Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1112.5531 · Physical Review B

Thermodynamic properties of quantum sine-Gordon spin chain system KCuGaF 6

Izumi Umegaki, Hidekazu Tanaka, Toshio Ono, Masaki Oshikawa, Kazumitsu Sakai

Published Apr 24, 2012• 15 citations
arXivHTMLPDF

Abstract

We investigated the thermodynamic properties of the spin-1/2 one-dimensional Heisenberg antiferromagnet KCuGaF${}_{6}$ by measuring the specific heat in magnetic fields. When this compound is subjected to a uniform magnetic field $\mathbit{H}$, a transverse staggered magnetic field $\mathbit{h}$ is induced in this compound owing to the staggered component of the $\mathbit{g}$ tensor and the Dzyaloshinskii-Moriya interaction with an alternating $\mathbit{D}$ vector. Consequently, the quantum sine-Gordon (SG) model is an effective model of this compound in a uniform magnetic field. In three different field directions, we observed a magnetic-field-induced gap, which increases with $H$. We analyzed experimental results using specific heat theory based on quantum SG theory. The thermodynamic property for $H\phantom{\rule{0.16em}{0ex}}\ensuremath{\parallel}\phantom{\rule{0.16em}{0ex}}c$ is very well described in terms of the elementary excitations characteristic of the quantum SG model, while for the other field directions significant contributions from other excitation modes beyond the framework of the quantum SG model were observed. For $H\phantom{\rule{0.16em}{0ex}}\ensuremath{\parallel}\phantom{\rule{0.16em}{0ex}}b$, a quantum phase transition between gapless and gapped ground states was observed.

DOI
10.1103/physrevb.85.144423

Related papers

Spin Dynamics in Quantum Sine-Gordon Spin Chains: High-Field ESR Studies

Sergei A. Zvyagin

Abstract A spin-1/2 Heisenberg antiferromagnetic chain is one of the most important paradigmatic models in quantum magnetism. Its ground state is a spin singlet, while the excitation spectrum is formed by gapless fractional excitations, spinons. The presence of alternating g-tensors and/or the staggered Dzyaloshinskii-Moriya interaction results in opening the energy gap $$\varDelta \propto H^{2/3}$$ Δ ∝ H 2 / 3 , once the magnetic field H is applied. A fairly good understanding of this phenomenon was achieved in the framework of the sine-Gordon quantum-field theory, taking into account the effective transverse staggered field induced by the applied uniform field. The theory predicts solitons and antisolitons as elementary excitations, as well as their bound states, breathers. Here, I review recent high-field electron spin resonance spectroscopy studies of such systems, focusing on peculiarities of their spin dynamics in the sine-Gordon regime and beyond.

Applied Magnetic Resonance•Feb 24, 2021•5 citations

Spinon, soliton and breather in the spin-1/2 antiferromagnetic chain KCuGaF$_6$

Izumi Umegaki, Hidekazu Tanaka, Nobuyuki Kurita +7 more

Elementary excitations of the S=1/2 one-dimensional antiferromagnet KCuGaF_6 were investigated by inelastic neutron scattering in zero and finite magnetic fields perpendicular to the (1, 1, 0) plane combined with specific heat measurements. KCuGaF$_6$ exhibits no long-range magnetic ordering down to 50 mK despite the large exchange interaction J/k_B=103 K. At zero magnetic field, well-defined spinon excitations were observed. The energy of the des Cloizeaux and Pearson mode of the spinon excitations is somewhat larger than that calculated with the above exchange constant. This discrepancy is mostly ascribed to the effective XY anisotropy arising from the large Dzyaloshinsky-Moriya interaction with an alternating D vector. KCuGaF_6 in a magnetic field is represented by the quantum sine-Gordon model, for which low-energy elementary excitations are composed of solitons, antisolitons and their bound states called breathers. Unlike the theoretical prediction, it was found that the energy of a soliton is smaller than that of the first breather, although the energy of the first breather coincides with that observed in a previous ESR measurement.

