arXiv:2306.01948 · Physical review. B./Physical review. B

Excitations of quantum Ising chain CoNb 2 O 6 in low transverse field: Quantitative description of bound states stabilized by off-diagonal exchange and applied field

Leonie Woodland, Izabella Lovas, Mark T. F. Telling, D. Prabhakaran, Leon Balents, R. Coldea

Published Nov 16, 2023• 11 citations

Abstract

We present experimental and theoretical evidence of novel bound state formation in the low transverse field ordered phase of the quasi-one-dimensional Ising-like material ${\text{CoNb}}_{2}{\text{O}}_{6}$. High-resolution single-crystal inelastic neutron scattering measurements observe that small transverse fields lead to a breakup of the spectrum into three parts, each evolving very differently upon increasing field. This can be naturally understood starting from the excitations of the ordered phase of the transverse field Ising model, domain wall quasiparticles (solitons). Here, the transverse field and a staggered off-diagonal exchange create one-soliton hopping terms with opposite signs. We show that this leads to a rich spectrum and a special field, when the strengths of the off-diagonal exchange and transverse field match, at which solitons become localized; the highest field investigated is very close to this special regime. We solve this case analytically and find three two-soliton continua, along with three novel bound states. Perturbing away from this novel localized limit, we find very good qualitative agreement with the experimental data. We also present calculations using exact diagonalization of a recently refined Hamiltonian model for ${\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}$ and using diagonalization of the two-soliton subspace, both of which provide a quantitative agreement with the observed spectrum. The theoretical models qualitatively and quantitatively capture a variety of nontrivial features in the observed spectrum, providing insight into the underlying physics of bound state formation.

DOI: 10.1103/physrevb.108.184417

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Two-dimensional coherent spectroscopy of CoNb2O6

Yoshito Watanabe, Simon Trebst, Ciarán Hickey

arXiv:2512.16829npj Quantum MaterialsAug 20, 20260 citations

Quasiparticle breakdown in the quasi-one-dimensional Ising ferromagnet CoNb2O6

Neil J. Robinson, Fabian H. L. Eßler, I. Cabrera +1 more

arXiv:1407.2794Physical Review BNov 6, 201433 citations

Glide symmetry breaking and Ising criticality in the quasi-1D magnet CoNb 2 O 6

Michele Fava, R. Coldea, S. A. Parameswaran

arXiv:2004.04169Proceedings of the National Academy of SciencesSep 25, 202044 citations

Experimental observation of quantum many-body excitations of E8 symmetry in the Ising chain ferromagnet CoNb2O6

Kirill Amelin, Johannes Engelmayer, J. Viirok +4 more

arXiv:2006.12956Physical review. B./Physical review. BSep 24, 202042 citations

Exchange mixing and soliton dynamics in the quantum spin chain CsCoCl3

Jon P. Goff, D. M. Tennant, S. E. Nagler

Physical review. B, Condensed matterDec 1, 199562 citations

Solitonic excitations in the Ising anisotropic chain BaCo2V2O8 under large transverse magnetic field

Quentin Faure, Shintaro Takayoshi, B. Grenier +6 more

arXiv:2107.02487Physical Review ResearchDec 29, 20217 citations

arXiv:2306.01948 · Physical review. B./Physical review. B

Excitations of quantum Ising chain CoNb 2 O 6 in low transverse field: Quantitative description of bound states stabilized by off-diagonal exchange and applied field

Leonie Woodland, Izabella Lovas, Mark T. F. Telling, D. Prabhakaran, Leon Balents, R. Coldea

Published Nov 16, 2023• 11 citations

arXiv HTML PDF

Abstract

We present experimental and theoretical evidence of novel bound state formation in the low transverse field ordered phase of the quasi-one-dimensional Ising-like material

{\text{CoNb}}_{2}{\text{O}}_{6}

. High-resolution single-crystal inelastic neutron scattering measurements observe that small transverse fields lead to a breakup of the spectrum into three parts, each evolving very differently upon increasing field. This can be naturally understood starting from the excitations of the ordered phase of the transverse field Ising model, domain wall quasiparticles (solitons). Here, the transverse field and a staggered off-diagonal exchange create one-soliton hopping terms with opposite signs. We show that this leads to a rich spectrum and a special field, when the strengths of the off-diagonal exchange and transverse field match, at which solitons become localized; the highest field investigated is very close to this special regime. We solve this case analytically and find three two-soliton continua, along with three novel bound states. Perturbing away from this novel localized limit, we find very good qualitative agreement with the experimental data. We also present calculations using exact diagonalization of a recently refined Hamiltonian model for

