LECTURES ON THE PHYSICS OF HIGHLY CORRELATED ELECTRON SYSTEMS VIII: Eighth Training Course in the Physics of Correlated Electron Systems and HighTc Superconductors

Strongly Correlated Electron Materials: Dynamical Mean‐Field Theory and Electronic Structure
View Description Hide DescriptionThese are introductory lectures to some aspects of the physics of strongly correlated electron systems. I first explain the main reasons for strong correlations in several classes of materials. The basic principles of dynamical mean‐field theory (DMFT) are then briefly reviewed. I emphasize the formal analogies with classical mean‐field theory and density functional theory, through the construction of free‐energy functionals of a local observable. I review the application of DMFT to the Mott transition, and compare to recent spectroscopy and transport experiments. The key role of the quasiparticle coherence scale, and of transfers of spectral weight between low‐ and intermediate or high energies is emphasized. Above this scale, correlated metals enter an incoherent regime with unusual transport properties. The recent combinations of DMFT with electronic structure methods are also discussed, and illustrated by some applications to transition metal oxides and f‐electron materials.

Electron‐Phonon Interaction and Strong Correlations in High‐Temperature Superconductors: One can not avoid the unavoidable
View Description Hide DescriptionThe important role of the electron‐phonon interaction (EPI) in explaining the properties of the normal state and pairing mechanism in high‐T_{ c } superconductors (HTSC) is discussed. A number of experimental results are analyzed such as: dynamical conductivity, Raman scattering, neutron scattering, ARPES, tunnelling measurements, isotope effect and etc. They give convincing evidence that the EPI is strong and dominantly contributes to pairing in HTSC oxides. It is argued that strong electronic correlations in conjunction with the pronounced (in relatively weakly screened materials) EPI are unavoidable ingredients for the microscopic theory of pairing in HTSC oxides. I present the well defined and controllable theory of strong correlations and the EPI. It is shown that strong correlations give rise to the pronounced forward scattering peak in the EPI — the FSP theory. The FSP theory explains in a consistent way several (crucial) puzzles such as much smaller transport coupling constant than the pairing one (λ_{ tr } ≪ λ_{ ph }), which are present if one interprets the results in HTSC oxides by the old Migdal‐Eliashberg theory for the EPI. The ARPES non‐shift puzzle — where the nodal kink at 70 meV is unshifted in the superconducting state while the anti‐nodal one at 40 meV is shifted, can be explained at present only by the FSP theory. It predicts also: (1) a knee‐like shape of the imaginary part of the self‐energy at what has been recently confirmed in ARPES measurements; (2) that the Coulomb scattering gives very small coupling constant λ_{ C } << λ_{ ph }, which is also confirmed in ARPES spectra where λ_{ C } < 0.4 and λ_{ ph } > 1. A number of other interesting predictions of the FSP theory are also discussed.

Monte Carlo Simulations of Quantum Systems with Global Updates
View Description Hide DescriptionWe start this series of lectures on quantum Monte Carlo methods with the simplest model for a strongly correlated system, namely an antiferromagnetic Heisenberg S‐1/2 chain. We will review methods for its simulation starting with the world‐line algorithm and then introducing the loop‐algorithm with global updates. We discuss next a model for doped antiferromagnets, with emphasis on the strong correlation limit that is central for high temperature superconductors and related materials, namely the so‐called t‐J model. An exact canonical transformation for this model that leads to a formulation with separated charge and spin degrees of freedom will be discussed. Results for a single hole in antiferromagnetic chains and planes will be summarized, giving an initial picture of charge dynamics in a quantum antiferromagnet. An additional algorithmic element, namely the determinantal method, will be introduced next, in order to deal with a finite number of charge degrees of freedom. Merging the loop‐ and the determinantal methods leads to a new one, the hybrid‐loop algorithm, that combines the efficiency of the loop‐algorithm for spins with the one of the determinantal method for fermions. Finally we discuss a first application of the hybrid‐loop algorithm, where the spectral function of the t‐J model in one dimension with finite doping is determined. There we can see how charge spin separation shows up in the one‐particle spectral function, and a detailed description can be achieved by comparison with an analitically soluble model, namely the t‐J model with 1/r ^{2} interaction. The results show that in addition to spinons and holons expected in one‐dimensional metals, antiholons with charge Q = 2e, spin S = 0, and twice the mass of the holons are necessary to describe the inverse photoemission spectra at finite doping.

Beyond RPA: dynamical exchange effects and the two‐dimensional electron gas
View Description Hide DescriptionDynamic exchange interactions can be introduced in the dielectric function via a dynamic local field factor. We study the effects of this inclusion on the energy‐loss function of a two‐dimensional electron gas, using the dynamic local field factor that we derived recently via the dynamical exchange decoupling method. The results are compared with the dielectric function in the Random Phase Approximation, showing a drastic influence of the dynamic exchange interactions.

Spectral functions and their applications
View Description Hide DescriptionWe give an introduction to the heat kernel technique and ζ‐function. Two applications are considered. First we derive the high temperature asymptotics of the free energy for boson fields in terms of the heat kernel expansion and ζ‐function. Another application is chiral anomaly for local (MIT bag) boundary conditions.

Local Mott metal‐insulator transition in confined fermions on optical lattices
View Description Hide DescriptionUsing quantum Monte Carlo (QMC) simulations we study the ground state properties of the one‐dimensional fermionic Hubbard model in traps with an underlying lattice. We show that this model displays quantum critical behavior at the boundaries of the local Mott‐insulating regions. A local compressibility defined to characterize the Mott‐insulating phase has a non‐trivial critical exponent. Both the local compressibility and the variance of the local density show universality with respect to the confining potential. We study the momentum distribution function and we find that it is not appropriate to characterize the transitions in the system.

Physical properties of correlated electrons in nanochains from EDABI method
View Description Hide DescriptionWe implement the recently proposed approach combining Exact Diagonalization in the Fock space with an Ab Initio method (EDABI) to obtain a fairly complete description of correlated nanochains. In particular, the microscopic parameters are determined and the evolution of the system properties is traced in a systematic manner as a function of the interatomic distance. Both ground‐state and dynamical correlation functions are discussed within a single scheme. The principal physical results are: (i) the appearance of mixed metallic and insulating features for a one‐dimensional nanochain in the half‐filled band case, and (ii) the transformation from a highly‐conducting nanometal to the charge‐ordered nanoinsulator away from the half‐filling. The analysis is performed using the Gaussian 1s‐like basis and includes long‐range Coulomb interactions.

Electronic Raman Scattering in Density Waves
View Description Hide DescriptionWe calculate the electronic Raman spectrum of pure conventional and unconventional density waves (U)DW in the mean field approximation. The calculation is carried out in the q → 0 long wavelength limit, retaining only the quasiparticle contribution. In analogy with unconventional superconductivity, the Raman spectra depend strongly on the polarization of the incoming and scattered light, which affects the low frequency power law behavior and the peak position in the spectra, and can be used to identify which type of gap structure is present in the DW. The Coulomb screening is also considered in the RPA, and we find that it can be ignored in the long wavelength limit due to the vanishing average of the Raman vertex.