Entropic topological invariant for a gapped one-dimensional system

Abstract

We propose an order parameter for a general one-dimensional gapped system with an open boundary condition. The order parameter can be computed from the ground state entanglement entropy of some regions near one of the boundaries. Hence, it is well-defined even in the presence of arbitrary interaction and disorder. We also show that it is invariant under a finite-depth local quantum circuit, suggesting its stability against an arbitrary local perturbation that does not close the energy gap. Further, it can unambiguously distinguish Majorana chain from a trivial chain under a global fermion parity conservation. We argue that the order parameter can be in principle measured in an optical lattice system.

5pages, 6 figures, minor changes. published version

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Cited by in corpus (7)

• Quantum circuit complexity of one-dimensional topological phases
• Entanglement topological invariants for one-dimensional topological superconductors
• Detecting edge degeneracy in interacting topological insulators through entanglement entropy
• Symmetry-Protected Topological Entanglement
• Characterizing the Bulk-Boundary Correspondence of one-dimensional non-Hermitian interacting systems by edge entanglement entropy
• Nonlocal Entanglement of 1D Thermal States Induced by Fermion Exchange Statistics
• Entanglement and edge effects in superpositions of many-body Fock states with spatial constraints