Abstract:

Systems of many strongly-interacting particles are key to explaining many phenomena: from the magnets in our everyday experience to more exotic phenomena such as superconductivity, quantum hall physics, and emergent gauge symmetries. However, the necessary quantum mechanical treatments of these systems involve Hilbert spaces that grow exponentially with the system volume, putting naive calculations out of reach. In this talk, I will motivate three useful principles for building models that are both relevant to nature and amenable to computer simulation in polynomial time: locality, symmetry, and small ultralocal Hilbert spaces. With classical computers we will see how locality as a guiding principle allows us to study antiferromagnetism and superconductivity with relativity, and how symmetry as a guiding principle allows us to detect conformal field theories using the quantum hall effect. Finally for quantum computers we make use of small ultralocal Hilbert spaces as a guiding principle, and then design and study resource-efficient qubit-friendly models that realize continuous gauge symmetries found in fundamental physics.

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**Refreshments will be served beginning at 3:30pm in the Olin Lobby.