David Adler Award in the Field of Materials Physics: Complexity in Correlated Electrons*

Studying materials is often complicated because of the interacting nature of electrons (correlated electrons), and the proliferation of interesting phases, including magnetism (ferro and antiferro), superconductivity, ferroelectricity, topological tendencies, and others. In this presentation, I will argue that the real situation is even more complex that what is often reported in textbooks. Once reliable computational many-body techniques are used as the tool of investigation for correlated electrons, a plethora of unanticipated phases is often unveiled. This strong “complexity” – namely the appearance of novel states and patterns difficult to anticipate a priori – primarily occurs when various tendencies are in competition. Thus, I will argue that the best place to look for interesting surprises is the “intermediate coupling” regime of model Hamiltonians. When the strength of couplings -- such as the on-site Hubbard repulsion, on-site Hund coupling, spin-orbit coupling in its many forms, etc. – are comparable, and in addition, many orbitals and even the lattice are active, this is where generic “frustration” tendencies could occur and create unexpected patterns and phases. This can occur even without invoking special lattice geometries, such as triangular, or long-range couplings. My talk will start with illustrations of these concepts from my early days as a scientist, and rapidly approach more recent times where computers unveiled new unforeseen phases, including various spin block phases, spirals stabilized without long-range interactions, frustrated phases in heterostructures, and others. Static and dynamic Majoranas will also be discussed. All this vast richness of states can be realized, and the discoveries accelerate, thanks to the growing availability of computational resources as well as the development of reliable computational techniques.