Interacting electrons : theory and computational approaches /

Interacting electrons : theory and computational approaches /

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Bibliographic Details
Author / Creator:Martin, Richard M., 1942- author.
Imprint:New York, NY : Cambridge University Press, 2016.
Description:xiv, 818 pages : illustrations ; 26 cm
Language:English
Subject:
Electronic structure.
Electrons.
Many-body problem.
Perturbation (Quantum dynamics)
Quantum theory.
Monte Carlo method.
Electronic structure.
Electrons.
Many-body problem.
Monte Carlo method.
Perturbation (Quantum dynamics)
Quantum theory.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/11028161
Hidden Bibliographic Details
Other authors / contributors:Reining, Lucia, author.
Ceperley, David, author.
ISBN:9780521871501
0521871506
Notes:Includes bibliographical references and index.
Summary:"Recent progress in the theory and computation of electronic structure is bringing an unprecedented level of capability for research. Many-body methods are becoming essential tools vital for quantitative calculations and understanding materials phenomena in physics, chemistry, materials science and other fields. This book provides a unified exposition of the most-used tools: many-body perturbation theory, dynamical mean field theory and quantum Monte Carlo simulations. Each topic is introduced with a less technical overview for a broad readership, followed by in-depth descriptions and mathematical formulation"--

MARC

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100 1 |a Martin, Richard M.,  |d 1942-  |e author.  |0 http://id.loc.gov/authorities/names/n2003007158  |1 http://viaf.org/viaf/26435197 
245 1 0 |a Interacting electrons :  |b theory and computational approaches /  |c Richard M. Martin, University of Illinois, Urbana-Champaign, Lucia Reining, Ecole Polytechnique, Palaiseau, David M. Ceperley, University of Illinois, Urbana-Champaign. 
264 1 |a New York, NY :  |b Cambridge University Press,  |c 2016. 
300 |a xiv, 818 pages :  |b illustrations ;  |c 26 cm 
336 |a text  |b txt  |2 rdacontent  |0 http://id.loc.gov/vocabulary/contentTypes/txt 
337 |a unmediated  |b n  |2 rdamedia  |0 http://id.loc.gov/vocabulary/mediaTypes/n 
338 |a volume  |b nc  |2 rdacarrier  |0 http://id.loc.gov/vocabulary/carriers/nc 
520 |a "Recent progress in the theory and computation of electronic structure is bringing an unprecedented level of capability for research. Many-body methods are becoming essential tools vital for quantitative calculations and understanding materials phenomena in physics, chemistry, materials science and other fields. This book provides a unified exposition of the most-used tools: many-body perturbation theory, dynamical mean field theory and quantum Monte Carlo simulations. Each topic is introduced with a less technical overview for a broad readership, followed by in-depth descriptions and mathematical formulation"--  |c Provided by publisher. 
504 |a Includes bibliographical references and index. 
