump pulses) when the symmetry of the pump-induced state differs from that of the external field. This is the case, when we consider the pairing response in a charge-ordered state or the charge-order response in a superconducting state. The situation is very different when the non-equilibrium state and the external probe field have the same symmetry. In this case, we observe significant changes of the response in magnitude but also due to mode coupling when moving away from an equilibrium state, indicating the failure of the linear-response assumption.

cond-mat.str-el↗

arXiv2017

Gutzwiller variational approach to the two-impurity Anderson model at particle-hole symmetry

We study Gutzwiller-correlated wave functions as variational ground states for the two-impurity Anderson model (TIAM) at particle-hole symmetry as a function of the impurity separation ${\bf R}$. Our variational state is obtained by applying the Gutzwiller many-particle correlator to a single-particle product state. We determine the optimal single-particle product state fully variationally from an effective non-interacting TIAM that contains a direct electron transfer between the impurities as variational degree of freedom. For a large Hubbard interaction $U$ between the electrons on the impurities, the impurity spins experience a Heisenberg coupling proportional to $V^2/U$ where $V$ parameterizes the strength of the on-site hybridization. For small Hubbard interactions we observe weakly coupled impurities. In general, for a three-dimensional simple cubic lattice we find discontinuous quantum phase transitions that separate weakly interacting impurities for small interactions from singlet pairs for large interactions.

cond-mat.str-el↗

arXiv2017

Coulomb matrix elements in multi-orbital Hubbard models

Coulomb matrix elements are needed in all studies in solid-state theory that are based on Hubbard-type multi-orbital models. Due to symmetries, the matrix elements are not independent. We determine a set of independent Coulomb parameters for a $d$-shell and a $f$-shell and all point groups with up to $16$ elements ($O_h$, $O$, $T_d$, $T_h$, $D_{6h}$, and $D_{4h}$). Furthermore, we express all other matrix elements as a function of the independent Coulomb parameters. Apart from the solution of the general point-group problem we investigate in detail the spherical approximation and first-order corrections to the spherical approximation.

cond-mat.str-el↗

arXiv2016

Non-interacting two-impurity Anderson model on a lattice at particle-hole symmetry

We study the non-interacting two-impurity Anderson model on a lattice using the Green function equation-of-motion method. A case of particular interest is the RKKY limit that is characterized by a small hybridization between impurities and host electrons and the absence of a direct coupling between the impurities. In contrast to the low-density case, at half band-filling and particle-hole symmetry, the RKKY interaction decays as the inverse square of the impurity distance along the axis of a simple cubic lattice. In the RKKY limit, for the spectral function we generically observe a small splitting of the single-impurity resonance into two peaks. For a vanishing density-density correlation function of the host electrons, we find only a broadened single peak in the local density of states.

cond-mat.str-el↗

arXiv2016

Interplay of Coulomb interaction and spin-orbit coupling

We employ the Gutzwiller variational approach to investigate the interplay of Coulomb interaction and spin-orbit coupling in a three-orbital Hubbard model. Already in the paramagnetic phase we find a substantial renormalization of the spin-orbit coupling that enters the effective single-particle Hamiltonian for the quasi-particles. Only close to half band-filling and for sizable Coulomb interaction we observe clear signatures of Hund's atomic rules for spin, orbital, and total angular momentum. For a finite local Hund's-rule exchange interaction we find a ferromagnetically ordered state. The spin-orbit coupling considerably reduces the size of the ordered moment, it generates a small ordered orbital moment, and it induces a magnetic anisotropy. To investigate the magnetic anisotropy energy, we use an external magnetic field that tilts the magnetic moment away from the easy axis $(1,1,1)$.

cond-mat.str-el↗

arXiv2016

Exchange couplings for Mn ions in CdTe: validity of spin models for dilute magnetic II-VI semiconductors

