Emergence of Long Period Antiferromagnetic Orders from Haldane Phase in S=1 Heisenberg Chains with D-Modulation

TL;DR

This study explores how spatial modulation of single-site anisotropy D in S=1 Heisenberg chains induces various antiferromagnetic orders, revealing new phases and orderings emerging from the Haldane phase.

Contribution

It demonstrates that D-modulation can freeze hidden order in the Haldane phase, leading to emergent long-period antiferromagnetic orders, extending understanding of phase transitions in spin chains.

Findings

Identification of multiple phases including Haldane, large-D, and Neel phases.

Emergence of long-period antiferromagnetic orders from hidden Haldane order.

Confirmation of phase behavior with longer D-modulation periods.

Abstract

The effect of spatial modulation of the single-site anisotropy D on the ground state of the S=1 Heisenberg chains is investigated. In the case of period 2 modulation, it is found that the phase diagram contains the Haldane phase, large-D phase, Neel phase of udud-type and u0d0-type. It is shown that the hidden antiferromagnetic order in the Haldane phase compatible with the spatial modulation of D-term get frozen resulting in the emergence of various types of Neel orders. The investigation of the model with longer period D-modulation also confirms this picture.