@article{TEXTUAL,
      recid = {11695},
      author = {Lapa, Matthew F.},
      title = {Topology of superconductors beyond mean-field theory},
      journal = {Physical Review Research},
      address = {2020-08-26},
      number = {TEXTUAL},
      abstract = {The study of topological superconductivity is largely  based on the analysis of mean-field Hamiltonians that  violate particle number conservation and have only  short-range interactions. Although this approach has been  very successful, it is not clear that it captures the  topological properties of real superconductors, which are  described by number-conserving Hamiltonians with long-range  interactions. To address this issue, we study topological  superconductivity directly in the number-conserving  setting. We focus on a diagnostic for topological  superconductivity that compares the fermion parity P of the  ground state of a system in a ring geometry and in the  presence of zero versus  Φ&lt;sub&gt;sc&lt;/sub&gt;=h/2e ≡ π flux of an  external magnetic field. A version of this diagnostic  exists in any dimension and provides a Z&lt;sub&gt;2&lt;/sub&gt;  -invariant ν = P&lt;sub&gt;0&lt;/sub&gt;P&lt;sub&gt;π&lt;/sub&gt; for topological  superconductivity. In this paper, we prove that the  mean-field approximation correctly predicts the value of ν  for a large family of number-conserving models of spinless  superconductors. Our result applies directly to the cases  of greatest physical interest, including p-wave and  p&lt;sub&gt;x&lt;/sub&gt; + ip&lt;sub&gt;y&lt;/sub&gt; superconductors in one and  two dimensions, and gives strong evidence for the validity  of the mean-field approximation in the study of (at least  some aspects of) topological superconductivity.},
      url = {http://knowledge.uchicago.edu/record/11695},
}