This award supports theoretical research and education on two significant themes in contemporary materials research. The first is the study of topological phases which can be broadly defined as phases of matter characterized by emergent gauge fields. These are to be contrasted with broken symmetry systems which exhibit emergent local order parameters in the sense of Landau. The second is the study of real time dynamics in quantum systems in and out of equilibrium. A significant set of topics involve ingredients from both themes.
The research is organized in four clusters.
The first cluster involves non-equilibrium dynamics near thermal and quantum critical points: the so called Kibble-Zurek problem first introduced into statistical mechanics with a cosmological motivation. The PI will build on the recent systematization of the Kibble-Zurek scaling limit and range over a set of model studies of the universal content using more traditional techniques as well as the newly introduced ideas of gauge-gravity duality or holography, detailed modeling appropriate to experimentally promising contexts, conceptual questions such as the relationship between linear response and fluctuations out of equilibrium and the identification of slow dynamics in topologically ordered systems.
The second cluster involves the quantum Hall system which continues to be interesting as the primary source of topologically ordered states. The research involves the physics of the non-abelian Pfaffian state that is observed at filling factor 5/2, a new field theory for the quantum Hall effect which is identified with proximity to a nematic instability and the physics of localization in a magnetic field in a long range correlated potential.
The third cluster involves a relatively new system produced by the search for qubits: superconducting circuit arrays. These allow for the creation of many-body systems where the particles are dressed photons or polaritons but necessarily involve an out of equilibrium element due to photon losses. The PI will study their many body physics in a regime not addressed to date, one which could allow the creation of topological states of photons. This work will also engage with the non-equilibrium aspects in order to make sense of the experiments that are envisaged.
The fourth cluster involves magnetic systems. The PI will develop a hydrodynamics for topologically ordered spin liquids thus paralleling the development of hydrodynamics for broken symmetry systems. This is particularly interesting in the context of searches for sharp signatures of spin liquids in experimental systems that are believed to such states. It is also proposed to examine a new frustrated magnetic Hamiltonian on the highly frustrated pyrochlore lattice which has been the source of much interesting physics.
NONTECHNICAL SUMMARY This award supports theoretical research and education on two frontier topics in theoretical materials research. The first is the study of new electronic states of matter in materials and the second is the study of quantum mechanical systems which are not in equilibrium.
A fundamental frontier activity in the physics of condensed matter is the identification and analysis of new phases of matter. Historically, most phases like these were understood to be examples of spontaneously broken symmetries, where the microscopic entities arrange themselves in particular static patterns that are less symmetric than the underlying forces between them. More recently, it has become clear that matter can exhibit a different family of phases where the symmetry remains unchanged but instead the constituents arrange themselves into fluctuating arrays of loops or more complex geometrical arrangements. Such phases also exhibit the phenomenon of fractionalization wherein their excitations manage to carry fractions of the quantum numbers, such as electrical charge, of the microscopic entities, such as electrons.
The study of such actual and potential phases is interesting for their intellectual challenge, to help make sense of an increasing set of laboratory realizations, and most recently, because a set of them have the potential to serve as a basis for the construction of a quantum computer which operates through the manipulation of quantum mechanical states. Such a computer can in principle be many times faster than the fastest supercomputers for certain algorithms.
This award supports fundamental theoretical research to advance the general theory of topological phases. Three experimental systems will be studied in detail; two of these are also of interest in the context of quantum computation. The second activity supported by this award is the study of quantum dynamics out of equilibrium. This is a difficult enterprise as the mathematical complexity is considerably greater than when systems are in equilibrium. Recent advances in the laboratory realization of cold atomic systems which can be readily prepared and studied out of equilibrium have present opportunities to advance understanding. The work supported by this award will focus on these and other experimental systems and is a direct descendant of some seminal work inspired by Cosmology by Kibble and Zurek and thus has intellectual connections to out of equilibrium behaviour of the universe itself!
