Harvard University Department of Physics

Quantum mechanics was originally developed by Schroedinger and Heisenberg as a theory of non-relativistic charged particles interacting via the Coulomb force, and successfully applied to a simple two-particle system like the hydrogen atom. However, among its most important applications has been the description of 10²³ particles found in macroscopic matter. The earliest example of this was the Sommerfeld-Bloch theory of electronic motion in metals, and its refined formulation in Landau's Fermi liquid theory. Although solving Schroedinger's wave equation for 10²³ interacting electrons appears an impossibly daunting task, Landau outlined a powerful strategy, involving the concept of "quasiparticles", which allowed an essentially exact description of the low temperature properties of metals. The quasiparticles have an essentially free electron-like character. Although interactions between the electrons do strongly renormalize various parameters in the effective Hamiltonian, the quantum dynamics of the quasiparticles is essentially that of nearly free electrons, each of which can be described independently by single-particle quantum mechanics.

Since the mid-80's, much attention has been lavished on a variety of transition metal compounds, whose physical properties do not fit easily into the Landau paradiagm. The most important among these compounds are ceramics, like YBa₂Cu₃O₇, in which the electronic motion occurs primarily in two-dimensional CuO₂ layers, and which display high temperature superconductivity. It is clear that electron-electron interactions are playing a much more fundamental role here, and the excitations are qualitatively different from individual electrons.

Subir Sachdev's research has focused on the classification of the many-body ground states of interacting electrons, especially in two spatial dimensions. Fundamental distinctions between such ground states imply that they cannot be smoothly connected to each other (whereas the Landau Fermi liquid is smoothly connected to the independent electron state). Such states are necessarily separated by quantum phase transitions at a quantum critical point (QCP). The QCP has novel properties and usually does not permit a quasiparticle description. Although the QCP is only a special point in the zero temperature phase diagram, it turns out to be a useful point of departure for understanding the physical properties of phases in its vicinity both at zero and non-zero temperatures. Remarkably, it is often the case that quantum mechanics is crucial to understanding the collective properties of 10²³ electrons in these materials, even at temperatures as high as room temperature and at the longest time and distance scales.