Philip Warren Anderson, one of the intellectual giants who shaped and nurtured the rapid growth of condensed-matter physics during the second half of the 20th century, died on 29 March 2020 in Princeton, New Jersey. He made fundamental contributions to diverse subfields, including antiferromagnetism, superexchange, dirty superconductors, the x-ray singularity problem, localization, superfluidity in helium-3, spin glasses, quantum spin liquids, local moments in metals, poor-man’s renormalization, and cuprate superconductivity. Many of those concepts now carry his name. He was a corecipient, along with Nevill Mott and John Van Vleck, of the 1977 Nobel Prize in Physics for “fundamental theoretical investigations of the electronic structure of magnetic and disordered systems.”

Philip Warren Anderson

Anderson was born on 13 December 1923 in Urbana, Illinois. After a stint at the Naval Research Laboratory during World War II, he obtained his PhD in 1949 from Harvard University, working under Van Vleck. In 1949 he joined Bell Labs and its group of talented physicists, which included Bernd Matthias, Peter Wolff, Robert Shulman, William Shockley, and Charles Kittel. Their strong influence on the company to invest in basic research had a great effect on the labs for the rest of the century. From 1967 to 1975, Anderson worked part time at Cambridge University before joining the faculty of Princeton University. In 1984, after retiring from Bell Labs, he started as a full-time professor and became emeritus in 1996.

Anderson is perhaps best known for his 1958 prediction that sufficiently strong disorder can turn metals into insulators via a process now known as Anderson localization. Before his work, the common view was that electron waves are extended throughout the material. Anderson showed that at low temperatures, disorder can cause the waves to be localized in space and stop conducting current.

In the 1950s and 1960s, Anderson elucidated how a combination of quantum mechanics and strong repulsion between electrons causes electron spins to form local moments; his insight laid the foundation of the modern theory of magnetism. After John Bardeen, Leon Cooper, and J. Robert Schrieffer proposed their pairing theory of superconductivity in 1957, Anderson became a major contributor to the topic. He was the first to recognize the importance of the phase of the superconducting wavefunction and how it is quantum mechanically conjugate to the number of Cooper pairs.

In principle, phase fluctuations lead to a collective mode of gapless excitations, an example of Goldstone’s theorem; such excitations are observed in neutral superfluids but not in superconductors. Anderson realized that the coupling of Cooper pairs to the electromagnetic field boosts the mode to a finite frequency, where it merges with the plasma mode. He proposed in 1962 that the mechanism removes the roadblock—namely, the problem of unwanted massless Goldstone particles—facing unified field theories based on broken symmetry. Two years later Peter Higgs and others reached the same conclusion via more formal routes. As Higgs wrote in his Nobel lecture, “The Goldstone massless mode became the longitudinal polarization of a massive spin-1 ‘photon,’ just as Anderson had suggested.” The Anderson–Higgs mechanism is now a cornerstone of both particle and condensed-matter physics.

A year after the 1986 discovery of high-temperature superconductivity in cuprates, Anderson published an enormously influential paper in Science pointing out that the key physics is the introduction of charge carriers (“holes”) into the insulating state that arises from strong electron–electron repulsion. He recalled a 1973 paper that introduced the notion of quantum spin liquids, in which magnetic moments fail to achieve long-range order because of quantum fluctuation and instead form a state that he dubbed a “resonating valence bond” (RVB). He proposed that in a cuprate, when holes are introduced into that state, it becomes a superconductor.

Those revolutionary ideas met stiff resistance from the community. Although the specific mechanism he proposed for superconductivity remains controversial, many of the ideas he introduced in the 1987 paper, including the notion that superconductivity is a favorable ground state in a strongly repulsive system, have gained wide acceptance. The RVB state is the archetypal example of a quantum spin liquid, currently a vigorous area of research.

Anderson also suggested that the excitations of a quantum spin liquid behave as electrons that have lost their charge but retain their spin. That early example of “fractionalization” has found support both in exactly soluble models and in real materials. Time will tell, but Anderson’s spin-liquid work may well be remembered as his most profound and prescient.

In a 1972 article entitled “More is different,” Anderson outlined the antireductionist view that each layer of nature is as worthy of fundamental investigation as the most microscopic ones. Those laws cannot anticipate, much less explain, the rich variety of macroscopic systems’ fascinating complex behavior, such as superconductivity, chaos, and emergent phenomena. That view has deeply influenced condensed-matter physics and other areas of science.

In addition to the Nobel Prize, Anderson was awarded the American Physical Society’s Oliver E. Buckley Prize in 1964 and the National Medal of Science in 1982. He had a lifelong interest in the game of Go dating from a yearlong visit to Japan in 1953–54, and he attained the rank of first-Dan master. In 2007 the Nihon Ki-in, Japan’s association for Go, gave him a lifetime achievement award.