Ground-state search as an optimization problem

A central goal in quantum many-body physics has been to identify microscopic models that realize new phases of matter. In the first part of this talk, we will discuss a simple 1D lattice model hosting distinct quantum phases, for which we will discuss emergent collective phenomena and delineate the phase diagram. Our goal will be to gain intuition through simple arguments and diagrams for how strongly correlated systems can be exactly solved for a few particles, both numerically and analytically. In the second part of this talk, we introduce a systematic approach for targeted, gradient-based phase discovery. Given a phase of interest, we define a “target-phase loss function”, which encodes sharp features of choice of the targeted quantum state. This replaces exhaustive phase search with a differentiable optimization problem in the space of Hamiltonian parameters. The method is broadly applicable to a wide range of symmetry-broken and topological orders and can be interfaced with most numerical solvers. We demonstrate our method in action across diverse settings, including charge-density waves and fractional quantum Hall states. No background in many-body physics will be assumed.