{\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}

and using diagonalization of the two-soliton subspace, both of which provide a quantitative agreement with the observed spectrum. The theoretical models qualitatively and quantitatively capture a variety of nontrivial features in the observed spectrum, providing insight into the underlying physics of bound state formation.

DOI: 10.1103/physrevb.108.184417

Related papers

Two-dimensional coherent spectroscopy of CoNb2O6

Yoshito Watanabe, Simon Trebst, Ciarán Hickey

Abstract With recent advances in terahertz (THz) sources and detection, two-dimensional coherent spectroscopy (2DCS), which allows one to probe nonlinear responses, now reaches the meV regime relevant for quasiparticle excitations in magnetic materials. This opens a promising route to reveal many-body phenomena that evade linear-response probes. To date, most experimental applications have focused on classical magnets, and a solid demonstration in a quantum magnet has yet to be established. Here we present a theoretical study of 2DCS in CoNb 2 O 6 , a quasi-one-dimensional Ising magnet that is believed to host fractionalized spinons which at low temperatures are confined by weak interchain coupling. Our analysis, which builds on an experimentally constrained effective S = 1/2 Hamiltonian, is found to reveal unambiguous 2DCS signatures of spinon deconfinement above the low-temperature ordered phase. Using a four-spinon approximation, we track these 2DCS signatures by sequentially building a faithful microscopic model for CoNb 2 O 6 , starting from the exactly solvable one-dimensional transverse-field Ising model (1 d TFIM) and successively adding additional interactions. In particular, adding a bond-dependent staggered YZ interaction to the 1 d -TFIM already reproduces many key spectral features of the full material Hamiltonian. Within this TFIM+YZ model, we find a series of bound states, including a four-spinon bound state that is distinct from the familiar two-spinon bound states. We further find that introducing a confinement potential suppresses sharp spinon-echo features, which are thought to reflect an underlying continuum of fractionalized excitations. Our results provide concrete predictions for future THz 2DCS experiments on CoNb 2 O 6 and related quasi-one-dimensional quantum magnets.Abstract With recent advances in terahertz (THz) sources and detection, two-dimensional coherent spectroscopy (2DCS), which allows one to probe nonlinear responses, now reaches the meV regime relevant for quasiparticle excitations in magnetic materials. This opens a promising route to reveal many-body phenomena that evade linear-response probes. To date, most experimental applications have focused on classical magnets, and a solid demonstration in a quantum magnet has yet to be established. Here we present a theoretical study of 2DCS in CoNb 2 O 6 , a quasi-one-dimensional Ising magnet that is believed to host fractionalized spinons which at low temperatures are confined by weak interchain coupling. Our analysis, which builds on an experimentally constrained effective S = 1/2 Hamiltonian, is found to reveal unambiguous 2DCS signatures of spinon deconfinement above the low-temperature ordered phase. Using a four-spinon approximation, we track these 2DCS signatures by sequentially building a faithful microscopic model for CoNb 2 O 6 , starting from the exactly solvable one-dimensional transverse-field Ising model (1 d TFIM) and successively adding additional interactions. In particular, adding a bond-dependent staggered YZ interaction to the 1 d -TFIM already reproduces many key spectral features of the full material Hamiltonian. Within this TFIM+YZ model, we find a series of bound states, including a four-spinon bound state that is distinct from the familiar two-spinon bound states. We further find that introducing a confinement potential suppresses sharp spinon-echo features, which are thought to reflect an underlying continuum of fractionalized excitations. Our results provide concrete predictions for future THz 2DCS experiments on CoNb 2 O 6 and related quasi-one-dimensional quantum magnets.

