The antiferromagnetic cross-coupled spin ladder: quantum fidelity and tensor networks approach

TL;DR

This paper uses tensor network states and quantum fidelity to analyze the phase diagram of an antiferromagnetic spin ladder, finding no evidence for the previously predicted columnar dimer phase and suggesting a simple phase boundary.

Contribution

It introduces a tensor network and fidelity-based approach to clarify the phase diagram of the antiferromagnetic spin ladder, resolving conflicting prior results.

Findings

No evidence for the columnar dimer phase.

The phase diagram likely has a single boundary between rung-singlet and Haldane phases.

Symmetry considerations support a simplified phase structure.

Abstract

We investigate the phase diagram of the cross-coupled Heisenberg spin ladder with antiferromagnetic couplings. For this model there have been conflicting results for the existence of the columnar dimer phase, which was predicted on the basis of weak coupling field theory renormalisation group arguments. The numerical work on this model has been based on various approaches, including exact diagonalization, series expansions and density-matrix renormalization group calculations. Using the recently developed tensor network states and ground-state fidelity approach for quantum spin ladders we find no evidence for the existence of the columnar dimer phase. We also provide an argument based on the symmetry of the Hamiltonian which suggests that the phase diagram for antiferromagnetic couplings consists of a single line separating the rung-singlet and Haldane phases.