Quantum Matter

Topological phases of matter

Topological phases are inherently quantum phenomena, in which materials exhibit precisely quantized features that are completely insensitive to microscopic imperfections. Classical examples include quantized Hall conductance in 2d electron systems in a magnetic field, quantized magneto-electric effects in electronic topological insulators, and emergent anyonic particles with fractional charge and statistics in fractional quantum Hall systems and spin-liquids. Topological phases of matter often exhibit exotic surface states with anomalous properties that would ordinarily be forbidden -- except at the boundary of a topological phase.

Our group seeks both to develop rigorous formal frameworks to classify topological phases of matter, and to model their experimental realizations in real-world materials to predict new robust electronic, optical, magnetic, and superconducting effects, and harness these capabilities for device applications and quantum information technology. On the formal side, our group leverages tools from quantum field theory, quantum information science, and algebraic topology to characterize topological phases and predict their measurable properties. In addition, we also collaborate closely with experimental groups to test theory predictions, and explore new effects and applications of topological materials.

Topics of past and ongoing interest include:

• • Physics of topological insulators, superconductors, and semi-metals (Weyl & Dirac semimetals)

  • Systematic classification of strongly interacting topological phases

  • Experimental realizations of topologically ordered systems with Abelian and Non-Abelian anyons, and devices for topological quantum computing

  • Anomalous properties of topological surface states, non-perturbative dualities, and surface topological orders

  • 3d topological orders, foliated topological orders & fractons

Interacting quantum fluids (non-Fermi liquids)

Gapless phases of matter with sufficienlty strong interactions to rule out a simple quasi-particle description remain some of the most theoretically challenging and poorly understood types of quantum matter, despite their experimental prevalence from the strange-metal phases of high-temperature cuprate superconductors, critical points in metallic systems, gapless spin-liquid materials, and non-Fermi liquid behavior from the interaction of magnetic textures with conducting electrons.

Our research explores new theoretical tools, such as topological insights from anomalies, duality transformations, and effective field theories to analyze interacting quantum fluids. Typically, however, such theory-only approaches rest on uncontrolled calculations that cannot make reliable ab initio predictions. To this end, a central element of our work is to explore new experimental contexts for non-Fermi liquids, predict new measurement techniques to probe their properties, and compare to theoretical predictions and refine our understanding of these exotic quantum phases.