Progress of Theoretical Physics Supplement

Magnetic Phases and Long-Range Ordering of the Haldane System in High Magnetic Fields

Isao Harada, Yoshihiro Nishiyama

Published Jan 1, 2002• 2 citations

Abstract

Critical properties of field-induced magnetic phases are investigated in the one-dimensional S=1 Haldane system with planar anisotropy, using the finite-temperature density-matrix renormalization group method. We point out that the underlying physics of the properties differs significantly between cases of different field directions: The magnetic phase is characterized as the gapless Tomonaga-Luttinger regime in one case and as the gapful soliton regime in the other. In connection with the information obtained for the one-dimensional spin chain, possible implications for the field-induced magnetic long-range ordering are discussed.

DOI: 10.1143/ptps.145.107

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Progress of Theoretical Physics Supplement

Magnetic Phases and Long-Range Ordering of the Haldane System in High Magnetic Fields

Isao Harada, Yoshihiro Nishiyama

Published Jan 1, 2002• 2 citations

Publisher

Abstract

DOI: 10.1143/ptps.145.107

Related papers

Spin-Reorientation Transition of Field-Induced Magnetic Ordering Phases in the Anisotropic Haldane System

Hiroshi Miyazaki, Tomohiko Hiwasa, Masataka Oko +1 more

A possible spin-reorientation transition in field-induced magnetic ordering phases of the S=1 Haldane system with large easy-plane anisotropy is proposed, using an effective Lagrangian formalism as well as the density matrix renormalization group method. Such a spin-reorientation transition is predicted in the case where the applied magnetic field is inclined from the easy axis of the anisotropy. We point out that this transition has a close connection with a variation of the order parameter even at zero temperature, although it is different from a quantum analog of the so-called spin-flop transition proposed for the system having a strong easy axis anisotropy. In connection with a novel phase observed recently in the Haldane system at high fields, we discuss possible implications for the field-induced magnetic ordering.A possible spin-reorientation transition in field-induced magnetic ordering phases of the S=1 Haldane system with large easy-plane anisotropy is proposed, using an effective Lagrangian formalism as well as the density matrix renormalization group method. Such a spin-reorientation transition is predicted in the case where the applied magnetic field is inclined from the easy axis of the anisotropy. We point out that this transition has a close connection with a variation of the order parameter even at zero temperature, although it is different from a quantum analog of the so-called spin-flop transition proposed for the system having a strong easy axis anisotropy. In connection with a novel phase observed recently in the Haldane system at high fields, we discuss possible implications for the field-induced magnetic ordering.

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Haldane phase, field-induced magnetic ordering, and Tomonaga-Luttinger liquid behavior in the spin-one chain compound NiC 2 O 4 · 2 NH 3

Shuo Li, Zhanlong Wu, Yanhong Wang +12 more

The Haldane phase is a celebrated example of a magnetic topological phase but rarely reported in materials. The authors show here an NMR study on the spin-1 chain magnet NiC ${}_{2}$ O ${}_{4}$ \ifmmode\cdot\else\textperiodcentered\fi{}2NH ${}_{3}$ , which determines its ground state to be a Haldane phase at zero field. An applied magnetic field induces a magnetic ordering at low temperatures and a Tomonaga-Luttinger liquid phase above the ordering temperature with attractive fermionic interactions.The Haldane phase is a celebrated example of a magnetic topological phase but rarely reported in materials. The authors show here an NMR study on the spin-1 chain magnet NiC${}_{2}$O${}_{4}$\ifmmode\cdot\else\textperiodcentered\fi{}2NH${}_{3}$, which determines its ground state to be a Haldane phase at zero field. An applied magnetic field induces a magnetic ordering at low temperatures and a Tomonaga-Luttinger liquid phase above the ordering temperature with attractive fermionic interactions.

arXiv:2411.19538Physical review. B./Physical review. BMay 29, 20251 citation

We use the dynamical density matrix renormalization group technique to show that the high-energy part of the spectrum of an

