arXiv subjects

O. Gunnarsson

Publications and source records attributed to O. Gunnarsson.

At least 19 recordsLinked to original sources

arXiv2017

Complementary views on electron spectra: From Fluctuation Diagnostics to real space correlations

We study the relation between the microscopic properties of a many-body system and the electron spectra, experimentally accessible by photoemission. In a recent paper [Phys. Rev. Lett. 114, 236402 (2015)], we introduced the "fluctuation diagnostics" approach, to extract the dominant wave vector dependent bosonic fluctuations from the electronic self-energy. Here, we first reformulate the theory in terms of fermionic modes, to render its connection with resonance valence bond (RVB) fluctuations more transparent. Secondly, by using a large-U expansion, where U is the Coulomb interaction, we relate the fluctuations to real space correlations. Therefore, it becomes possible to study how electron spectra are related to charge, spin, superconductivity and RVB-like real space correlations, broadening the analysis of an earlier work [Phys. Rev. B 89, 245130 (2014)]. This formalism is applied to the pseudogap physics of the two-dimensional Hubbard model, studied in the dynamical cluster approximation. We perform calculations for embedded clusters with up to 32 sites, having three inequivalent K-points at the Fermi surface. We find that as U is increased, correlation functions gradually attain values consistent with an RVB state. This first happens for correlation functions involving the antinodal point and gradually spreads to the nodal point along the Fermi surface. Simultaneously a pseudogap opens up along the Fermi surface. We relate this to a crossover from a Kondo-like state to an RVB-like localized cluster state and to the presence of RVB and spin fluctuations. These changes are caused by a strong momentum dependence in the cluster bath-couplings along the Fermi surface. We also show, from a more algorithmic perspective, how the time-consuming calculations in fluctuation diagnostics can be drastically simplified.

cond-mat.str-el↗

arXiv2017

Breakdown of traditional many-body theories for correlated electrons

Starting from the (Hubbard) model of an atom, we demonstrate that the uniqueness of the mapping from the interacting to the noninteracting Green's function, $G\to G_0$, is strongly violated, by providing numerous explicit examples of different $G_0$ leading to the same physical $G$. We argue that there are indeed infinitely many such $G_0$, with numerous crossings with the physical solution. We show that this rich functional structure is directly related to the divergence of certain classes of (irreducible vertex) diagrams, with important consequences for traditional many-body physics based on diagrammatic expansions. Physically, we ascribe the onset of these highly non-perturbative manifestations to the progressive suppression of the charge susceptibility induced by the formation of local magnetic moments and/or RVB states in strongly correlated electron systems.

cond-mat.str-el↗

arXiv2016

Non-perturbative landscape of the Mott-Hubbard transition: Multiple divergence lines around the critical endpoint

We analyze the highly non-perturbative regime surrounding the Mott-Hubbard metal-to-insulator transition (MIT) by means of dynamical mean field theory calculations at the two-particle level. By extending the results of Schäfer, et al. [Phys. Rev. Lett. 110, 246405 (2013)] we show the existence of infinitely many lines in the phase diagram of the Hubbard model where the local Bethe-Salpeter equations, and the related irreducible vertex functions, become singular in the charge as well as the particle-particle channel. These divergence lines accumulate around the critical Mott endpoint in accordance with the interpretation as precursors of the MIT. By comparing our numerical data with analytical calculations of increasing complexity, such as for the disordered Binary Mixture and Falicov-Kimball (FK) models, as well as for the atomic limit (AL) case, (i) we identify two different kinds of divergences lines; (ii) we classify them in terms of the frequency-structure of the associated singular eigenvectors; (iii) we investigate their relation to the multiple branches in the Luttinger-Ward formalism. Moreover, we could distinguish the situations where the multiple divergences simply reflect the emergence of an underlying, unique energy scale $ν^*$ below which perturbation theory does no longer apply, from those where the breakdown of perturbation theory affects, not trivially, different energy regimes. Finally, we discuss the implications of our results on the theoretical understanding of the non-perturbative physics around the MIT and for future developments of many-body algorithms applicable in this regime.

