Advanced Solid State Physics Philip Phillips Westview Press, Boulder, Colo., 2003. $100.00, $55.00 paper (386 pp.). ISBN 0-8133-4015-2, ISBN 0-8133-4014-4 paper

An important task of theoretical physics is to understand the motion of electrons in metals, semiconductors, and other materials of technological importance. At first, the task seems immensely complex: One has to consider the quantum theory of 10^{23} electrons interacting with each other and with a lattice of ions that can themselves move away from the positions dictated by the crystal lattice. Remarkably, physicists have developed a successful and accurate theory of the electronic properties of materials, and its basic principles rely on little more than the material in a first undergraduate course in quantum mechanics.

Felix Bloch’s theory of metals—the foundation of theories of more general materials—begins with the seemingly radical assumption that electrons moving in a periodic lattice potential do not interact with each other. Many excellent texts in solid-state physics, such as the classic texts by Charles Kittel and by Neil Ashcroft and David Mermin, cover the theory. It has been the basis of research in theoretical solidstate physics for the past half century.

Sophisticated techniques in many-body physics have been developed to account for the electron interactions neglected in Bloch’s theory, and the results of those techniques vindicate the independent-electron assumption for a wide variety of interesting systems. The interactions dress each electron with a cloud of particle—hole pairs, but near the Fermi surface the dressed particle (the “quasiparticle”) behaves much as an ordinary electron would. It has total charge *−e*, a total spin 1/2, and weak residual interactions with other quasi-particles. Those interactions appear as quasiclassical energy shifts in Lev Landau’s elegant Fermi-liquid theory. The Bardeen-Cooper-Schrieffer (BCS) theory shows that a weak residual attractive interaction between the quasi-particles could lead to electron pairing, and the condensation of those pairs describes superconductivity. Such advanced developments are surely important and necessary for a complete quantitative explanation of experiments, but their core remains the simple framework of Bloch’s theory.

In the past two decades or so, exciting research has focused on more profound departures from Bloch’s theory. Often a workable theory requires inclusion of electron—electron interactions at the outset, not as an afterthought. Understanding such a theory requires entirely new concepts and paradigms. Students who have completed the typical graduate curriculum in solid-state physics may be unfamiliar with such constructs. Instead, they may have gotten the impression that the independent-electron theory is infallible, and thus may use it inappropriately.

*Advanced Solid State Physics * by Philip Phillips attempts to redress that situation and to give students a modern perspective that is not tied so strongly to the independent-electron picture. The book’s scope is ambitious and far-reaching. It begins with Bloch’s theory, proceeds through the perturbative methods of many-body theory that enhance Bloch’s theory, and then discusses a variety of currently interesting physical situations in which electron interactions are paramount.

The strongest feature of Phillips’s book is its excellent choice and presentation of modern topics. Interspersed among sections on traditional Bloch—Landau—BCS theory, these topics will help to prevent students from being lulled by the successes of the independent-electron picture. The book begins with the Hartree—Fock theory of the interacting electron gas, and discusses that theory’s success in describing the alkali metals. There follows an interesting discussion of magnetic moments and the nontrivial electron correlations associated with the Kondo effect. Similarly, a discussion of the successes of Fermi-liquid theory is followed by a treatment of its breakdown in the one-dimensional Luttinger liquid. The discussion of those advanced topics introduces the renormalization group and bosonization, which surely belong in the arsenal of every theory student. The book ends by concisely introducing central concepts in localization theory, metal—insulator transitions, quantum phase-transition theory, and the quantum Hall effect.

No other text has such a wide scope, and readers will appreciate the concise sweep through nearly a century of developments in solid-state theory. But if a broad sweep is the book’s unique strength, it also leads to a weakness. A short book cannot cover all its topics in any depth, and uninitiated readers may find it difficult to rely on this book alone. For instance, the book assumes no prior knowledge of second quantization or the renormalization group, but its terse survey of those key concepts surely needs to be supplemented by other reading. Fortunately, other excellent texts cover most such topics, and Phillips provides a useful list of references.

*Advanced Solid State Physics * can serve as a valuable centerpiece of an up-to-date advanced graduate course. The main topics and central concepts are all presented compactly. Where the discussion is cursory, the book can be a useful starting point for in-depth exploration through other sources.