Quantum phase transitions to topological Haldane phases in spin-one chains studied by linked-cluster expansions

TL;DR

This paper employs linked-cluster expansions to study quantum phase transitions between trivial and topological Haldane phases in spin-one chains, analyzing critical points and exponents for different models.

Contribution

It introduces a detailed perturbative approach to identify phase transitions and critical behavior in spin-one chains with topological phases.

Findings

Linked-cluster expansions effectively locate critical points in dimerized chains.

The method's effectiveness varies with the model's correlation length.

Extrapolation works well for dimerized chains but not for anisotropic chains.

Abstract

We use linked-cluster expansions to analyze the quantum phase transitions between symmetry unbroken trivial and topological Haldane phases in two different spin-one chains. The first model is the spin-one Heisenberg chain in the presence of a single-ion anisotropy while the second one is the dimerized spin-one Heisenberg chain. For both models we determine the ground-state energy and the one-particle gap inside the non-topological phase as a high-order series using perturbative continuous unitary transformations. Extrapolations of the gap series are applied to locate the quantum critical point and to extract the associated critical exponent. We find that this approach works unsatisfactory for the anisotropic chain, since the quality of the extrapolation appears insufficient due to the large correlation length exponent. In contrast, extrapolation schemes display very good convergence for the gap closing in the case of the dimerized spin-one Heisenberg chain.