In this talk, I explore two examples of how the symmetry of a microscopic lattice or topology of an underlying non-interacting band structure can be imprinted in the excitations of strongly-correlated insulators. First, I show that previously-unnoticed crystal symmetry constraints drastically alter the understanding of Ising quantum criticality in the quasi-1D magnetic insulator CoNb2O6, resolving decade-old puzzles related to the dispersion of confined 'kinks' in the ordered phase and the decay of spin-flip quasiparticles in the paramagnetic phase . Turning next to the correlated quantum anomalous Hall insulator recently observed in twisted bilayer graphene near the magic angle, I show that this state supports stable, weakly-dispersing flat bands of neutral bosonic excitons with substantial Berry curvature , and argue that these can under certain conditions form a new hierarchy of bosonic fractional quantum Hall liquids .
 M. Fava, R. Coldea, and S.A. Parameswaran, arXiv:2004.04169 (2020).
 Y.H. Kwan, Y. Hu, S.H. Simon, and S.A. Parameswaran, arXiv:2003.11560 (2020).
 Y.H. Kwan, Y. Hu, S.H. Simon, and S.A. Parameswaran, arXiv:2003.11559 (2020).
For meeting link info, contact Prof. Vedika Khemani: vkhemani [at] stanford [dot] edu