arXiv:2512.16829npj Quantum MaterialsAug 20, 20260 citations

Quasiparticle breakdown in the quasi-one-dimensional Ising ferromagnet CoNb2O6

Neil J. Robinson, Fabian H. L. Eßler, I. Cabrera +1 more

We present experimental and theoretical evidence that an interesting quantum many-body effect---quasiparticle breakdown---occurs in the quasi-one-dimensional spin- $\frac{1}{2}$ Ising-like ferromagnet ${\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}$ in its paramagnetic phase at high transverse field as a result of explicit breaking of spin inversion symmetry. We propose a quantum spin Hamiltonian capturing the essential one-dimensional physics of ${\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}$ and determine the exchange parameters of this model by fitting the calculated single-particle dispersion to the one observed experimentally in applied transverse magnetic fields [1]. We present high-resolution inelastic neutron scattering measurements of the single-particle dispersion which observe ``anomalous broadening'' effects over a narrow energy range at intermediate energies. We propose that this effect originates from the decay of the one particle mode into two-particle states. This decay arises from (i) a finite overlap between the one-particle dispersion and the two-particle continuum in a narrow energy-momentum range and (ii) a small misalignment of the applied field away from the direction perpendicular to the Ising axis in the experiments, which allows for nonzero matrix elements for decay by breaking the ${\mathbb{Z}}_{2}$ spin inversion symmetry of the Hamiltonian.We present experimental and theoretical evidence that an interesting quantum many-body effect---quasiparticle breakdown---occurs in the quasi-one-dimensional spin-$\frac{1}{2}$ Ising-like ferromagnet ${\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}$ in its paramagnetic phase at high transverse field as a result of explicit breaking of spin inversion symmetry. We propose a quantum spin Hamiltonian capturing the essential one-dimensional physics of ${\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}$ and determine the exchange parameters of this model by fitting the calculated single-particle dispersion to the one observed experimentally in applied transverse magnetic fields [1]. We present high-resolution inelastic neutron scattering measurements of the single-particle dispersion which observe ``anomalous broadening'' effects over a narrow energy range at intermediate energies. We propose that this effect originates from the decay of the one particle mode into two-particle states. This decay arises from (i) a finite overlap between the one-particle dispersion and the two-particle continuum in a narrow energy-momentum range and (ii) a small misalignment of the applied field away from the direction perpendicular to the Ising axis in the experiments, which allows for nonzero matrix elements for decay by breaking the ${\mathbb{Z}}_{2}$ spin inversion symmetry of the Hamiltonian.

arXiv:1407.2794Physical Review BNov 6, 201433 citations

Glide symmetry breaking and Ising criticality in the quasi-1D magnet CoNb 2 O 6

Michele Fava, R. Coldea, S. A. Parameswaran

We construct a microscopic spin-exchange Hamiltonian for the quasi-one-dimensional (1D) Ising magnet [Formula: see text] that captures detailed and hitherto-unexplained aspects of its dynamic spin structure factor. We perform a symmetry analysis that recalls that an individual Ising chain in this material is buckled, with two sites in each unit cell related by a glide symmetry. Combining this with numerical simulations benchmarked against neutron scattering experiments, we argue that the single-chain Hamiltonian contains a staggered spin-exchange term. We further argue that the transverse-field-tuned quantum critical point in [Formula: see text] corresponds to breaking this glide symmetry, rather than an on-site Ising symmetry as previously believed. This gives a unified microscopic explanation of the dispersion of confined states in the ordered phase and quasiparticle breakdown in the polarized phase at high transverse field.We construct a microscopic spin-exchange Hamiltonian for the quasi-one-dimensional (1D) Ising magnet [Formula: see text] that captures detailed and hitherto-unexplained aspects of its dynamic spin structure factor. We perform a symmetry analysis that recalls that an individual Ising chain in this material is buckled, with two sites in each unit cell related by a glide symmetry. Combining this with numerical simulations benchmarked against neutron scattering experiments, we argue that the single-chain Hamiltonian contains a staggered spin-exchange term. We further argue that the transverse-field-tuned quantum critical point in [Formula: see text] corresponds to breaking this glide symmetry, rather than an on-site Ising symmetry as previously believed. This gives a unified microscopic explanation of the dispersion of confined states in the ordered phase and quasiparticle breakdown in the polarized phase at high transverse field.