We employ density-functional theory (DFT) in the generalized gradient approximation (GGA) and its extensions GGA+$U$ and GGA+Gutzwiller to calculate the magnetic exchange couplings between pairs of Mn ions substituting Cd in a CdTe crystal at very small doping. DFT(GGA) overestimates the exchange couplings by a factor of three because it underestimates the charge-transfer gap in Mn-doped II-VI semiconductors. Fixing the nearest-neighbor coupling $J_1$ to its experimental value in GGA+$U$, in GGA+Gutzwiller, or by a simple scaling of the DFT(GGA) results provides acceptable values for the exchange couplings at 2nd, 3rd, and 4th neighbor distances in Cd(Mn)Te, Zn(Mn)Te, Zn(Mn)Se, and Zn(Mn)S. In particular, we recover the experimentally observed relation $J_4>J_2,J_3$. The filling of the Mn 3$d$-shell is not integer which puts the underlying Heisenberg description into question. However, using a few-ion toy model the picture of a slightly extended local moment emerges so that an integer $3d$-shell filling is not a prerequisite for equidistant magnetization plateaus, as seen in experiment.

cond-mat.str-el↗

arXiv2016

Quasi-particle bands and structural phase transition of iron from Gutzwiller Density-Functional Theory

We use the Gutzwiller Density Functional Theory to calculate ground-state properties and bandstructures of iron in its body-centered-cubic (bcc) and hexagonal-close-packed (hcp) phases. For a Hubbard interaction $U=9\, {\rm eV}$ and Hund's-rule coupling $J=0.54\, {\rm eV}$ we reproduce the lattice parameter, magnetic moment, and bulk modulus of bcc iron. For these parameters, bcc is the ground-state lattice structure at ambient pressure up to a pressure of $p_{\rm c}=41\, {\rm GPa}$ where a transition to the non-magnetic hcp structure is predicted, in qualitative agreement with experiment ($p_{\rm c}^{\rm exp}=10\ldots 15\, {\rm GPa}$). The calculated bandstructure for bcc iron is in good agreement with ARPES measurements. The agreement improves when we perturbatively include the spin-orbit coupling.

cond-mat.str-el↗

arXiv2016

Approximation schemes for the study of multi-band Gutzwiller wave functions

The minimum of the Gutzwiller energy functional depends on the number of parameters considered in the variational state. For a three-orbital Hubbard model we find that the frequently used diagonal Ansatz is very accurate in high-symmetry situations. For lower symmetry, induced by a crystal-field splitting or the spin-orbit coupling, the discrepancies in energy between the most general and a diagonal Gutzwiller Ansatz can be quite significant. We discuss approximate schemes that may be employed in multi-band cases where a minimization of the general Gutzwiller energy functional is too demanding numerically.

cond-mat.str-el↗

arXiv2015

Coexistence of Nematic Order and Superconductivity in the Hubbard Model

We study the interplay of nematic and superconducting order in the two-dimensional Hubbard model and show that they can coexist, especially when superconductivity is not the energetically dominant phase. Due to a breaking of the $C_4$ symmetry, the coexisting phase inherently contains admixture of the $s$-wave pairing components. As a result, the superconducting gap exhibits very non-standard features including changed nodal directions. Our results also show that in the optimally doped regime the superconducting phase is typically unstable towards developing nematicity (breaking of the $C_4$ symmetry). This has implications for the cuprate high-$T_c$ superconductors, for which in this regime the so-called intertwined orders have recently been observed. Namely, the coexisting phase may be viewed as a precursor to such more involved patterns of symmetry breaking.

cond-mat.str-el↗

arXiv2015

Gutzwiller variational wave function for multi-orbital Hubbard models in finite dimensions

We develop a diagrammatic method for the evaluation of general multi-band Gutzwiller wave functions in finite dimensions. Our approach provides a systematic improvement of the widely used Gutzwiller approximation. As a first application we investigate itinerant ferromagnetism and correlation-induced deformations of the Fermi surface for a two-band Hubbard model on a square lattice.

cond-mat.str-el↗

arXiv2015

Evaluation techniques for Gutzwiller wave functions in finite dimensions

We give a comprehensive introduction into a diagrammatic method that allows for the evaluation of Gutzwiller wave functions in finite spatial dimensions. We discuss in detail some numerical schemes that turned out to be useful in the real-space evaluation of the diagrams. The method is applied to the problem of d-wave superconductivity in a two-dimensional single-band Hubbard model. Here, we discuss in particular the role of long-range contributions in our diagrammatic expansion. We further reconsider our previous analysis on the kinetic energy gain in the superconducting state.