cond-mat.str-el↗

arXiv2016

Parquet decomposition calculations of the electronic self-energy

The parquet decomposition of the self-energy into classes of diagrams, those associated with specific scattering processes, can be exploited for different scopes. In this work, the parquet decomposition is used to unravel the underlying physics of non-perturbative numerical calculations. We show the specific example of dynamical mean field theory (DMFT) and its cluster extensions (DCA) applied to the Hubbard model at half-filling and with hole doping: These techniques allow for a simultaneous determination of two-particle vertex functions and self-energies, and hence, for an essentially "exact" parquet decomposition at the single-site or at the cluster level. Our calculations show that the self-energies in the underdoped regime are dominated by spin scattering processes, consistent with the conclusions obtained by means of the fluctuation diagnostics approach [Phys. Rev. Lett. 114, 236402 (2015)]. However, differently from the latter approach, the parquet procedure displays important changes with increasing interaction: Even for relatively moderate couplings, well before the Mott transition, singularities appear in different terms, with the notable exception of the predominant spin-channel. We explain precisely how these singularities, which partly limit the utility of the parquet decomposition, and - more generally - of parquet-based algorithms, are never found in the fluctuation diagnostics procedure. Finally, by a more refined analysis, we link the occurrence of the parquet singularities in our calculations to a progressive suppression of charge fluctuations and the formation of an RVB state, which are typical hallmarks of a pseudogap state in DCA.

cond-mat.str-el↗

arXiv2015

Self-energy enhancements in doped Mott insulators

We analyze enhancements in the magnitude of the self-energy for electrons far away from the Fermi surface in doped Mott insulators using the dynamical cluster approximation to the Hubbard model. For large onsite repulsion, U, and hole doping, the magnitude of the self-energy for imaginary frequencies at the top of the band (k=(pi,pi) is enhanced with respect to the self-energy magnitude at the bottom of the band (k=(0,0)). The self-energy behavior at these two k-points is switched for electron doping. Although the hybridization is much larger for (0,0) than for (pi,pi), we demonstrate that this is not the origin of this difference. Isolated clusters under a downward shift of the chemical potential, mu<U/2, at half-filling reproduce the overall self-energy behavior at (0,0) and (pi,pi) found in low hole doped embedded clusters. This happens although there is no change in the electronic structure of the isolated clusters. Our analysis shows that a downward shift of the chemical potential which weakly hole dopes the Mott insulator can lead to a large enhancement of the (pi,pi) self-energy which is not necessarily associated with electronic correlation effects, even in embedded clusters.

cond-mat.str-el↗

arXiv2014

Fluctuation diagnostics of the electron self-energy: Origin of the pseudogap physics

We demonstrate how to identify which physical processes dominate the low-energy spectral functions of correlated electron systems. We obtain an unambiguous classification through an analysis of the equation of motion for the electron self-energy in its charge, spin and particle-particle representations. Our procedure is then employed to clarify the controversial physics responsible for the appearance of the pseudogap in correlated systems. We illustrate our method by examining the attractive and repulsive Hubbard model in two-dimensions. In the latter, spin fluctuations are identified as the origin of the pseudogap, and we also explain why $d-$wave pairing fluctuations play a marginal role in suppressing the low-energy spectral weight, independent of their actual strength.

cond-mat.str-el↗

arXiv2014

Efficient real frequency solver for dynamical mean field theory

We here present how a self-consistent solution of the dynamical mean field theory equations can be obtained using exact diagonalization of an Anderson impurity model with accuracies comparable to those found using renormalization group or quantum Monte Carlo methods. We show how one can solve a correlated quantum impurity coupled to several hundred uncorrelated bath sites, using a restricted active basis set. The number of bath sites determines the resolution of the obtained spectral function, which consists of peaks roughly spaced by the band width divided by the number of bath sites. The self-consistency cycles are fully performed on the real frequency axis and expressed as numerical stable matrix operations. The same impurity solver has been used on Ligand Field and finite size cluster calculations and is capable of treating involved Hamiltonians including the full rotational invariant Coulomb interaction, spin-orbit coupling and low symmetry crystal-fields. The proposed method allows for the calculation of a variety of correlation functions at little extra cost.

