The treatment of many-body problems of solid-state physics

Charles Paul Enz

Wolfgang von der Linden

Roberts, James Lannis

A systematic procedure is developed for solving the eigenvalue problem for a broad class of Hamiltonian operators containing no terms higher than quadratic in generalized coordinates and th e ir conjugate momenta.The development is oriented toward practical applications in the area of the many-body problem.The procedure accomplishes a canonical reduction of such a Hamiltonian to the form of the Hamiltonian for a collection of non interacting bosons, with the eigenvalues of the Hamiltonian expressed in terms of the solutions to a single secular equation.Application of the results to systems of interacting identical bosons is discussed, including a presentation of a useful calculatlonal technique.The procedures developed are illu s tra te d by detailed treatments of two specific problems of interest in physics.The f i r s t problem considered is an exactly solvable separable potential model of p a rtic le fie ld theory.This problem consists of the description of a collection of lig h t bosons interacting with an in fin ite ly heavy boson via a simple separable po ten tia l.Interest in this problem centers on its use as a test case for approximation techniques to be used on more complicated systems.The second and more r e a lis tic problem investigated is the polaron problem of solid state physics.This problem involves the Iv description of the motion of a single conduction electron within an ionic solid.The polaron consists of the conduction electron together with its self-induced polarization field.The polaron problem is oif interest not only because of its value in solid state physics, but also because it, too, is useful as a testing ground for approximation techniques.Finally, broad applicational aspects of the procedures developed are discussed.

W. M. C. Foulkes, Luboš Mitáš, Richard J. Needs +1 more

This article describes the variational and fixed-node diffusion quantum Monte Carlo methods and how they may be used to calculate the properties of many-electron systems. These stochastic wave-function-based approaches provide a very direct treatment of quantum many-body effects and serve as benchmarks against which other techniques may be compared. They complement the less demanding density-functional approach by providing more accurate results and a deeper understanding of the physics of electronic correlation in real materials. The algorithms are intrinsically parallel, and currently available high-performance computers allow applications to systems containing a thousand or more electrons. With these tools one can study complicated problems such as the properties of surfaces and defects, while including electron correlation effects with high precision. The authors provide a pedagogical overview of the techniques and describe a selection of applications to ground and excited states of solids and clusters.

Jaime Merino, A. Levy Yeyati

David J. Griffiths, Darrell F. Schroeter

Changes and additions to the new edition of this classic textbook include a new chapter on symmetries, new problems and examples, improved explanations, more numerical problems to be worked on a computer, new applications to solid state physics, and consolidated treatment of time-dependent potentials.