Strange correlators for topological quantum systems from bulk-boundary correspondence

Abstract

"Strange" correlators provide a tool to detect topological phases arising in many-body models by computing the matrix elements of suitably defined two-point correlations between the states under investigation and trivial reference states. Their effectiveness depends on the choice of the adopted operators. In this paper we give a systematic procedure for this choice, discussing the advantages of choosing operators using the bulk-boundary correspondence of the systems under scrutiny. Via the scaling exponents, we directly relate the algebraic decay of the strange correlators with the scaling dimensions of gapless edge modes operators. We begin our analysis with lattice models hosting symmetry-protected topological phases and we analyze the sums of the strange correlators, pointing out that integrating their moduli substantially reduces cancellations and finite-size effects. We also analyze instances of systems hosting intrinsic topological order, as well as strange correlators between states with different nontrivial topologies. Our results for both translational and non-translational invariant cases, and in presence of on-site disorder and long-range couplings, extend the validity of the strange correlators approach for the diagnosis of topological phases of matter, and indicate a general procedure for their optimal choice.

28 pages, 10 figures

References in corpus (12)

• Surface codes: Towards practical large-scale quantum computation
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Kitaev chains with long-range pairing
• Multipartite entanglement in topological quantum phases
• Finite-size energy gap in weak and strong topological insulators
• Symmetry-protected sign problem and magic in quantum phases of matter
• Topological aspects of the critical three-state Potts model
• Strange correlations in spin-1 Heisenberg antiferromagnets
• Detecting Subsystem Symmetry Protected Topological Order Through Strange Correlators
• Field theory of symmetry-protected valence bond solid states in (2+1) dimensions
• Softening of Majorana edge states by long-range couplings
• Finite-size scaling analysis of two-dimensional deformed Affleck-Kennedy-Lieb-Tasaki states

Cited by in corpus (5)

• Universal structure of measurement-induced information in many-body ground states
• Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems
• Higher-Order Cellular Automata Generated Symmetry-Protected Topological Phases and Detection Through Multi-Point Strange Correlators
• Can multipartite entanglement be characterized by two-point connected correlation functions ?
• Spurious Strange Correlators in Symmetry-Protected Topological Phases