cond-mat.str-el↗

arXiv2013

Pseudogap and singlet formation in cuprate and organic superconductors

The pseudogap phase occurring in cuprate and organic superconductors is analyzed based on the dynamical cluster approximation (DCA) approach to the Hubbard model. A cluster embedded in a self-consistent bath is studied. With increasing Coulomb repulsion, U, the antinodal point [k=(pi,0)] displays a gradual suppression of spectral density of states around the Fermi energy which is not observed at the nodal point [k=(pi/2,pi/2)]. The opening of the antinodal pseudogap is related to the internal structure of the cluster and the much weaker bath-cluster couplings at the antinodal than nodal point. The role played by internal cluster correlations is elucidated from a simple four-level model. For small U, the cluster levels form Kondo singlets with their baths leading to a peak in the spectral density. As U is increased a localized state is formed localizing the electrons in the cluster. If this cluster localized state is non-degenerate, the Kondo effect is destroyed and a pseudogap opens up in the spectra at the anti-nodal point. The pseudogap can be understood in terms of destructive interference between different paths for electrons hopping between the cluster and the bath. However, electrons at the nodal points remain in Kondo states up to larger U since they are more strongly coupled to the bath. The strong correlation between the (pi,0) and (0,pi) cluster levels in the localized state leads to a large correlation energy gain which is important for localizing electrons and opening up a pseudogap. Such scenario is in contrast with two independent Mott transitions found in two-band systems with different bandwidths in which the localized cluster electron does not correlate strongly with any other cluster electron for intermediate U. The important intracluster sector correlations are associated with the resonating valence bond (RVB) character of the cluster.

cond-mat.str-el↗

arXiv2013

Divergent Precursors of the Mott-Hubbard Transition at the Two-Particle Level

Identifying the fingerprints of the Mott-Hubbard metal-insulator transition may be quite elusive in correlated metallic systems if the analysis is limited to the single particle level. However, our dynamical mean-field calculations demonstrate that the situation changes completely if the frequency dependence of the two-particle vertex functions is considered: The first non-perturbative precursors of the Mott physics are unambiguously identified well inside the metallic regime by the divergence of the local Bethe-Salpeter equation in the charge channel. At low temperatures this occurs in the region where incoherent high-energy features emerge in the spectral function, while at high temperatures it is traceable up to the atomic-limit.

cond-mat.str-el↗

arXiv2012

Pseudogap in cuprate and organic superconductors

We study the pseudogap present in cuprate and organic superconductors. We use the dynamical cluster approximation (DCA), treating a cluster embedded in a bath. As the Coulomb interaction is increased, cluster-bath Kondo states are destroyed and bound cluster states formed. We show that this leads to a pseudogap. Due to weaker coupling to the bath for the anti-nodal point, this happens first for this point, explaining the k-dependence of the pseudogap. The pseudogap can be understood in terms of preformed d-wave pairs, but it does not prove the existence of such pairs.

cond-mat.str-el↗

arXiv2011

Isotope effect in the pseudogap of high-temperature superconducting copper oxides

We study cuprates within Dynamical Cluster Approximation and find the pseudogap displays an isotope effect of the same sign as observed experimentally. Notwithstanding the non-phononic origin of the pseudogap the interplay between electronic repulsion and retarded phonon-mediated attraction gives rise to an isotope dependence of the antinodal spectra. Due to the strong momentum differentiation, such interplay is highly non-trivial and leads to the simultaneous presence of heavier quasiparticles along the nodal direction. We predict an isotope effect in electron-doped materials.

cond-mat.str-el↗

arXiv2010

Analytical continuation of imaginary axis data for optical conductivity

We compare different methods for performing analytical continuation of spectral data from the imaginary time or frequency axis to the real frequency axis for the optical conductivity sigma(omega). We compare the maximum entropy (MaxEnt), singular value decomposition (SVD), sampling and Pade methods for analytical continuation. We also study two direct methods for obtaining sigma(0). For the MaxEnt approach we focus on a recent modification. The data are split up in batches, a separate MaxEnt calculation is done for each batch and the results are averaged. For the problems studied here, we find that typically the SVD, sampling and modified MaxEnt methods give comparable accuracy, while the Pade approximation is usually less reliable.

cond-mat.str-el↗

arXiv2010

Fourier transformation and response functions

We improve on Fourier transforms (FT) between imaginary time $τ$ and imaginary frequency $ω_n$ used in certain quantum cluster approaches using the Hirsch-Fye method. The asymptotic behavior of the electron Green's function can be improved by using a "sumrule" boundary condition for a spline. For response functions a two-dimensional FT of a singular function is required. We show how this can be done efficiently by splitting off a one-dimensional part containing the singularity and by performing a semi-analytical FT for the remaining more innocent two-dimensional part.

