Many-Body Physics: Unfinished Revolution

The study of many-body physics has provided a scientific playground of surprise and continuing revolution over the past half century. The serendipitous discovery of new states and properties of matter, phenomena such as superfluidity, the Meissner, the Kondo and the fractional quantum hall effects, have driven the development of new conceptual frameworks for our understanding about collective behavior, the ramifications of which have spread far beyond the confines of terrestrial condensed matter physicsto cosmology, nuclear and particle physics. Here I shall selectively review some of the developments in this field, from the cold-war period, until the present day. I describe how, with the discovery of new classes of collective order, the unfolding puzzles of high temperature superconductivity and quantum criticality, the prospects for major conceptual discoveries remain as bright today as they were more than half a century ago. 1 Emergent Matter: a new Frontier Since the time of the Greeks, scholars have pondered over the principles that govern the universe on its tiniest and most vast scales. The icons that exemplify these frontiers are very well known the swirling galaxy denoting the cosmos and the massive accelerators used to probe matter at successively smaller scalesfrom the atom down to the quark and beyond. These traditional frontiers of physics are largely concerned with reductionism: the notion that once we know the laws of nature that operate on the smallest possible scales, the mysteries of the universe will finally be revealed to us[1]. Over the last century and a half, a period that stretches back to Darwin and Boltzmannscientists have also become fascinated by another notion: the idea that to understand nature, one also needs to understand and study the principles that govern collective behavior of vast assemblies of matter. For a wide range of purposes, we already know the microscopic laws that govern matter on the tiniest scales. For example, a gold atom can be completely understood with the Schrödinger equation and the laws of quantum mechanics established more than seventy years ago. Yet, a gold atom is spherical and featurelessquite unlike the lustrous malleable and conducting metal which human society so prizes. To understand how crystalline assemblies of gold atoms acquire the properties of metallic gold, we need new principles– principles that describe the collective behavior of matter when humungous numbers of gold atoms congregate to form a metallic crystal. It is the search for these new principles that defines the frontiers of manybody physics in the realms of condensed matter physics and its closely related 2 Piers Coleman Ann. Henri Poincaré discipline of statistical mechanics. In this informal article, I shall talk about the evolution of our ideas about the collective behavior of matter since the advent of quantum mechanics, hoping to give a sense of how often unexpected experimental discovery has seeded the growth of conceptually new ideas about collective matter. Given the brevity of the article, I must apologize for the necessarily selective nature of this discussion. In particular, I have had to make a painful decision to leave out a discussion of the many-body physics of localization and that of spin glasses. I do hope future articles will have opportunity to redress this imbalance. The past seventy years of development in many-body physics has seen a period of unprecedented conceptual and intellectual development. Experimental discoveries of remarkable new phenomena, such as superconductivity, superfluidity, criticality, liquid crystals, anomalous metals, antiferromagnetism and the quantized Hall effect, have each prompted a renaissance in areas once thought to be closed to further fruitful intellectual study. Indeed, the history of the field is marked by the most wonderful and unexpected shifts in perspective and understanding that have involved close linkages between experiment, new mathematics and new concepts. I shall discuss three eras:the immediate aftermath of quantum mechanics— many-body physics in the cold war, and the modern era of correlated matter physics. Over this period, physicists’ view of the matter has evolved dramaticallyas witnessed by the evolution in our view of “electricity” from the idea of the degenerate electron gas, to the concept of the Fermi liquid, to new kinds of electron fluid, such as a the Luttinger liquid or fractional quantum Hall state. Progress was not smooth and gradual, but often involved the agony, despair and controversy of the creative process. Even the notion that an electron is a fermion was controversial. Wolfgang Pauli, inventor of the exclusion principle could not initially envisage that this principle would apply beyond the atom to macroscopically vast assemblies of degenerate electrons; indeed, he initially preferred the idea that electrons were bosons. Pauli arrived at the realization that the electron fluid is a degenerate Fermi gas with great reluctance, and at the end of 1925[2] gave way, writing in a short note to Schrödinger that read “With a heavy heart, I have decided that Fermi Dirac, not Einstein is the correct statistics, and I have decided to write a short note on paramagnetism.” Wolfgang Pauli, letter to Schrödinger, November 1925[2]. 2 Unsolved riddles of the 1930s The period of condensed matter physics between the two world-wars was characterized by a long list of unsolved mysteries in the area of magnetism and Vol. 4, 2003 Many Body Physics: Unfinished Revolution 3