Close to the absolute zero of temperature, when pushed to the edge between two phases of matter, simple lattice Hamiltonians of spins can display the incredibly rich phenomena of "quantum criticality". Quantum critical ground states are described by the most complex wavefunctions known to physicists, yet they can be categorized by "universality classes" that are independent of the details of the Hamiltonians that realize them. In this colloquium I will show how such quantum critical spin systems can arise in real-world materials, and explain our successes in developing quantum many-body simulations of a new universality class of deconfined quantum critical points.

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