Physical footprints of intrinsic sign problems

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The sign problem is a widespread numerical hurdle preventing us from simulating the equilibrium behaviour of many interesting models, most notably the Hubbard model. Research aimed at solving the sign problem, via various clever manipulations, has been thriving for a long time with various recent exciting results. The complementary question, of whether some phases of matter forbid the existence of any sign-free microscopic model, has received attention only recently. In this talk, I’ll review recent progress and discuss a novel and quite general criteria we obtained for when a topological quantum field theory has no sign-free microscopic model. I’ll also point out relations to sign problems in frustrated magnets and to the notion of quantum supremacy.