arXiv:1510.08200•Oct 28, 2015•0 citations

Field-induced gap in Cu benzoate and other S=12 antiferromagnetic chains

Ian K. Affleck, Masaki Oshikawa

Recent experiments on the $S=\frac{1}{2}$ antiferromagnetic chain compound, Cu benzoate, discovered an unexpected gap scaling as approximately the $\frac{2}{3}$ power of an applied magnetic field. A theory of this gap, based on an effective staggered field, orthogonal to the applied uniform field, resulting from a staggered gyromagnetic tensor and a Dzyaloshinskii-Moriya interaction, leading to a sine-Gordon quantum field theory, has been developed. Here we discuss many aspects of this subject in considerable detail, including a review of the $S=\frac{1}{2}$ chain in a uniform field, a spin-wave theory analysis of the uniform plus staggered field problem, exact amplitudes for the scaling of gap, staggered susceptibility and staggered magnetization with field or temperature, intensities of soliton and breather peaks in the structure function, and field and temperature dependence of the total susceptibility.

arXiv:cond-mat/9905002•Physical review. B, Condensed matter•Jul 1, 1999•309 citations

Thermodynamic Properties of theS=1/2 Heisenberg Chain with Staggered Dzyaloshinsky–Moriya Interaction

Naokazu Shibata, Kazuo Ueda

Thermodynamic properties of the S=1/2 Heisenberg chain in transverse staggered magnetic field H^y_s and uniform magnetic field H^x perpendicular to the staggered field is studied by the finite-temperature density-matrix renormalization-group method. The uniform and staggered magnetization and specific heat are calculated from zero temperature to high temperatures up to T/J=4 under various strength of magnetic fields from H^y_s/J, H^x/J=0 to 2.4. The specific heat and magnetization of the effective Hamiltonian of the Yb_4As_3 are also presented, and field induced gap formation and diverging magnetic susceptibility at low temperature are shown.

arXiv:cond-mat/0107561•Journal of the Physical Society of Japan•Dec 15, 2001•33 citations

Spinon, soliton, and breather in the spin- 12 antiferromagnetic chain compound KCuGaF6

Izumi Umegaki, Hidekazu Tanaka, Nobuyuki Kurita +7 more

Elementary excitations of the $S=\frac{1}{2}$ one-dimensional antiferromagnet ${\mathrm{KCuGaF}}_{6}$ were investigated by inelastic neutron scattering in zero and finite magnetic fields perpendicular to the $(1,1,0)$ plane combined with specific heat measurements. ${\mathrm{KCuGaF}}_{6}$ exhibits no long-range magnetic ordering down to 50 mK despite the large exchange interaction $J/{k}_{\mathrm{B}}=103$ K. At zero magnetic field, well-defined spinon excitations were observed. The energy of the des Cloizeaux and Pearson [J. des Cloizeaux and J. J. Pearson, Phys. Rev. 128, 2131 (1962)] mode of the spinon excitations is somewhat larger than that calculated with the above exchange constant. This discrepancy is mostly ascribed to the effective $XY$ anisotropy arising from the large Dzyaloshinsky-Moriya [T. Moriya, Phys. Rev. 120, 91 (1960)] interaction with an alternating $\mathbit{D}$ vector. ${\mathrm{KCuGaF}}_{6}$ in a magnetic field is represented by the quantum sine-Gordon model, for which low-energy elementary excitations are composed of solitons and antisolitons and their bound states called breathers. Unlike the theoretical prediction, it was found that the energy of a soliton is smaller than that of the first breather, although the energy of the first breather coincides with that observed in a previous electron spin resonance measurement.

