Entanglement spectrum of a topological phase in one dimension

By Frank Pollmann, Erez Berg, Ari M. Turner, M. Oshikawa. 2009

918 citations recorded by the source corpus.

We show that the Haldane phase of S=1 chains is characterized by a double degeneracy of the entanglement spectrum. The degeneracy is protected by a set of symmetries (either the dihedral group of $\pi$-rotations about two orthogonal axes, time-reversal symmetry, or bond centered inversion symmetry), and cannot be lifted unless either a phase boundary to another, "topologically trivial", phase is crossed, or the symmetry is broken. More generally, these results offer a scheme to classify gapped phases of one dimensional systems. Physically, the degeneracy of the entanglement spectrum can be observed by adiabatically weakening a bond to zero, which leaves the two disconnected halves of the system in a finitely entangled state.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/e181cdbc3110c2e1a9e4931cde5d55fc371349ee

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

Citations in the corpus

Long-Range Entanglement from Measuring Symmetry-Protected Topological Phases (2021, background): “Its Hamiltonian is a just nearest-neighbor antiferromagnetic coupling: This spin chain is known to be gapped [127], forming a nontrivial SPT phase for the Z 2 × Z 2 group of π -rotations generated by R γ = n e iπS γn with γ = x, y, z [21, 126, 128, 129].”
Quantum Information Meets Quantum Matter (2015, background): “Readers interested in these recent developments could refer to the review articles [16] and [19].”
Gapped boundary phases of topological insulators via weak coupling (2016, background): “Yet subtle features of the bulk physics force nontrivial behavior on the boundary of a material that is in an SPT phase.”
Symmetric Gapped Interfaces of SPT and SET States: Systematic Constructions (2017, background): “Since SPT states are equivalent to simple product states if we remove their global symmetry, one quickly obtained their classification in 1+1D [9–11], in terms of projective representations [12] of the symmetry group G.”
Classification of Interacting Topological Floquet Phases in One Dimension (2016, methodology): “system with open boundary conditions [32,42].”