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Publication Detail
Uncomputability of phase diagrams
  • Publication Type:
    Journal article
  • Publication Sub Type:
  • Authors:
    Bausch J, Cubitt TS, Watson JD
  • Publication date:
  • Journal:
    Nature Communications
  • Volume:
  • Issue:
  • Status:
© 2021, The Author(s). The phase diagram of a material is of central importance in describing the properties and behaviour of a condensed matter system. In this work, we prove that the task of determining the phase diagram of a many-body Hamiltonian is in general uncomputable, by explicitly constructing a continuous one-parameter family of Hamiltonians H(φ), where φ∈ R, for which this is the case. The H(φ) are translationally-invariant, with nearest-neighbour couplings on a 2D spin lattice. As well as implying uncomputablity of phase diagrams, our result also proves that undecidability can hold for a set of positive measure of a Hamiltonian’s parameter space, whereas previous results only implied undecidability on a zero measure set. This brings the spectral gap undecidability results a step closer to standard condensed matter problems, where one typically studies phase diagrams of many-body models as a function of one or more continuously varying real parameters, such as magnetic field strength or pressure.
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