S=1

Heisenberg chain, placed in a strong external magnetic field

H

exceeding the Haldane gap $\ensuremath{\Delta}$, contains edge singularities, similar to those known to exist in the low-energy spectral response. It is demonstrated that in the frequency range $\ensuremath{\omega}\ensuremath{\gtrsim}\ensuremath{\Delta}$ the longitudinal (with respect to the applied field) dynamical structure factor is dominated by the power-law singularity ${S}^{\ensuremath{\Vert}}(q=\ensuremath{\pi},\ensuremath{\omega})\ensuremath{\propto}{(\ensuremath{\omega}\ensuremath{-}{\ensuremath{\omega}}_{0})}^{\ensuremath{-}{\ensuremath{\alpha}}^{\ensuremath{'}}}$. We study the behavior of the high-energy edge exponent ${\ensuremath{\alpha}}^{\ensuremath{'}}$ and the edge ${\ensuremath{\omega}}_{0}$ as functions of the magnetic field. The existence of edge singularities at high energies is directly related to the Tomonaga-Luttinger liquid character of the ground state at $H>\ensuremath{\Delta}$ and is expected to be a general feature of one-dimensional gapped spin systems in high magnetic fields.

We use inelastic neutron scattering to measure magnetic fluctuations as a function of transverse magnetic field and temperature in a single crystal of the coupled Haldane chain compound

\mathrm{SrNi}{}_{2}{\text{V}}_{2}{\text{O}}_{8}

with uniaxial anisotropy. At the base temperature (2 K), spin excitations confirm a field-induced quantum phase transition from the disordered Haldane (gapped singlet) state to a gapped long-range ordered state through a quantum critical point (QCP) (${\ensuremath{\mu}}_{0}{H}_{c}\ensuremath{\approx}11.5$ T). At elevated temperatures in the vicinity of the QCP, both the energy and linewidth of the lowest triplet mode scale linearly with temperature, in accordance with quantum criticality. We also demonstrate that the experimental field dependence of the triplet excitation modes at the base temperature is in agreement with the bosonic and macroscopic models, but is in contrast to the fermionic and perturbative models.

Motivated by intense research on two-dimensional spin-

\frac{1}{2}

Kitaev materials, Kitaev spin chains and ladders, though geometrically limited, have been studied for their numerical simplicity and insights into extended Kitaev models. The phase diagrams under the magnetic field were also explored for these quasi-one-dimensional models. For an isotropic Kitaev chain, it was found that a magnetic field polarizes the ground state except along the symmetric field angle, where the chain is found to remain gapless up to a critical field strength where it enters an intriguing soliton phase before reaching the polarized state at higher field strengths. Here we study an anisotropic Kitaev chain under a magnetic field using the density matrix renormalization group technique, where the ground state has a macroscopic degeneracy with a finite gap in the absence of the magnetic field. When the field is mainly aligned parallel to the strong bond, four-site and large unit-cell ordered phases arise. In a certain angle of the field, another ordered phase characterized by a uniform chirality with six-site periodicity emerges. We employ a perturbation theory to understand such field-induced ordered phases. The effective model uncovers the presence of transverse Ising and Dzyaloshinskii-Moriya interactions between unit cells, as well as further-neighbor Ising interaction induced by the magnetic field, which collectively explain the mechanisms behind these ordered states. Open questions and challenges are also discussed.

The Haldane phase is a celebrated example of a magnetic topological phase but rarely reported in materials. The authors show here an NMR study on the spin-1 chain magnet NiC

{}_{2}

{}_{4}

\ifmmode\cdot\else\textperiodcentered\fi{}2NH

{}_{3}

, which determines its ground state to be a Haldane phase at zero field. An applied magnetic field induces a magnetic ordering at low temperatures and a Tomonaga-Luttinger liquid phase above the ordering temperature with attractive fermionic interactions.