Revision 2

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Title · changed: Revision 1: Which phases of matter carry an intrinsic sign problem; Revision 2: Which phases of matter carry an intrinsic sign problem?
Plain: Many phases of matter with one-way edge currents provably cannot be simulated sign-free by any model built from local terms. Which other phases share this obstruction is open.
Precise: Ringel and Kovrizhin (2017) and Golan, Smith and Ringel (2020) showed that chiral topological phases for which exp(2 pi i c/24) (c the chiral central charge) differs from every topological spin cannot be realized by any local sign-free Hamiltonian. Determine whether non-chiral topological orders, gapless phases (e.g. non-Fermi liquids or Fermi surfaces with nontrivial Luttinger volume) or symmetry-enriched phases carry intrinsic sign problems, and give a complete criterion. An answer is a classification with proofs.
Settled by: A theorem extending the chiral criterion to all gapped phases, or explicit sign-free local models for the remaining phases.
Kind: well-posed
Answer type: classification
References: (empty)
Literature status: partially-resolved
Status note: The chiral case covered by the topological-spin criterion was settled by 2020; non-chiral and gapless cases remain open.
Posed since: 2017

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