Holography, Supersymmetry and Numerics in Quantum Critical and Quantum Lifshitz Theories

PROJECT SUMMARY During the past decade there has been increasing cross-fertilization between certain aspects of condensed matter theory and high energy theory. The realization that many strongly coupled condensed matter systems can be recast as gauge theories, combined with powerful methods derived from gauge/gravity duality and supersymmetry, has made it possible to nonperturbatively compute equilibrium and transport properties of quantum critical points in two space dimensions for the first time. In a second development, the coming of age of the field of ultracold atomic gases, and the unprecedented level of time-dependent experimental control that can be applied to the Hamiltonian of the system, has brought forth a surge of interest in states far from equilibrium, such as the evolution of systems under quenches (where a parameter of the Hamiltonian is changed abruptly) through quantum phase transitions. Thirdly, the continued investigation of topologically ordered states in condensed matter systems has recently taken a huge leap forward with the discovery of noninteracting topological insulators, and the development of new ways of probing properties of topologically ordered states, such as entanglement entropy and spectrum. Topologically ordered states are central objects of study in quantum computation and quantum information theory. The investigators propose several projects which are at this emerging interface, and draw upon their different and complementary skills. It is proposed to investigate quantum spin models in two space dimensions, and the gauge theories which emerge from them, near Lifshitz fixed points, by using large-N techniques as well as AdS/CFT duality to understand their nonperturbative aspects. At finite N, it is proposed to investigate supersymmetric versions of such spin models, and to make use of the powerful nonperturbative techniques of extended supersymmetry to obtain exact information about analogous fixed points. A crucial part of the proposal is to perform numerical simulations on these and related models, which will provide unbiased information. It is proposed to study the nonequilibrium properties of systems far from equilibrium, at or near quantum criticality, using AdS/CFT duality extended to time-dependent perturbations of the theory, such as quantum quenches and thermalization. Previous results in this framework have been largely limited to near-equilibrium transport properties. It is proposed to investigate the response of topological states of matter to strongly timedependent processes, and study the response of their specifically topological properties to such perturbations. This would be the first such study to make use of holographic techniques. Intellectual Merit: The successful completion of these projects will lead to new ways to understand quantum critical and quantum Lifshitz points, the nonequilibrium behavior near such points, and the response of topological states subject to time-dependent perturbations. Broader Impact: The results from the study of topologically ordered states will have impact on the subfield on quantum information theory. Further, two postdocs will receive multidisciplinary training in the techniques of this emerging interface field. 4