arXiv:2004.04169Proceedings of the National Academy of SciencesSep 25, 202044 citations

Experimental observation of quantum many-body excitations of E8 symmetry in the Ising chain ferromagnet CoNb2O6

Kirill Amelin, Johannes Engelmayer, J. Viirok +4 more

Close to the quantum critical point of the transverse-field Ising spin-chain model, an exotic dynamic spectrum was predicted to emerge upon a perturbative longitudinal field. The dynamic spectrum consists of eight particles and is governed by the symmetry of the ${E}_{8}$ Lie algebra. Here we report on high-resolution terahertz spectroscopy of quantum spin dynamics in the ferromagnetic Ising-chain material ${\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}$ . At 0.25 K in the magnetically ordered phase we identify characteristics of the first six ${E}_{8}$ particles, ${\mathrm{m}}_{1}$ to ${\mathrm{m}}_{6}$ , and the two-particle $({\mathrm{m}}_{1}+{\mathrm{m}}_{2})$ continuum in an applied transverse magnetic field of ${B}_{c}^{\text{1D}}=4.75 \mathrm{T}$ , before the three-dimensional magnetic order is suppressed above ${B}_{c}^{\text{3D}}\ensuremath{\approx}5.3 \mathrm{T}$. The observation of the higher-energy particles $({\mathrm{m}}_{3} \mathrm{to} {\mathrm{m}}_{6})$ above the low-energy two-particle continua features quantum many-body effects in the exotic dynamic spectrum.Close to the quantum critical point of the transverse-field Ising spin-chain model, an exotic dynamic spectrum was predicted to emerge upon a perturbative longitudinal field. The dynamic spectrum consists of eight particles and is governed by the symmetry of the ${E}_{8}$ Lie algebra. Here we report on high-resolution terahertz spectroscopy of quantum spin dynamics in the ferromagnetic Ising-chain material ${\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}$. At 0.25 K in the magnetically ordered phase we identify characteristics of the first six ${E}_{8}$ particles, ${\mathrm{m}}_{1}$ to ${\mathrm{m}}_{6}$, and the two-particle $({\mathrm{m}}_{1}+{\mathrm{m}}_{2})$ continuum in an applied transverse magnetic field of ${B}_{c}^{\text{1D}}=4.75 \mathrm{T}$, before the three-dimensional magnetic order is suppressed above ${B}_{c}^{\text{3D}}\ensuremath{\approx}5.3 \mathrm{T}$. The observation of the higher-energy particles $({\mathrm{m}}_{3} \mathrm{to} {\mathrm{m}}_{6})$ above the low-energy two-particle continua features quantum many-body effects in the exotic dynamic spectrum.

