Michael Fleischhauer
Recent experiments have demonstrated that spin-orbit coupling can give rise to density-dependent Peierls phases associated with the transport of Rydberg spin excitations in atom arrays [1]. This nonlinear hopping provides a natural way for the implementation of a variety of non-trivial spin systems ranging from topological lattice models to lattice gauge theories, anyon physics and spin liquids. After discussing the microscopic origin of the nonlinear transport and its application for the realization of simple lattice gauge theories and anyon physics, I will consider two specific models in more detail, a one-dimensional zig-zag ladder and a two-dimensional honeycomb lattice model. Here the competition between nearest-neighbor density-density interaction, linear and nonlinear transport and frustration gives rise to a variety of interesting phases and phenomena. In the zig-zag model effective gauge fields emerge leading to liquids or lattices of vortices of excitation currents. In the honeycomb model we find some evidence for chiral spin liquid behavior.
[1 ] V. Lienhard, P. Scholl, S. Weber, D. Barredo, S. de Leseleuc, R. Bai, N. Lang, M. Fleischhauer, H. P. Büchler, T. Lahaye, and A. Browaeys, Phys. Rev. X 10, 021031 (2020)