Bulk-edge correspondence in the Haldane phase of the bilinear-biquadratic spin-1 Hamiltonian Articles uri icon

publication date

  • May 2021

start page

  • 053102

end page

  • 053131

issue

  • 5

volume

  • 2021

International Standard Serial Number (ISSN)

  • 1742-5468

abstract

  • The Haldane phase is the prototype of symmetry protected topological (SPT) phases of spin chain systems. It can be protected by several symmetries having in common the degeneracy of the entanglement spectrum (ES). Here we explore in depth this degeneracy for the spin-1 Affleck-Kennedy-Lieb-Tasaki and bilinear-biquadratic Hamiltonians and show the emergence of a bulk-edge correspondence that relates the low energy properties of the entanglement Hamiltonian of a periodic chain and that of the physical Hamiltonian of an open chain. We find that the ES can be described in terms of two spins-1/2 behaving as the effective spins at the end of the open chain. In the case of non-contiguous partitions, we find that the entanglement Hamiltonian is given by the spin-1/2 Heisenberg Hamiltonian, which suggests a relationship between SPT phases and conformal field theory. We finally investigate the string order parameter and the relation with the bulk-edge correspondence.

keywords

  • entanglement in topological phase, quantum information, topological; phases of matter, density matrix renormalisation group