Fradkin has worked in many areas in theoretical condensed matter physics and is notably broad and versatile in his research topics. Among his most researched areas in condensed matter include the fractional quantum Hall systems and high-temperature superconductivity. He is considered one of the earliest proponents of, and one of the leading figures in, using quantum field theoretical concepts and methods in condensed matter physics, and is well known for popularizing such approaches through his early book Field Theories of Condensed Matter Physics in 1991. In his doctoral work at Stanford, he made major contributions to lattice gauge theories, where his results have, among other things, had far-reaching applications and implications to two-dimensional quantum spin liquids and other topologically ordered phases in two-dimensional lattices. He has done many important works in the area of fractional quantum Hall physics, in which he gave the first fermionic Chern-Simons field theory for the effect, described various field theories for non-Abelian fractional quantum Hall states, quantum Hall edge physics and, more recently, theories for describing nematicity and geometry in the fractional quantum Hall regime. One of his most influential works has been the introduction and elucidation of the powerful new paradigm in quantum many-body physics of electronic liquid crystalline phases in various strongly correlated systems, in particular in quantum Hall systems and high-temperature superconductors, and, more recently in this area, elucidation of the notion and significance of "intertwined orders" in the context of cuprate high-temperature superconductors and more generally in strongly correlated systems. He has also made important contributions to the physics of quantum dimer models, models for unconventional quantum phase transitions involving topologically ordered phases, and quantum entanglement properties of these and related problems. He also gave one of the earliest approaches to higher dimensional bosonization of fermionic field theories as well as two-dimensional Fermi surfaces and has later applied them to important problems in condensed matter. Some of his other important works in recent times that have not already been mentioned above include a graph-theoretic lattice discretization scheme for Chern-Simons theories and its applications to condensed matter problems, and novel field theoretic approaches to describe fractional topological insulators.