arXiv:2006.12956Physical review. B./Physical review. BSep 24, 202042 citations

Exchange mixing and soliton dynamics in the quantum spin chain CsCoCl3

Jon P. Goff, D. M. Tennant, S. E. Nagler

The lowest-lying excited states in the S=1/2 one-dimensional Ising-like antiferromagnet ${\mathrm{CsCoCl}}_{3}$ consist of domain-wall (soliton) pair states. Although the dynamical response function S(Q,\ensuremath{\omega}) has been calculated for these states, it has not proved possible to explain the results of neutron scattering and Raman experiments without recourse to the introduction of extra terms in the spin Hamiltonian. We argue against the two modifications to the Hamiltonian of ${\mathrm{CsCoCl}}_{3}$ proposed in previous papers, a staggered field term arising from a mean field approach to exchange mixing, and next-nearest-neighbor intrachain coupling, as being unphysical. Instead we derive a nearest-neighbor effective Hamiltonian, which takes account of the mixing of higher ${\mathrm{Co}}^{2+}$ ion crystal-field levels in a self-consistent manner. We also present a high-resolution inelastic neutron scattering experiment on ${\mathrm{CsCoCl}}_{3}$ , which has allowed the dispersion of the excited states across the Brillouin zone to be studied more carefully than before. These results give a direct measure of S(Q,\ensuremath{\omega}) in the one-dimensional phase where there is a continuum of excited states, and in the three-dimensionally ordered phases, where weak interchain interactions split the continuum into a ``Zeeman ladder'' of discrete states. The predictions of our theory are found to be in quantitative agreement with experiment.The lowest-lying excited states in the S=1/2 one-dimensional Ising-like antiferromagnet ${\mathrm{CsCoCl}}_{3}$ consist of domain-wall (soliton) pair states. Although the dynamical response function S(Q,\ensuremath{\omega}) has been calculated for these states, it has not proved possible to explain the results of neutron scattering and Raman experiments without recourse to the introduction of extra terms in the spin Hamiltonian. We argue against the two modifications to the Hamiltonian of ${\mathrm{CsCoCl}}_{3}$ proposed in previous papers, a staggered field term arising from a mean field approach to exchange mixing, and next-nearest-neighbor intrachain coupling, as being unphysical. Instead we derive a nearest-neighbor effective Hamiltonian, which takes account of the mixing of higher ${\mathrm{Co}}^{2+}$ ion crystal-field levels in a self-consistent manner. We also present a high-resolution inelastic neutron scattering experiment on ${\mathrm{CsCoCl}}_{3}$, which has allowed the dispersion of the excited states across the Brillouin zone to be studied more carefully than before. These results give a direct measure of S(Q,\ensuremath{\omega}) in the one-dimensional phase where there is a continuum of excited states, and in the three-dimensionally ordered phases, where weak interchain interactions split the continuum into a ``Zeeman ladder'' of discrete states. The predictions of our theory are found to be in quantitative agreement with experiment.

Physical review. B, Condensed matterDec 1, 199562 citations

Solitonic excitations in the Ising anisotropic chain BaCo2V2O8 under large transverse magnetic field

Quentin Faure, Shintaro Takayoshi, B. Grenier +6 more

We study the dynamics of the quasi-one-dimensional Ising-Heisenberg antiferromagnet ${\mathrm{BaCo}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}$ under a transverse magnetic field. Combining inelastic neutron scattering experiments and theoretical analyses by field theories and numerical simulations, we mainly elucidate the structure of the spin excitation spectrum in the high-field phase, appearing above the quantum phase transition point ${\ensuremath{\mu}}_{0}{H}_{c}\ensuremath{\approx}10\phantom{\rule{0.28em}{0ex}}\mathrm{T}$. We find that it is characterized by collective solitonic excitations superimposed on a continuum. These solitons are strongly bound in pairs due to the effective staggered field induced by the nondiagonal $g$ tensor of the compound and are topologically different from the fractionalized spinons in the weak-field region. The dynamical susceptibility numerically calculated with the infinite time-evolving block decimation method shows an excellent agreement with the measured spectra, which enables us to identify the dispersion branches with elementary excitations. The lowest-energy dispersion has an incommensurate nature and has a local minimum at an irrational wave number due to the applied transverse field.We study the dynamics of the quasi-one-dimensional Ising-Heisenberg antiferromagnet ${\mathrm{BaCo}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}$ under a transverse magnetic field. Combining inelastic neutron scattering experiments and theoretical analyses by field theories and numerical simulations, we mainly elucidate the structure of the spin excitation spectrum in the high-field phase, appearing above the quantum phase transition point ${\ensuremath{\mu}}_{0}{H}_{c}\ensuremath{\approx}10\phantom{\rule{0.28em}{0ex}}\mathrm{T}$. We find that it is characterized by collective solitonic excitations superimposed on a continuum. These solitons are strongly bound in pairs due to the effective staggered field induced by the nondiagonal $g$ tensor of the compound and are topologically different from the fractionalized spinons in the weak-field region. The dynamical susceptibility numerically calculated with the infinite time-evolving block decimation method shows an excellent agreement with the measured spectra, which enables us to identify the dispersion branches with elementary excitations. The lowest-energy dispersion has an incommensurate nature and has a local minimum at an irrational wave number due to the applied transverse field.

arXiv:2107.02487Physical Review ResearchDec 29, 20217 citations

We present experimental and theoretical evidence of novel bound state formation in the low transverse field ordered phase of the quasi-one-dimensional Ising-like material

{\text{CoNb}}_{2}{\text{O}}_{6}

{\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}

We present experimental and theoretical evidence that an interesting quantum many-body effect---quasiparticle breakdown---occurs in the quasi-one-dimensional spin-

