Research Projects

Understanding how a network of interacting units behave collectively is a unifying challenge for modern science. While, for historical reasons, the behavior of quantum systems has been largely studied on regular lattices, modern network science has shown that more structured coupling can radically alter global properties, such as critical phenomena and disease spreading, and produce new physical phenomena, such as explosive transitions, in classical systems. On the other hand, experimental advances in cooling and trapping techniques have made it possible to engineer arbitrary connectivity in atomic and photonic setups. Clearly, there is a huge potential for fundamental discovery and technological applications at this new frontier at the intersection of quantum condensed matter and network science. The proposed work will advance this frontier by focusing on the role of network topology in two intrinsically quantum phenomena: kinetic magnetism and entanglement. Though all magnetism has a quantum origin, the more commonly studied mechanism of exchange coupling can be modeled with classical spins. However, magnetism can also arise from minimizing the kinetic energy of a doped carrier (e.g., a hole), which results from quantum interference between different paths. This depends solely on the lattice topology and does not have a classical counterpart. Triangles or odd loops in the lattice cause kinetic frustration and, despite recent experiments, there is no general understanding of how this affects the magnetic order. By studying complex networks we plan to systematically add units of frustration and analyze their impact. Based on preliminary results our hypothesis is that these units bind spin impurities, reducing the net magnetization. We will test this hypothesis by using a blend of numerical and semi-analytical methods on a range of network families with tunable structural properties. Our findings will establish how local structures control global ordering, allowing one to tune the magnetization by embedding these structures. Another thread of the proposed work will explore how one can harness the connectivity to create long-range entanglement shared by multiple qubits. Such multipartite entanglement is both of fundamental interest and essential for a number of quantum information tasks. However, they are very challenging to produce and maintain in a many-body setting, especially with a local drive. We will explore how this can be achieved in a star topology where multiple spin chains are incoherently driven at a common center site. From symmetry considerations we expect it will be possible to maximally entangle the outermost qubits, using each leg as a communication channel. Additionally, the confluence of dynamical and permutation symmetries will allow us to formulate a non-Abelian symmetry that protects entangled states from decoherence. This will provide an experimental setting to probe such symmetries and stabilize multipartite entanglement.