cond-mat.str-el↗

arXiv2014

Gutzwiller Density Functional Theory: a formal derivation and application to ferromagnetic nickel

We present a detailed derivation of the Gutzwiller Density Functional Theory that covers all conceivable cases of symmetries and Gutzwiller wave functions. The method is used in a study of ferromagnetic nickel where we calculate ground state properties (lattice constant, bulk modulus, spin magnetic moment) and the quasi-particle band structure. Our method resolves most shortcomings of an ordinary Density Functional calculation on nickel. However, the quality of the results strongly depends on the particular choice of the double-counting correction. This constitutes a serious problem for all methods that attempt to merge Density Functional Theory with correlated-electron approaches based on Hubbard-type local interactions.

cond-mat.str-el↗

arXiv2013

Even-parity spin-triplet pairing for orbitally degenerate correlated electrons by purely repulsive interactions

We demonstrate the stability of a spin-triplet paired s-wave (with an admixture of extended s-wave) state for the case of purely repulsive interactions in a degenerate two-band Hubbard model. We further show that near half-filling the considered kind of superconductivity can coexist with antiferromagnetism. The calculations have been carried out with the use of the so-called statistically consistent Gutzwiller approximation for the case of a square lattice. The absence of a stable paired state when analyzed in the Hartree-Fock-BCS approximation allows us to claim that the electron correlations in conjunction with the Hund's rule exchange play the crucial role in stabilizing the spin-triplet superconducting state. A sizable hybridization of the bands suppresses the paired state.

cond-mat.supr-con↗

arXiv2012

The Gutzwiller Density Functional Theory

In this tutorial presentation, we give a comprehensive introduction into the Gutzwiller variational approach and its merger with the density functional theory. The merits of this method are illustrated by a discussion of results for two-band Hubbard models and realistic multi-band Hamiltonians for iron-pnictide systems.

cond-mat.str-el↗

arXiv2012

Variational study of Fermi-surface deformations in Hubbard models

We study the correlation-induced deformation of Fermi surfaces by means of a new diagrammatic method which allows for the analytical evaluation of Gutzwiller wave functions in finite dimensions. In agreement with renormalization-group results we find Pomeranchuk instabilities in two-dimensional Hubbard models for sufficiently large Coulomb interactions.

cond-mat.str-el↗

arXiv2012

Numerical minimisation of Gutzwiller energy functionals

We give a comprehensive introduction into an efficient numerical scheme for the minimisation of Gutzwiller energy functionals in studies on multi-band Hubbard models. Our method covers all conceivable cases of Gutzwiller variational wave functions and has been used successfully in previous numerical studies.

cond-mat.str-el↗

arXiv2011

Gutzwiller theory of band magnetism in LaOFeAs

We use the Gutzwiller variational theory to calculate the ground-state phase diagram and quasi-particle bands of LaOFeAs. The Fe3d--As4p Wannier-orbital basis obtained from density-functional theory defines the band part of our eight-band Hubbard model. The full atomic interaction between the electrons in the iron orbitals is parameterized by the Hubbard interaction U and an average Hund's-rule interaction J. We reproduce the experimentally observed small ordered magnetic moment over a large region of (U,J) parameter space. The magnetically ordered phase is a stripe spin-density wave of quasi-particles.

cond-mat.str-el↗

arXiv2010

Antiferromagnetic order in multi-band Hubbard models for iron-pnictides

We investigate multi-band Hubbard models for the three iron 3$d$-$t_{2g}$ bands and the two iron 3$d$-$e_g$ bands in ${\rm La O Fe As}$ by means of the Gutzwiller variational theory. Our analysis of the paramagnetic ground state shows that neither Hartree--Fock mean-field theories nor effective spin models describe these systems adequately. In contrast to Hartree--Fock-type approaches, the Gutzwiller theory predicts that antiferromagnetic order requires substantial values of the local Hund's-rule exchange interaction. For the three-band model, the antiferromagnetic moment fits experimental data for a broad range of interaction parameters. However, for the more appropriate five-band model, the iron $e_g$ electrons polarize the $t_{2g}$ electrons and they substantially contribute to the ordered moment.

cond-mat.str-el↗