Physical Review B•Nov 9, 2015•22 citations

Field-induced gap in a quantum spin- 12 chain in a strong magnetic field

Sergei A. Zvyagin, Erik Čižmár, Mykhaylo Ozerov +4 more

Magnetic excitations in copper pyrimidine dinitrate, a spin-1/2 antiferromagnetic chain with alternating $g$-tensor and Dzyaloshinskii-Moriya interactions that exhibits a field-induced spin gap, are probed by means of pulsed-field electron-spin-resonance spectroscopy. In particular, we report on a minimum of the gap in the vicinity of the saturation field ${H}_{\mathrm{sat}}=48.5$ T associated with a transition from the sine-Gordon region (with soliton-breather elementary excitations) to a spin-polarized state (with magnon excitations). This interpretation is fully confirmed by the quantitative agreement over the entire field range of the experimental data with the density matrix renormalization group calculations for a spin-1/2 Heisenberg chain with a staggered transverse field.

arXiv:1010.6141•Physical Review B•Feb 22, 2011•24 citations
We investigated the thermodynamic properties of the spin-1/2 one-dimensional Heisenberg antiferromagnet KCuGaF6{}_{6}6​ by measuring the specific heat in magnetic fields. When this compound is subjected to a uniform magnetic field \mathbitH\mathbit{H}\mathbitH, a transverse staggered magnetic field \mathbith\mathbit{h}\mathbith is induced in this compound owing to the staggered component of the \mathbitg\mathbit{g}\mathbitg tensor and the Dzyaloshinskii-Moriya interaction with an alternating \mathbitD\mathbit{D}\mathbitD vector. Consequently, the quantum sine-Gordon (SG) model is an effective model of this compound in a uniform magnetic field. In three different field directions, we observed a magnetic-field-induced gap, which increases with HHH. We analyzed experimental results using specific heat theory based on quantum SG theory. The thermodynamic property for H\ensuremath∥cH\phantom{\rule{0.16em}{0ex}}\ensuremath{\parallel}\phantom{\rule{0.16em}{0ex}}cH\ensuremath∥c is very well described in terms of the elementary excitations characteristic of the quantum SG model, while for the other field directions significant contributions from other excitation modes beyond the framework of the quantum SG model were observed. For H\ensuremath∥bH\phantom{\rule{0.16em}{0ex}}\ensuremath{\parallel}\phantom{\rule{0.16em}{0ex}}bH\ensuremath∥b, a quantum phase transition between gapless and gapped ground states was observed.
Abstract A spin-1/2 Heisenberg antiferromagnetic chain is one of the most important paradigmatic models in quantum magnetism. Its ground state is a spin singlet, while the excitation spectrum is formed by gapless fractional excitations, spinons. The presence of alternating g-tensors and/or the staggered Dzyaloshinskii-Moriya interaction results in opening the energy gap Δ∝H2/3\varDelta \propto H^{2/3}Δ∝H2/3 Δ ∝ H 2 / 3 , once the magnetic field H is applied. A fairly good understanding of this phenomenon was achieved in the framework of the sine-Gordon quantum-field theory, taking into account the effective transverse staggered field induced by the applied uniform field. The theory predicts solitons and antisolitons as elementary excitations, as well as their bound states, breathers. Here, I review recent high-field electron spin resonance spectroscopy studies of such systems, focusing on peculiarities of their spin dynamics in the sine-Gordon regime and beyond.
Spinon, soliton and breather in the spin-1/2 antiferromagnetic chain KCuGaF6_66​
Elementary excitations of the S=1/2 one-dimensional antiferromagnet KCuGaF_6 were investigated by inelastic neutron scattering in zero and finite magnetic fields perpendicular to the (1, 1, 0) plane combined with specific heat measurements. KCuGaF6_66​ exhibits no long-range magnetic ordering down to 50 mK despite the large exchange interaction J/k_B=103 K. At zero magnetic field, well-defined spinon excitations were observed. The energy of the des Cloizeaux and Pearson mode of the spinon excitations is somewhat larger than that calculated with the above exchange constant. This discrepancy is mostly ascribed to the effective XY anisotropy arising from the large Dzyaloshinsky-Moriya interaction with an alternating D vector. KCuGaF_6 in a magnetic field is represented by the quantum sine-Gordon model, for which low-energy elementary excitations are composed of solitons, antisolitons and their bound states called breathers. Unlike the theoretical prediction, it was found that the energy of a soliton is smaller than that of the first breather, although the energy of the first breather coincides with that observed in a previous ESR measurement.
