intro
Emergent phenomena
Paradigmatic cases
Antiferromagnetism
Superconductivity
Overview of the school
jones
Introduction
The density as basic variable
An "approximate practical method"
Density functional formalism
Single-particle description of a many-electron system.
Exchange-correlation energy and the xc-hole
DF theory to 1990
Condensed matter
Chemistry
Progress to 1990
After the breakthrough
Progress and problems
An application
Summary and outlook
koch
Indistinguishable particles
Symmetric and antisymmetric wave functions
Reduced density matrices
Slater determinants
Hartree-Fock
Second quantization
Creation and annihilation operators
Representation of Slater determinants
Representation of n-body operators
Vacuum state and electron-hole transformation
Many-body states
Hubbard model
BCS state
Conclusions
pavarini
Magnetism in strongly-correlated systems
The Hubbard model
Itinerant magnetism
Isolated magnetic ions
Interacting localized moments
The Kondo model
Formalism
Matsubara Green functions
Linear response theory
Magnetic susceptibility
eder
Introduction
Notation and brief review of field theory
Proof of the theorem by Luttinger and Ward
Statement of the theorem
The case of no interactions
Calculation of the derivative of the grand potential
Definition and properties of the Luttinger-Ward functional
Calculation of the Luttinger-Ward potential
The variational cluster approximation
Applications of the VCA
Metal-insulator transition in a dimer
Photoemission spectra of NiO, CoO and MnO
Summary
Appendix: A theorem on determinants
lichtenstein
Introduction
From Stoner to Hubbard
From LDA to DMFT
Realistic DMFT scheme
Solution of quantum impurity problem
Hirsch-Fye quantum Monte Carlo
Continuous-time quantum Monte Carlo
Fluctuation exchange approximation
Effective magnetic interactions in LDA+DMFT
LDA+DMFT results for itinerant ferromagnetic metals
Conclusions
krauth
Introduction
Markov chains and incompressible flow
A priori probabilities
Local algorithm, faster-than-the-clock algorithms
Cluster algorithms
Coupling approach
wessel
Introduction
World lines and local updates
Suzuki-Trotter decomposition
World lines
Local updates
The continuous-time limit
Stochastic series expansion
Configuration space
Observables
Local updates
The loop algorithm
Worms, operator loops, and directed loops
The sign problem
Quantum Heisenberg Model 101
schnack
Introduction
Substances
Theoretical techniques and results
Hamiltonian
Evaluating the spectrum
Evaluation of thermodynamic observables
General properties of spectra
Magnetocalorics
keimer
Introduction
Magnetic order
Charge order
Spin fluctuations
Spin-fluctuation-mediated superconductivity
Challenges for theory
Outlook
tremblay
Introduction
The Hubbard model
Weakly and strongly correlated antiferromagnets
Antiferromagnets: A qualitative discussion
Contrasting methods for weak and strong coupling antiferromagnets and their normal state
Weakly and strongly correlated superconductivity
Superconductors: A qualitative discussion
Contrasting methods for weakly and strongly correlated superconductors
High-temperature superconductors and organics: the view from dynamical mean-field theory
Quantum cluster approaches
Normal state and pseudogap
Superconducting state
Conclusion
pickett
Overview: Why this topic? What kinds of correlated states?
Very basic theoretical background
Weak coupling
Strong coupling
Doped 2D ionic insulators: general aspects
A broad view of the theoretical challenge
Density of states ; generalized susceptibility
Electronic screening by a sparse electron gas
Dynamics of the coupled ion-electron system
Electron-phonon coupling in 2D HTS metal MgB2 class
The surprise of MgB2
Superconductor design: attempts within the MgB2 class
Doped 2D ionic insulators: examples
Transition metal nitridochlorides HfNCl and ZrNCl
The TiNCl sister compound
Overview of the transition metal nitridohalides
Related classes of materials
Transition metal dichalcogenides and oxides: a class, or individuals?