505 0 0 |a Machine generated contents note:  |g 1.  |t The many-electron problem: introduction --  |t Summary --  |g 1.1.  |t The electronic structure problem --  |g 1.2.  |t Why is this problem hard? --  |g 1.3.  |t Why is the independent-electron picture so successful? --  |g 1.4.  |t Development of theoretical approaches to the many-body problem --  |g 1.5.  |t The many-body problem and computation --  |g 1.6.  |t The scope of this book --  |t Select Further Reading --  |g 2.  |t Signatures of electron correlation --  |t Summary --  |g 2.1.  |t What is meant by correlation? --  |g 2.2.  |t Ground-state and thermodynamic properties --  |g 2.3.  |t Magnetism and local moments --  |g 2.4.  |t Electron addition and removal: the bandgap problem and more --  |g 2.5.  |t Satellites and sidebands --  |g 2.6.  |t Particle-hole and collective excitations --  |g 2.7.  |t The Kondo effect and heavy fermions --  |g 2.8.  |t Mott insulators and metal-insulator transitions --  |g 2.9.  |t Lower dimensions: stronger interaction effects --  |g 2.10.  |t Wrap-up --  |g 3.  |t Concepts and models for interacting electrons --  |t Summary --  |g 3.1.  |t The Wigner transition and the homogeneous electron system --  |g 3.2.  |t The Mott transition and the Hubbard model --  |g 3.3.  |t Magnetism and spin models --  |g 3.4.  |t Normal metals and Fermi liquid theory --  |g 3.5.  |t The Kondo effect and the Anderson impurity model --  |g 3.6.  |t The Luttinger theorem and the Friedel sum rule --  |t Select Further Reading --  |t Exercises --  |g 4.  |t Mean fields and auxiliary systems --  |t Summary --  |g 4.1.  |t The Hartree and Hartree-Fock approximations --  |g 4.2.  |t Weiss mean field and the Curie-Weiss approximation --  |g 4.3.  |t Density functional theory and the Kohn-Sham auxiliary system --  |g 4.4.  |t The Kohn-Sham electronic structure --  |g 4.5.  |t Extensions of the Kohn-Sham approach --  |g 4.6.  |t Time-dependent density and current density functional theory --  |g 4.7.  |t Symmetry breaking in mean-field approximations and beyond --  |g 4.8.  |t Wrap-up --  |t Select Further Reading --  |t Exercises --  |g 5.  |t Correlation functions --  |t Summary --  |g 5.1.  |t Expectation values and correlation functions --  |g 5.2.  |t Static one-electron properties --  |g 5.3.  |t Static two-particle correlations: density correlations and the structure factor --  |g 5.4.  |t Dynamic correlation functions --  |g 5.5.  |t Response functions --  |g 5.6.  |t The one-particle Green's function --  |g 5.7.  |t Useful quantities derived from the one-particle Green's function --  |g 5.8.  |t Two-particle Green's functions --  |t Select Further Reading --  |t Exercises --  |g 6.  |t Many-body wavefunctions --  |t Summary --  |g 6.1.  |t Properties of the many-body wavefunction --  |g 6.2.  |t Boundary conditions --  |g 6.3.  |t The ground-state wavefunction of insulators --  |g 6.4.  |t Correlation in two-electron systems --  |g 6.5.  |t Trial function local energy, Feynman-Kac formula, and wavefunction quality --  |g 6.6.  |t The pair product or Slater-Jastrow wavefunction --  |g 6.7.  |t Beyond Slater determinants --  |t Exercises --  |g 7.  |t Particles and quasi-particles --  |t Summary --  |g 7.1.  |t Dynamical equations and Green's functions for coupled systems --  |g 7.2.  |t The self-energy and the Dyson equation --  |g 7.3.  |t Illustration: a single state coupled to a continuum --  |g 7.4.  |t Interacting systems: the self-energy and spectral function --  |g 7.5.  |t Quasi-particles --  |g 7.6.  |t Quasi-particle equations --  |g 7.7.  |t Separating different contributions to a Dyson equation --  |g 7.8.  |t Wrap-up --  |t Select Further Reading --  |t Exercises --  |g 8.  |t Functionals in many-particle physics --  |t Summary --  |g 8.1.  |t Density functional theory and the Hartree-Fock approximation --  |g 8.2.  |t Functionals of the Green's function G and self-energy E --  |g 8.3.  |t Functionals of the screened interaction W --  |g 8.4.  |t Generating functionals --  |g 8.5.  |t Conservation laws and conserving approximations --  |g 8.6.  |t Wrap-up --  |t Select Further Reading --  |t Exercises --  |g 9.  |t Many-body perturbation theory: expansion in the interaction --  |t Summary --  |g 9.1.  |t The Coulomb interaction and perturbation theory --  |g 9.2.  |t Connecting the interacting and non-interacting systems --  |g 9.3.  |t Telling the story of particles: diagrams --  |g 9.4.  |t Making the story easier: two theorems --  |g 9.5.  |t Dyson equation for the one-particle Green's function, and the self-energy --  |g 9.6.  |t Diagrammatic expansion at non-vanishing temperature --  |g 9.7.  |t Self-consistent perturbation theory: from bare to dressed building blocks --  |g 9.8.  |t The Luttinger-Ward functional --  |g 9.9.  |t Wrap-up --  |t Select Further Reading --  |t Exercises --  |g 10.  |t Many-body perturbation theory via functional derivatives --  |t Summary --  |g 10.1.  |t The equation of motion --  |g 10.2.  |t The functional derivative approach --  |g 10.3.  |t Dyson equations --  |g 10.4.  |t Conservation laws --  |g 10.5.  |t A starting point for approximations --  |g 10.6.  |t Wrap-up --  |t Select Further Reading --  |t Exercises --  |g 11.  |t The RPA and the GW approximation for the self-energy --  |t Summary --  |g 11.1.  |t Hedin's equations --  |g 11.2.  |t Neglecting vertex corrections in the polarizability: the RPA --  |g 11.3.  |t Neglecting vertex corrections in the self-energy: the GW approximation --  |g 11.4.  |t Link between the GWA and static mean-field approaches --  |g 11.5.  |t Ground-state properties from the GWA --  |g 11.6.  |t The GWA in the homogeneous electron gas --  |g 11.7.  |t The GWA in small model systems --  |g 11.8.  |t Wrap-up --  |t Select Further Reading --  |t Exercises --  |g 12.  |t GWA calculations in practice --  |t Summary --  |g 12.1.  |t The task: a summary --  |g 12.2.  |t Frequently used approximations --  |g 12.3.  |t Core and valence --  |g 12.4.  |t Different levels of self-consistency --  |g 12.5.  |t Frequency integrations --  |g 12.6.  |t GW calculations in a basis --  |g 12.7.  |t Scaling and convergence --  |g 12.8.  |t Wrap-up --  |t Select Further Reading --  |t Exercises --  |g 13.  |t GWA calculations: illustrative results --  |t Summary --  |g 13.1.  |t From the HEG to a real semiconductor: silicon as a prototype system --  |g 13.2.  |t Materials properties in the GWA: an overview --  |g 13.3.  |t Energy levels in finite and low-dimensional systems --  |g 13.4.  |t Transition metals and their oxides --  |g 13.5.  |t GW results for the ground state --  |g 13.6.  |t A comment on temperature --  |g 13.7.  |t Wrap-up --  |t Select Further Reading --  |t Exercises --  |g 14.  |t RPA and beyond: the Bethe-Salpeter equation --  |t Summary --  |g 14.1.  |t The two-particle correlation function and measurable quantities --  |g 14.2.  |t The two-particle correlation function: basic relations --  |g 14.3.  |t The RPA: what can it yield? --  |g 14.4.  |t Beyond the RPA: spin and frequency structure of the BSE --  |g 14.5.  |t The Bethe-Salpeter equation in the GW approximation --  |g 14.6.  |t A two-body Schrödinger equation --  |g 14.7.  |t Importance and analysis of electron-hole interaction effects --  |g 14.8.  |t Bethe-Salpeter calculations in practice --  |g 14.9.  |t Applications --  |g 14.10.  |t Extensions --  |g 14.11.  |t Linear response using Green's functions or density functionals --  |g 14.12.  |t Wrap-up --  |t Select Further Reading --  |t Exercises --  |g 15.  |t Beyond the GW approximation --  |t Summary --  |g 15.1.  |t The need to go beyond GW: analysis and observations --  |g 15.2.  |t Iterating Hedin's equations --  |g 15.3.  |t Effects of vertex corrections --  |g 15.4.  |t The T-matrix and related approximations --  |g 15.5.  |t Beyond the T-matrix approximation: combining channels --  |g 15.6.  |t T-matrix and related approaches in practice --  |g 15.7.  |t Cumulants in electron spectroscopy --  |g 15.8.  |t Use of exact constraints --  |g 15.9.  |t Retrospective and outlook --  |t Select Further Reading --  |t Exercises --  |g 16.  |t Dynamical mean-field theory --  |t Summary --  |g 16.1.  |t Auxiliary systems and embedding in Green's function methods --  |g 16.2.  |t Overview of DMFT --  |g 16.3.  |t Expansion around an atomic limit: low energy scales and strong temperature dependence --  |g 16.4.  |t Background for mean-field theories and auxiliary systems --  |g 16.5.  |t Dynamical mean-field equations --  |g 16.6.  |t Self-energy functional and variational equations --  |g 16.7.  |t Static properties and density matrix embedding --  |g 16.8.  |t Single-site DMFA in a two-site model --  |g 16.9.  |t The Mott transition in infinite dimensions --  |g 16.10.  |t Hybridized bands and consequences for the Mott transition --  |g 16.11.  |t Interacting bands and spin transitions --  |g 16.12.  |t Wrap-up --  |t Select Further Reading --  |t Exercises 
505 0 0 |g  --  |g 17.  |t Beyond the single-site approximation in DMFT --  |t Summary --  |g 17.1.  |t Supercells and clusters --  |g 17.2.  |t Cellular DMFA --  |g 17.3.  |t Dynamic cluster approximation --  |g 17.4.  |t Variational cluster and nested cluster approximations --  |g 17.5.  |t Extended DMFT and auxiliary bosons --  |g 17.6.  |t Results for Hubbard models in one, two, and three dimensions --  |g 17.7.  |t Wrap-up --  |t Select Further Reading --  |t Exercises --  |g 18.  |t Solvers for embedded systems --  |t Summary --  |g 18.1.  |t The problem(s) to be solved --  |g 18.2.  |t Exact diagonalization and related methods --  |g 18.3.  |t Path-integral formulation in terms of the action --  |g 18.4.  |t Auxiliary-field methods and the Hirsch-Fye algorithm --  |g 18.5.  |t CTQMC: expansion in the interaction --  |g 18.6.  |t CTQMC: expansion in the hybridization --  |g 18.7.  |t Dynamical interactions in CTQMC --  |g 18.8.  |t Other methods --  |g 18.9.  |t Wrap-up --  |t Select Further Reading --  |t Exercises --  |g 19.  |t Characteristic hamiltonians for solids with d and f states --  |t Summary --  |g 19.1.  |t Transition elements: atomic-like behavior and local moments --  |g 19.2.  |t Hamiltonian in a localized basis: crystal fields, bands, Mott-Hubbard vs. charge transfer --  |g 19.3.  |t Effective interaction hamiltonian --  |g 19.4.  |t Identification of localized orbitals --  |g 19.5.  |t Combining DMFT and DFT --  |g 19.6.  |t Static mean-field approximations: DFT+U, etc. --  |g 19.7.  |t Wrap-up --  |t Select Further Reading --  |t Exercises --  |g 20.  |t Examples of calculations for solids with d and f states --  |t Summary --  |g 20.1.  |t Kondo effect in realistic multi-orbital problems --  |g 20.2.  |t Lanthanides -- magnetism, volume collapse, heavy fermions, mixed valence, etc. --  |g 20.3.  |t Actinides -- transition from band to localized --  |g 20.4.  |t Transition metals -- local moments and ferromagnetism: Fe and Ni 
650 0 |a Electronic structure.  |0 http://id.loc.gov/authorities/subjects/sh85042372 
