Quantum Entanglement and Topological Order in Hole-Doped Valence Bond Solid States

Abstract

We present a detailed analysis of topological properties of the valence bond solid (VBS) states doped with fermionic holes. As concrete examples, we consider the supersymmetric extension of the SU(2)- and the SO(5) VBS states, dubbed UOSp(1|2) and UOSp(1|4) supersymmetric VBS states, respectively. Specifically, we investigate the string-order parameters and the entanglement spectra of these states to find that, even when the parent states (bosonic VBS states) do not support the string order, they recover it when holes are doped and the fermionic sector appears in the entanglement spectrum. These peculiar properties are discussed in light of the symmetry-protected topological order. To this end, we characterize a few typical classes of symmetry-protected topological orders in terms of supermatrix-product states (SMPS). From this, we see that the topological order in the bulk manifests itself in the transformation properties of the SMPS in question and thereby affects the structure of the entanglement spectrum. Then, we explicitly relate the existence of the string order and the structure of the entanglement spectrum to explain the recovery and the stabilization of the string order in the supersymmetric systems.

22 pages, 12 figures, supplementary material is available upon request, minor corrections

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Cited by in corpus (10)

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• Momentum-Space Entanglement Spectrum of Bosons and Fermions with Interactions
• Phase diagrams of one-dimensional half-filled two-orbital SU(N) cold fermions systems
• Symmetry-protected topological phases in two-leg SU(N) spin ladder with unequal spins
• Ferromagnetism in the SU(N) Kondo lattice model -- SU(N) double exchange and supersymmetry
• "Haldane" phases with ultracold fermionic atoms in double-well optical lattices
• Long-range magnetic order and interchain interactions in the $S=2$ chain system MnCl${}_3$(bpy)
• Antiferromagnetic Ordering in MnF(salen)
• Interrelations among frustration-free models via Witten's conjugation
• Computational Characterization of Symmetry-Protected Topological Phases in Open Quantum Systems