LixNbO2: a triangular lattice, single band correlated superconductor
NaxCoO2
Doped transition metal dichalcogenides; recently CuxTiSe2
NaAlSi: unusual self-doped semimetallic superconductor
Doped hydrocarbons: organic crystals
Summary of main points
heid
Introduction
Electron-ion Hamiltonian and adiabatic approximation
Phenomenological theory of lattice dynamics
Density functional perturbation theory
Lattice dynamics from first principles
Linear response formulation
Phonons in periodic lattices
Electron phonon coupling
Density functional perturbation approach to electron phonon vertex
Phonon self-energy and linewidth
Phonon mediated pairing interaction and superconductivity
Electron self-energy effects
Summary
ummarino
Introduction
Imaginary-axis Eliashberg equations
Nambu formalism
Migdal-Eliashberg theory
Coulomb pseudopotential
Real-axis Eliashberg equations
Simplified approaches
BCS limit
Critical temperature
Relation between real- and imaginary-axis formulation
Padé method for analytic continuation
Marsiglio, Schossmann, and Carbotte formulation
Tunneling inversion of the standard Eliashberg equations
Approximations of the standard Eliashberg equations
Cuprate high-temperature superconductors
Multi-band Eliashberg theory
Iron pnictide superconductors
Gaps, critical temperature, and upper critical magnetic field
Interaction mechanism
Conclusion
ceperley
The path integral formalism
Quantum statistics with path integrals
Bosons
Fermions
Restricted path integral method
Exchange of localized particles
PIMC calculations of supersolid helium
Lexicon of the quantum-classical isomorphism
zhang
Introduction
Formalism
Ground-state projection
Slater determinant space
Hubbard-Stratonovich transformation
A simple example
Ground-State AFQMC Methods
Free-projection AFQMC
Why and how does the sign problem occur?
The constrained path Monte Carlo method
The phaseless formalism for complex auxiliary-fields
Illustrative results
Concluding remarks
Acknowledgments
A few basics of Monte Carlo techniques
schollwoeck
DMRG: A young adult
Matrix product states
Matrix product operators
Normalization and compression
Time-evolution: tDMRG, TEBD, tMPS
Overlaps and expectation values
Finite-temperature simulations
Ground states with MPS: DMRG
Constructing the MPO representation of a Hamiltonian
Dynamical DMRG
Outlook: DMRG in two dimensions
eisert
Correlations and entanglement in quantum many-body systems
Quantum many-body systems
Clustering of correlations
Entanglement in ground states and area laws
The notion of the `physical corner of Hilbert space'
Matrix product states
Preliminaries
Definitions and preparations of matrix product states
Computation of expectation values and numerical techniques
Parent Hamiltonians, gauge freedom, geometry, and symmetries
Tools in quantum information theory and quantum state tomography
Higher-dimensional tensor network states
Higher-dimensional projected entangled pair states
Multi-scale entanglement renormalization
Fermionic and continuum models
Fermionic models
Continuum models
index
Blank Page

lgli/Pavarini E., Koch E. (eds.) Autumn School on Correlated Electrons 2013. Emergent Phenomena in Correlated Matter (Juelich, 2013)(ISBN 9783893368846)(O)(562s)_PS_.pdf

lgrsnf/Pavarini E., Koch E. (eds.) Autumn School on Correlated Electrons 2013. Emergent Phenomena in Correlated Matter (Juelich, 2013)(ISBN 9783893368846)(O)(562s)_PS_.pdf

zlib/Physics/Quantum Physics/Eva Pavarini, Erik Koch, Ulrich Schollwöck/Emergent Phenomena in Correlated Matter_25041129.pdf

Emergent phenomena in correlated matter lecture notes of the Autumn School Correlated Electrons 2013, at Forschungszentrum Jülich, 23 - 27 September 2013

Eva Pavarini; Erik Koch; Ulrich Schollwöck; Institute for Advanced Simulation; Autumn School Correlated Electrons

Forschungszentrum Jülich, Inst. for Advanced Simulation

Schriften des Forschungszentrums Jülich, Jülich, 2013

Germany, Germany

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2023-05-10