Strange Correlator for 1D Fermionic Symmetry-Protected Topological Phases

TL;DR

This paper demonstrates that strange correlators, combining fermionic and bosonic operators, effectively diagnose 1D fermionic symmetry-protected topological phases by exhibiting long-range order in topologically nontrivial cases.

Contribution

It introduces a method to diagnose 1D fermionic SPT phases using combined strange correlators and transfer matrix analysis, extending previous approaches.

Findings

Strange correlators show long-range order in nontrivial topological phases.

The method applies transfer matrix analysis to classify phases.

Concrete examples validate the approach.

Abstract

Strange correlators are useful tools for diagnosing symmetry-protected topological states from their bulk wave functions. We study strange correlators for one-dimensional fermionic symmetry-protected topological states using fixed-point wave functions, and show that a combination of strange correlators constructed using fermion annihilation operators and bosonic order parameters can fully diagnose the classification from such wave functions. By converting the strange correlator to a correlation in a one-dimensional statistical problem described by transfer matrices, we show that when the wave function is topologically nontrivial, the corresponding strange correlator exhibits a long-range-order behavior, which can be analyzed from the symmetry properties of the transfer matrices constructed from the fixed-point wave function. Our general argument is demonstrated by several concrete examples.