A Mind Over Matter

Philip W. Anderson (1923–2020) is widely regarded as one of the most accomplished and influential physicists of the second half of the twentieth century. Educated at Harvard, he served during World War II as a radar engineer, and began a thirty-five year career at Bell Laboratories in 1949. He was soon recognized as one of the pre-eminent theoretical physicists in the world, specializing in understanding the collective behavior of the vast number of atoms and electrons in a sample of solid matter. He won a one-third share of the 1977 Nobel Prize for Physics for his discovery of a phenomenon common to all waves in disordered matter called Anderson localization and the development of the Anderson impurity model to study magnetism. At Cambridge and Princeton Universities, Anderson led the way in transforming solid-state physics into the deep, subtle, and coherent discipline known today as condensed matter physics. He developed the concepts of broken symmetry and emergence and championed the concept of complexity as an organizing principle to attack difficult problems inside and outside physics. In 1971, Anderson was the first scientist to challenge the claim of high-energy particle physicists that their work was the most deserving of federal funding. Later, he testified before Congress opposing the Superconducting Super Collider particle accelerator. Anderson was a dominant figure in his field for almost fifty years. At an age when most scientists think about retirement, he made a brilliant contribution to many-electron theory and applied it to a novel class of high-temperature superconductors.

Time dependent reduced density matrix functional theory at strong correlation: insights from a two-site Anderson impurity model

The one-body density matrix has recently attracted considerable attention as promising key quantity for the description of systems out of equilibrium. Its time evolution is given in terms of the...

Improved strong-coupling perturbation theory of the symmetric Anderson impurity model

In a previous work [N. H. Tong, Phys. Rev. B 92 (2015) 165126], an equation-of-motion-based series expansion formalism was used to do the second-order strong-coupling expansion for the single-particle Green function of the Anderson impurity model (AIM). In this paper, we improve this theory in two aspects. We first use a more accurate scheme to self-consistently calculate the averages that appear in [Formula: see text]. In the resummation process, we use updated coefficients for the continued fraction (CF), guided by the formally exact CF from the Mori–Zwanzig theory. These changes lead to more accurate impurity spin responses to the magnetic bias of the bath. Combined with the dynamical mean-field theory, our theory gives improved description for the antiferromagnetism of Hubbard model at half-filling.

Exact real-time dynamics of single-impurity Anderson model from a single-spin hybridization-expansion

In this work we introduce a modified real-time continuous-time hybridization-expansion quantum Monte Carlo solver for a time-dependent single-orbital Anderson impurity model: CT-1/2-HYB-QMC. In the proposed method the diagrammatic expansion is performed only for one out of the two spin channels, while the resulting effective single-particle problem for the other spin is solved semi-analytically for each expansion diagram. CT-1/2-HYB-QMC alleviates the dynamical sign problem by reducing the order of sampled diagrams and makes it possible to reach twice as long time scales in comparison to the standard CT-HYB method. We illustrate the new solver by calculating an electric current through impurity in paramagnetic and spin-polarized cases.