cond-mat.str-el↗

arXiv2010

Analytical continuation of imaginary axis data using maximum entropy

We study the maximum entropy (MaxEnt) approach for analytical continuation of spectral data from imaginary times to real frequencies. The total error is divided in a statistical error, due to the noise in the input data, and a systematic error, due to deviations of the default function, used in the MaxEnt approach, from the exact spectrum. We find that the MaxEnt approach in its classical formulation can lead to a nonoptimal balance between the two types of errors, leading to an unnecessary large statistical error. The statistical error can be reduced by splitting up the data in several batches, performing a MaxEnt calculation for each batch and averaging. This can outweigh an increase in the systematic error resulting from this approach. The output from the MaxEnt result can be used as a default function for a new MaxEnt calculation. Such iterations often lead to worse results due to an increase in the statistical error. By splitting up the data in batches, the statistical error is reduced and and the increase resulting from iterations can be outweighed by a decrease in the systematic error. Finally we consider a linearized version to obtain a better understanding of the method.

physics.data-an↗

arXiv2007

Interplay between electron-phonon and Coulomb interactions in cuprates

Evidence for strong electron-phonon coupling in high-Tc cuprates is reviewed, with emphasis on the electron and phonon spectral functions. Effects due to the interplay between the Coulomb and electron-phonon interactions are studied. For weakly doped cuprates, the phonon self-energy is strongly reduced due to correlation effects, while there is no corresponding strong reduction for the electron self-energy. Polaron formation is studied, focusing on effects of Coulomb interaction and antiferromagnetic correlations. It is argued that experimental indications of polaron formation in undoped cuprates are due to a strong electron-phonon interaction for these systems.

cond-mat.str-el↗

arXiv2007

Comment on ``Collapse of Coherent Quasiparticle States in $θ$-(BEDT-TTF)$_2$I$_3$ Observed by Optical Spectroscopy''

Recently, Takenaka et al. reported that the resistivity rho(T) of theta-(BEDT-TTF)_2I_3 (theta-ET) exceeds the Ioffe-Regel resistivity by a factor of 50 at large temperatures T (``bad metal''). This was ascribed to strong correlation. We argue that the optical conductivity sigma(omega) implies that correlation is not very strong, and that correlation gives no general strong suppression of sigma(omega). The large rho(T) is primarily due to a downturn in sigma(omega) at small omega, earlier emphasized by Takenaka et al. as the explanation for bad metal behavior of high-T_c cuprates. We argue, however, that for cuprates strong correlation is the main effect. The data of Takenaka et al. puts theta-ET in a new class of bad metals.

cond-mat.mtrl-sci↗

arXiv2006

Electronic thermal conductivity at high temperatures: Violation of the Wiedemann-Franz law in narrow band metals

We study the electronic part of the thermal conductivity kappa of metals. We present two methods for calculating kappa, a quantum Monte-Carlo (QMC) method and a method where the phonons but not the electrons are treated semiclassically (SC). We compare the two methods for a model of alkali-doped C60, A3C60, and show that they agree well. We then mainly use the SC method, which is simpler and easier to interpret. We perform SC calculations for Nb for large temperatures T and find that kappa increases with T as kappa(T)=a+bT, where a and b are constants, consistent with a saturation of the mean free path, l, and in good agreement with experiment. In contrast, we find that for A3C60, kappa(T) decreases with T for very large T. We discuss the reason for this qualitatively in the limit of large T. We give a quantum-mechanical explanation of the saturation of l for Nb and derive the Wiedemann-Franz law in the limit of T much smaller than W, where W is the band width. In contrast, due to the small W of A3C60, the assumption T much smaller than W can be violated. We show that this leads to kappa(T) \sim T^{-3/2} for very large T and a strong violation of the Wiedemann-Franz law.

cond-mat.mtrl-sci↗

arXiv2006

Sum rules and vertex corrections for electron-phonon interactions

We derive sum rules for the phonon self-energy and the electron-phonon contribution to the electron self-energy of the Holstein-Hubbard model in the limit of large Coulomb interaction U. Their relevance for finite U is investigated using exact diagonalization and dynamical mean-field theory. Based on these sum rules, we study the importance of vertex corrections to the electron-phonon interactionin a diagrammatic approach. We show that they are crucial for a sum rule for the electron self-energy in the undoped system while a sum rule related to the phonon self-energy of doped systems is satisfied even if vertex corrections are neglected. We provide explicit results for the vertex function of a two-site model.

cond-mat.str-el↗