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Uncovering and exploiting emergent phenomena in quantum matter

Emergence is a ubiquitous feature of quantum condensed matter systems: the collective low-energy behavior of an interacting quantum many-body system oftentimes exhibits behavior profoundly different from that of the constituent degrees of freedom. In this talk, I will present a survey of recent results on one- and two-dimensional quantum systems which dramatically demonstrate this concept. In the first part of the talk, I will focus on a set of problems in which we are able to * uncover * — mainly through computational lines of attack — novel and striking emergent behavior in (1) the kagome Heisenberg antiferromagnet and (2) the half-filled Landau level. I will discuss the emergence and entanglement structure of fermionic spinons and composite fermions, respectively, in these two paradigmatic quantum condensed matter systems. In the last part of the talk, I will switch gears and discuss how we can * exploit * emergent quantum phenomena for technological gain. In particular, I will discuss how Majorana fermions can emerge as zero-energy features of certain superconducting wires and how these Majorana zero modes can in principle be used to build superior quantum computing hardware. I will describe our recently proposed protocols — as well as corresponding numerical simulations — aimed at verifying topological (“perfect”) protection of quantum information in present-day devices being pursued vigorously by experimental groups at Microsoft and elsewhere. Finally, I will conclude by discussing several future directions of research in these areas.