At the frontier of our efforts to understand collective phenomena is the search for unconventional phases of matter. Many ideas for exotic phases shaped by strong quantum fluctuations have been explored in recent years, motivated by the difficulty of explaining various strongly correlated materials, such as cuprates and heavy fermion systems. Perhaps the most promising platform for characterizing and observing such phases are geometrically frustrated quantum magnets.
High temperature superconductivity of cuprates is one of the greatest challenges in many-body quantum physics. Since their discovery in 1986, the field of condensed matter physics has been flooded with an enormous number of new ideas, theoretical and experimental techniques. While the superconducting phenomenology in cuprates has been understood very well, the origin of superconductivity is still mysterious. It is believed that the secret to high temperature superconductivity is hidden in the strong correlations that electrons experience in the so called “normal” and “pseudogap” states. Several experimental and theoretical developments suggested that certain aspects of pseudogap dynamics may result from a quantum liquid state of vortices that destroy the long-range phase coherence of robust Cooper pairs.
In recent years, atomic physics has opened a new frontier for the exploration of strongly correlated many-body systems. Atoms can be cooled to sub-nanokelvin temperatures, trapped in a small volume and placed in artificial crystalline potentials or electromagnetic fields created by lasers. Furthermore, interactions between atoms can be controlled. This enables simulations of electronic materials with more ideal properties than found in nature, and testing or developing theories of condensed matter in a new environment. Novel forms of quantum matter can also be engineered using ultra-cold atoms.
A new class of materials with strong spin-orbit coupling, known as topological insulators (TI), are bulk insulators with edge or surface conduction channels that respect the time-reversal (TR) symmetry. In that sense they are similar to quantum Hall systems, which however are not invariant under TR due to the externally applied magnetic field. The Rashba spin-orbit coupling found in TI materials has a “dynamical” symmetry that can shape incompressible quantum liquids in the presence of strong quantum fluctuations, without an analogue in quantum Hall states. Such quantum liquids can exhibit new and not yet experimentally discovered topological orders with Abelian or non-Abelian fractional statistics.