Recent experiments on the S=12S=\frac{1}{2}S=21​ antiferromagnetic chain compound, Cu benzoate, discovered an unexpected gap scaling as approximately the 23\frac{2}{3}32​ power of an applied magnetic field. A theory of this gap, based on an effective staggered field, orthogonal to the applied uniform field, resulting from a staggered gyromagnetic tensor and a Dzyaloshinskii-Moriya interaction, leading to a sine-Gordon quantum field theory, has been developed. Here we discuss many aspects of this subject in considerable detail, including a review of the S=12S=\frac{1}{2}S=21​ chain in a uniform field, a spin-wave theory analysis of the uniform plus staggered field problem, exact amplitudes for the scaling of gap, staggered susceptibility and staggered magnetization with field or temperature, intensities of soliton and breather peaks in the structure function, and field and temperature dependence of the total susceptibility.
Thermodynamic properties of the S=1/2 Heisenberg chain in transverse staggered magnetic field H^y_s and uniform magnetic field H^x perpendicular to the staggered field is studied by the finite-temperature density-matrix renormalization-group method. The uniform and staggered magnetization and specific heat are calculated from zero temperature to high temperatures up to T/J=4 under various strength of magnetic fields from H^y_s/J, H^x/J=0 to 2.4. The specific heat and magnetization of the effective Hamiltonian of the Yb_4As_3 are also presented, and field induced gap formation and diverging magnetic susceptibility at low temperature are shown.
Elementary excitations of the S=12S=\frac{1}{2}S=21​ one-dimensional antiferromagnet KCuGaF6{\mathrm{KCuGaF}}_{6}KCuGaF6​ were investigated by inelastic neutron scattering in zero and finite magnetic fields perpendicular to the (1,1,0)(1,1,0)(1,1,0) plane combined with specific heat measurements. KCuGaF6{\mathrm{KCuGaF}}_{6}KCuGaF6​ exhibits no long-range magnetic ordering down to 50 mK despite the large exchange interaction J/kB=103J/{k}_{\mathrm{B}}=103J/kB​=103 K. At zero magnetic field, well-defined spinon excitations were observed. The energy of the des Cloizeaux and Pearson [J. des Cloizeaux and J. J. Pearson, Phys. Rev. 128, 2131 (1962)] mode of the spinon excitations is somewhat larger than that calculated with the above exchange constant. This discrepancy is mostly ascribed to the effective XYXYXY anisotropy arising from the large Dzyaloshinsky-Moriya [T. Moriya, Phys. Rev. 120, 91 (1960)] interaction with an alternating $\mathbit{D}$ vector. KCuGaF6{\mathrm{KCuGaF}}_{6}KCuGaF6​ in a magnetic field is represented by the quantum sine-Gordon model, for which low-energy elementary excitations are composed of solitons and antisolitons and their bound states called breathers. Unlike the theoretical prediction, it was found that the energy of a soliton is smaller than that of the first breather, although the energy of the first breather coincides with that observed in a previous electron spin resonance measurement.
Magnetic excitations in copper pyrimidine dinitrate, a spin-1/2 antiferromagnetic chain with alternating ggg-tensor and Dzyaloshinskii-Moriya interactions that exhibits a field-induced spin gap, are probed by means of pulsed-field electron-spin-resonance spectroscopy. In particular, we report on a minimum of the gap in the vicinity of the saturation field Hsat=48.5{H}_{\mathrm{sat}}=48.5Hsat​=48.5 T associated with a transition from the sine-Gordon region (with soliton-breather elementary excitations) to a spin-polarized state (with magnon excitations). This interpretation is fully confirmed by the quantitative agreement over the entire field range of the experimental data with the density matrix renormalization group calculations for a spin-1/2 Heisenberg chain with a staggered transverse field.