Geometric complexity in quantum matter: intrinsic sign problems in topological phases

Abstract: The infamous sign problem leads to an exponential complexity in Monte Carlo simulations of generic many-body quantum systems. Nevertheless, many phases of matter are known to admit a sign-problem-free representative, allowing efficient simulations on classical computers. Motivated by long standing open problems in many-body physics, as well as fundamental questions in quantum complexity, the possibility of intrinsic sign problems, where a phase of matter admits no sign-problem-free representative, was recently raised but remains largely unexplored. I will describe results establishing the existence, and the geometric origin, of intrinsic sign problems in a broad class of topological phases in 2+1 dimensions. Within this class, these results exclude the possibility of 'stoquastic' Hamiltonians for bosons, and of sign-problem-free determinantal Monte Carlo algorithms for fermions. The talk is based on Phys. Rev. Research 2, 043032 and 033515.

condensed mattermathematical physics

Audience: researchers in the topic

Quantum Matter meets Maths (IST, Lisbon)

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