Quantum phase transitions driven by rhombic-type single-ion anisotropy in the S=1 Haldane chain

Abstract

The spin-1 Haldane chain is an example of the symmetry-protected-topological (SPT) phase in one dimension. Experimental realization of the spin chain materials usually involves both the uniaxial-type, $D(S^z{)}^2$, and the rhombic-type, $E[(S^x{)}^2-(S^y{)}^2]$, single-ion anisotropies. Here, we provide a precise ground-state phase diagram for spin-1 Haldane chain with these single-ion anisotropies. Using quantum numbers, we find that the ${\mathbb{Z}}_2$ symmetry breaking phase can be characterized by double degeneracy in the entanglement spectrum. Topological quantum phase transitions take place on particular paths in the phase diagram, from the Haldane phase to the Large-$E_x$, Large-$E_y$, or Large-$D$ phases. The topological critical points are determined by the level spectroscopy method with a newly developed parity technique in the density matrix renormalization group [Phys. Rev. B 86, 024403 (2012)], and the Haldane-Large-$D$ critical point is obtained with an unprecedentedly precision, $(D/J{)}_c=0.9684713(1)$. Close to this critical point, a small rhombic single-ion anisotropy $|E|/J\ll 1$ can destroy the Haldane phase and bring the system into a $y$-Néel phase. We propose that the compound [Ni(HF${}_2$)(3-Clpy)${}_4$]BF${}_4$ is a candidate system to search for the $y$-Néel phase.

Supplemental Material is included

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Cited by in corpus (18)

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• First Principle Study for Optical Properties of TMDC/Graphene Heterostructures
• A Near-Ideal Molecule-Based Haldane Spin-Chain
• Determining the anisotropy and exchange parameters of polycrystalline spin-1 magnets
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• High-pressure inelastic neutron scattering study of the anisotropic $S=1$ spin chain [Ni(HF${}_2$)(3-Clpyradine)${}_4$]BF${}_4$
• Reduced basis surrogates for quantum spin systems based on tensor networks
• Magnetic Phases of Spatially-Modulated Spin-1 Chains in Rydberg Excitons: Classical and Quantum Simulations
• Exploring quantum phase transitions by the cross derivative of the ground state energy
• Inelastic neutron scattering study of the anisotropic $S=1$ spin chain [Ni(HF${}_2$)(3-Clpyridine)${}_4$]BF${}_4$
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• Promising regimes for the observation of topological degeneracy in spin chains
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• Dynamically generated quadrupole polarization using Floquet adiabatic evolution
• Haldane phase, field-induced magnetic ordering and Tomonaga-Luttinger liquid behavior in a spin-one chain compound NiC${}_2$O${}_4$$\cdot$2NH${}_3$