Ground-state fidelity of the spin-1 Heisenberg chain with single ion anisotropy: quantum renormalization group and exact diagonalization approaches

TL;DR

This paper investigates the phase diagram of the spin-1 Heisenberg chain with single ion anisotropy using ground-state fidelity and numerical methods, identifying phase boundaries and topological phases.

Contribution

It introduces a quantum renormalization group approach to determine phase boundaries and employs exact diagonalization with a non-local order parameter for phase transition detection.

Findings

Phase boundaries between Néel, Haldane, and large-D phases identified.

Quantum renormalization group effectively traces symmetry-protected topological phases.

Accurate location of Haldane to large-D phase transition using non-local order parameter.

Abstract

We study the phase diagram of the anisotropic spin-1 Heisenberg chain with single ion anisotropy (D) using a ground-state fidelity approach. The ground-state fidelity and its corresponding susceptibility are calculated within the quantum renormalization group scheme where we obtained the renormalization of fidelity preventing to calculate the ground state. Using this approach, the phase boundaries between the antiferromagnetic N\'{e}el, Haldane and large-D phases are obtained for the whole phase diagram, which justifies the application of quantum renormalization group to trace the symmetery protected topological phases. In addition, we present numerical exact diagonalization (Lanczos) results in, which we employ a recently introduced non-local order parameter to locate the transition from Haldane to large-D phase accurately.