The ‘strange’ correlator provides a tool to detect phase phases occurring in many-body models by computing the matrix elements of a well-defined two-point correlation between the state under investigation and a trivial reference state. Offers. Their effectiveness depends on the choice of operators employed. In this paper, we present a systematic procedure for this selection and discuss the advantages of selecting operators using the bulk boundary correspondence of the system under scrutiny. Via the scaling exponent, we directly relate the algebraic decay of the queer correlator to the scaling dimension of the gapless edge-mode operator. We start our analysis from a lattice model that hosts a symmetry-protected topological phase, analyze the sum of queer correlators, and point out that integrating their coefficients significantly reduces cancellation and finite-size effects. increase. We also analyze instances of systems that host intrinsic topological order and strange correlations between states with different nontrivial topologies. Our results for both translation-invariant and non-translation-invariant cases, and in the presence of on-site disturbances and long-range couplings, extend the effectiveness of the queer correlator approach for diagnosing topological phases of matter. , which shows the general procedure for those best choices.

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