Entanglement in noncritical inhomogeneous quantum chains Articles uri icon

publication date

  • November 2021

start page

  • 1

end page

  • 15

issue

  • 19

volume

  • 104

International Standard Serial Number (ISSN)

  • 1098-0121

Electronic International Standard Serial Number (EISSN)

  • 1550-235X

abstract

  • We study an inhomogeneous critical Ising chain in a transverse field whose couplings decay exponentially from the center. In the strong inhomogeneity limit, we apply Fisher's renormalization group to show that the ground state is formed by concentric singlets similar to those of the rainbow state of the XX model. In the weak inhomogeneity limit, we map the model to a massless Majorana fermion living in a hyperbolic space-time, where, using conformal field theory techniques, we derive the entanglement entropy and show that it presents a linear scaling. We also study an inhomogeneous noncritical Ising model that for weak inhomogeneity is mapped to a massive Majorana fermion, while for strong inhomogeneity regime, it exhibits trivial and nontrivial topological phases and a separation between regions with high and low entanglement. We also present the entanglement Hamiltonian of the model.