650 0 |a Electrons.  |0 http://id.loc.gov/authorities/subjects/sh85042423 
650 0 |a Many-body problem.  |0 http://id.loc.gov/authorities/subjects/sh85080793 
650 0 |a Perturbation (Quantum dynamics)  |0 http://id.loc.gov/authorities/subjects/sh85100182 
650 0 |a Quantum theory.  |0 http://id.loc.gov/authorities/subjects/sh85109469 
650 0 |a Monte Carlo method.  |0 http://id.loc.gov/authorities/subjects/sh85087032 
650 7 |a Electronic structure.  |2 fast  |0 (OCoLC)fst00907474 
650 7 |a Electrons.  |2 fast  |0 (OCoLC)fst00907642 
650 7 |a Many-body problem.  |2 fast  |0 (OCoLC)fst01008543 
650 7 |a Monte Carlo method.  |2 fast  |0 (OCoLC)fst01025819 
650 7 |a Perturbation (Quantum dynamics)  |2 fast  |0 (OCoLC)fst01058907 
650 7 |a Quantum theory.  |2 fast  |0 (OCoLC)fst01085128 
700 1 |a Reining, Lucia,  |e author.  |0 http://id.loc.gov/authorities/names/no2015152984  |1 http://viaf.org/viaf/122145003302261301860 
700 1 |a Ceperley, David,  |e author.  |0 http://id.loc.gov/authorities/names/n85006488  |1 http://viaf.org/viaf/1428602 
903 |a HeVa 
880 0 0 |6 505-00  |a Contents note continued:  |g 20.5.  |t Transition metal oxides: overview --  |g 20.6.  |t Vanadium compounds and metal-insulator transitions --  |g 20.7.  |t NiO - charge-transfer insulator, antiferromagnetism, and doping --  |g 20.8.  |t MnO - metal-insulator and spin transitions --  |g 20.9.  |t Wrap-up --  |t Select Further Reading --  |t Exercises --  |g 21.  |t Combining Green's functions approaches: an outlook --  |t Summary --  |g 21.1.  |t Taking advantage of different Green's function methods --  |g 21.2.  |t Partitioning the system --  |g 21.3.  |t Combining different levels of diagrammatic approaches --  |g 21.4.  |t Combining Green's function methods: GW and DMFT --  |g 21.5.  |t Dynamical interactions and constrained RPA --  |g 21.6.  |t Consequences of dynamical interactions --  |g 21.7.  |t Diagrammatic extensions: dynamical vertex approximation and dual fermions --  |g 21.8.  |t Wrap-up --  |t Select Further Reading --  |t Exercises --  |g 22.  |t Introduction to stochastic methods --  |t Summary --  |g 22.1.  |t Simulations --  |g 22.2.  |t Random walks and Markov chains --  |g 22.3.  |t The Metropolis Monte Carlo method --  |g 22.4.  |t Computing error bars --  |g 22.5.  |t The "heat bath" algorithm --  |g 22.6.  |t Remarks --  |t Select Further Reading --  |t Exercises --  |g 23.  |t Variational Monte Carlo --  |t Summary --  |g 23.1.  |t Details of the variational Monte Carlo method --  |g 23.2.  |t Optimizing trial wavefunctions --  |g 23.3.  |t The momentum distribution and single-particle density matrix --  |g 23.4.  |t Non-local pseudopotentials --  |g 23.5.  |t Finite-size effects --  |g 23.6.  |t VMC for lattice models --  |g 23.7.  |t Excitations and orthogonality --  |g 23.8.  |t Strengths and weaknesses of VMC --  |t Select Further Reading --  |t Exercises --  |g 24.  |t Projector quantum Monte Carlo --  |t Summary --  |g 24.1.  |t Types and properties of projectors --  |g 24.2.  |t The diffusion Monte Carlo method --  |g 24.3.  |t Exact fermion methods: the sign or phase problem --  |g 24.4.  |t The fixed-node and fixed-phase methods --  |g 24.5.  |t Mixed estimators, exact estimators, and the overlap --  |g 24.6.  |t Non-local pseudopotentials in PMC --  |g 24.7.  |t Projector auxiliary-field quantum Monte Carlo methods --  |g 24.8.  |t Applications of projector MC --  |g 24.9.  |t The pluses and minuses of projector MC --  |t Select Further Reading --  |t Exercises --  |g 25.  |t Path-integral Monte Carlo --  |t Summary --  |g 25.1.  |t The path-integral representation --  |g 25.2.  |t Exchange of localized electrons --  |g 25.3.  |t Quantum statistics and PIMC --  |g 25.4.  |t Ground-state path integrals (GSPI) --  |g 25.5.  |t Finite-temperature QMC for the Hubbard model --  |g 25.6.  |t Estimating real-time correlation functions --  |g 25.7.  |t Correlation-function QMC for excitations --  |t Select Further Reading --  |t Exercises --  |g 26.  |t Concluding remarks --  |t Appendix A Second quantization --  |t Summary --  |g A.1.  |t First quantization --  |g A.2.  |t Second quantization --  |t Select Further Reading --  |t Appendix B Pictures --  |t Summary --  |g B.1.  |t Schrödinger picture --  |g B.2.  |t Heisenberg picture --  |g B.3.  |t Interaction picture --  |t Select Further Reading --  |t Exercises --  |t Appendix C Green's functions: general properties --  |t Summary --  |g C.1.  |t Green's functions for differential equations --  |g C.2.  |t Fourier transforms and spectral representations --  |g C.3.  |t Frequency integrals --  |g C.4.  |t From many-body to few-body Green's functions --  |g C.5.  |t The thermodynamic limit --  |t Select Further Reading --  |t Exercises --  |t Appendix D Matsubara formulation for Green's functions for Tnot=to0 --  |t Summary --  |g D.1.  |t Green's functions at Tnot=to 0: Matsubara frequencies --  |g D.2.  |t Analytic properties in the complex-frequency plane --  |g D.3.  |t Illustration of the structure of G°(iwn) and G°(τ) --  |g D.4.  |t The grand potential Ω --  |g D.5.  |t Transformation to real frequencies --  |t Select Further Reading --  |t Exercises --  |t Appendix E Time ordering, contours, and non-equilibrium --  |t Summary --  |g E.1.  |t The task --  |g E.2.  |t The contour interpretation --  |g E.3.  |t Contours for all purposes --  |t Select Further Reading --  |t Appendix F Hedin's equations in a basis --  |t Summary --  |g F.1.  |t Generalization of Hedin's equations --  |g F.2.  |t Hedin's equations in a basis --  |t Select Further Reading --  |t Appendix G Unique solutions in Green's function theory --  |t Summary --  |g G.1.  |t Which G°Boundary conditions in time --  |g G.2.  |t Which GSelf-consistent Dyson equations --  |g G.3.  |t Convergence of perturbation expansions and consequences --  |t Select Further Reading --  |t Exercises --  |t Appendix H Properties of functionals --  |t Summary --  |g H.1.  |t Functionals and functional equations --  |g H.2.  |t Legendre transformations and invertibility --  |g H.3.  |t Examples of functionals for the total energy in Kohn-Sham DFT calculations --  |g H.4.  |t Free-energy functionals for spin systems and proof of invertibility --  |g H.5.  |t Extension to quantum spins and density functional theory --  |t Select Further Reading --  |t Exercises --  |t Appendix I Auxiliary systems and constrained search --  |t Summary --  |g I.1.  |t Auxiliary system to reproduce selected quantities --  |g I.2.  |t Constrained search with an interacting auxiliary system --  |t Exercises --  |t Appendix J Derivation of the Luttinger theorem --  |t Summary --  |t Select Further Reading --  |t Exercises --  |t Appendix K Gutzwiller and Hubbard approaches --  |t Summary --  |g K.1.  |t Gutzwiller approach in terms of the wavefunction --  |g K.2.  |t Hubbard approach in terms of the Green's function --  |g K.3.  |t Two scenarios for the Mott transition --  |t Select Further Reading --  |t Exercises. 
929 |a cat 
999 f f |i b65e9de6-cb18-59cf-895b-e01afba04ca9  |s 6730fe8b-79be-5f50-93c6-64575c510441 
928 |t Library of Congress classification  |a QC176.8.E4 M368 2016  |l JCL  |c JCL-Sci  |i 9520881 
927 |t Library of Congress classification  |a QC176.8.E4 M368 2016  |l JCL  |c JCL-Sci  |e MAYB  |e CRERAR  |b 113658740  |i 9767331 
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