This award supports theoretical research and education to explore the properties of strongly interacting quantum matter, as realized in a wide variety of transition metal compounds, and in systems of trapped ultra-cold atoms. Special attention will be paid to layered compounds with antiferromagnetism and higher temperature superconductivity: examples are the cuprates, the pnictide compounds, the Bechgaard salts, and rare-earth heavy-fermion compounds.
The PI has proposed a common phase diagram which has successfully described the variation in physical properties as a function of temperature, applied magnetic field, and a tuning parameter like electron density or pressure, across these comprehensive series of materials. Central actors in this phase diagram are quantum phase transitions, involving the onset of spin magnetism and other orders, in metals and superconductors. The PI has described the strong-coupling structure of the theory of such transitions in two spatial dimensions, and proposed to develop the theory to produce new experimental tests of our understanding. The theory also allows for more exotic intermediate phases, with subtle types of quantum entanglement or 'topological order;' the PI will study their features while making contact with experimental studies on certain organic insulators. The theories of strong quantum correlations will also be applied to experiments on trapped ultra-cold atoms, and to electron spin physics in graphene. Finally, there are also remarkable connections between the possible phases of strongly interacting quantum matter, and the states of gravitational theories in anti-de Sitter space, through a gauge-gravity duality. The PI will continue his research at this interface area.
This award also supports education at the graduate and postdoctoral level, as well as outreach to the public and the preparation of the next edition of an authoritative textbook in the field.
NONTECHNICAL SUMMARY
This award supports theoretical research and education with the aim to explore quantum matter. Quantum matter is formed when large numbers of interacting particles are at temperatures low enough so that the concepts of quantum mechanics play a crucial role in determining its distinguishing characteristics. For electrons in solids, the needed 'low' temperatures can be even higher than room temperature. For gases of trapped atoms, ultra-cold temperatures about one billionth of a degree from the absolute zero of temperature are needed. Remarkably, a common set of ideas has found application across this wide range of energy scales.
Some of the most interesting phases of quantum matter are associated with the interplay between magnetism and superconductivity. Electrons may be thought of as tiny magnets and magnetism arises from the co-operative arrangement of the magnetic axes of the electrons. Superconductivity is the ability of pairs of electrons to carry electrical current without dissipation. The PI will study how by varying material parameters, it is possible to drive a system of electrons from a magnetic to a superconducting state, across a variety of 'quantum phase transitions.' Such phase transitions are analogous to familiar thermal transitions, like water changing to steam, but are associated here with subtle quantum correlations between the electrons. Concepts from the theory of quantum phase transitions inform our understanding of the measureable properties of quantum matter in the laboratory.
The PI will also explore emerging connections between the theory of quantum matter, and seemingly unrelated work on the quantum theory of black hole horizons. These fields share a common interest in how many particles can become 'entangled' with each other quantum mechanically across large distances; their distinct approaches to entanglement have led to mutually beneficial insights.
This award also supports education at the graduate and postdoctoral level, as well as outreach to the public and the preparation of the next edition of an authoritative textbook in the field.
The high temperature superconductors have the ability to conduct electricty without resistance, and have been the focus much research over the past two decades. It has become clear in recent years that an understanding of their physical properties requires us to develop a theory for the consequences of quantum entanglement over long length scales. Our project advanced the frontier of theories of quantum entanglement of large numbers of particles in several different directions. Over a certain range of electron densities these compounds exhibit exotic types of ordering phenomena which have been the focus of numerous scanning tunnelling microscopy experiments: our theories led to a new method of analyzing these experiments which have opened up a deeper understanding of these enigmatic superconductors. We have also studied the role of quantum entanglement in a new class of insulators known as "spin liquids." While these don't have any direct technological importance, they display subtle types of long-range quantum entanglement which have fascinated theorists over the past decade. Here too our work led to a new understanding of experimental data. An unintended consequence of our work was the development of remarkable connections between studies of quantum entanglement in quantum materials (described above) and studies by string theorists of quantum entanglement near the horizon of black holes. These connections have led to new insights in both fields. In particular, they led us to the development of theories of a "strange metal" region in the phase diagram of the high temperature superconductors.