\frac{1}{2}

Ising-like ferromagnet

{\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}

in its paramagnetic phase at high transverse field as a result of explicit breaking of spin inversion symmetry. We propose a quantum spin Hamiltonian capturing the essential one-dimensional physics of

{\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}

and determine the exchange parameters of this model by fitting the calculated single-particle dispersion to the one observed experimentally in applied transverse magnetic fields [1]. We present high-resolution inelastic neutron scattering measurements of the single-particle dispersion which observe ``anomalous broadening'' effects over a narrow energy range at intermediate energies. We propose that this effect originates from the decay of the one particle mode into two-particle states. This decay arises from (i) a finite overlap between the one-particle dispersion and the two-particle continuum in a narrow energy-momentum range and (ii) a small misalignment of the applied field away from the direction perpendicular to the Ising axis in the experiments, which allows for nonzero matrix elements for decay by breaking the

{\mathbb{Z}}_{2}

spin inversion symmetry of the Hamiltonian.

{E}_{8}

Lie algebra. Here we report on high-resolution terahertz spectroscopy of quantum spin dynamics in the ferromagnetic Ising-chain material

{\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}

. At 0.25 K in the magnetically ordered phase we identify characteristics of the first six

{E}_{8}

particles,

{\mathrm{m}}_{1}

{\mathrm{m}}_{6}

, and the two-particle

({\mathrm{m}}_{1}+{\mathrm{m}}_{2})

continuum in an applied transverse magnetic field of

{B}_{c}^{\text{1D}}=4.75 \mathrm{T}

, before the three-dimensional magnetic order is suppressed above ${B}_{c}^{\text{3D}}\ensuremath{\approx}5.3 \mathrm{T}$. The observation of the higher-energy particles

({\mathrm{m}}_{3} \mathrm{to} {\mathrm{m}}_{6})

above the low-energy two-particle continua features quantum many-body effects in the exotic dynamic spectrum.

The lowest-lying excited states in the S=1/2 one-dimensional Ising-like antiferromagnet

{\mathrm{CsCoCl}}_{3}

consist of domain-wall (soliton) pair states. Although the dynamical response function S(Q,\ensuremath{\omega}) has been calculated for these states, it has not proved possible to explain the results of neutron scattering and Raman experiments without recourse to the introduction of extra terms in the spin Hamiltonian. We argue against the two modifications to the Hamiltonian of

{\mathrm{CsCoCl}}_{3}

proposed in previous papers, a staggered field term arising from a mean field approach to exchange mixing, and next-nearest-neighbor intrachain coupling, as being unphysical. Instead we derive a nearest-neighbor effective Hamiltonian, which takes account of the mixing of higher

{\mathrm{Co}}^{2+}

ion crystal-field levels in a self-consistent manner. We also present a high-resolution inelastic neutron scattering experiment on

{\mathrm{CsCoCl}}_{3}

, which has allowed the dispersion of the excited states across the Brillouin zone to be studied more carefully than before. These results give a direct measure of S(Q,\ensuremath{\omega}) in the one-dimensional phase where there is a continuum of excited states, and in the three-dimensionally ordered phases, where weak interchain interactions split the continuum into a ``Zeeman ladder'' of discrete states. The predictions of our theory are found to be in quantitative agreement with experiment.

We study the dynamics of the quasi-one-dimensional Ising-Heisenberg antiferromagnet

{\mathrm{BaCo}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}

under a transverse magnetic field. Combining inelastic neutron scattering experiments and theoretical analyses by field theories and numerical simulations, we mainly elucidate the structure of the spin excitation spectrum in the high-field phase, appearing above the quantum phase transition point ${\ensuremath{\mu}}_{0}{H}_{c}\ensuremath{\approx}10\phantom{\rule{0.28em}{0ex}}\mathrm{T}$. We find that it is characterized by collective solitonic excitations superimposed on a continuum. These solitons are strongly bound in pairs due to the effective staggered field induced by the nondiagonal

g

tensor of the compound and are topologically different from the fractionalized spinons in the weak-field region. The dynamical susceptibility numerically calculated with the infinite time-evolving block decimation method shows an excellent agreement with the measured spectra, which enables us to identify the dispersion branches with elementary excitations. The lowest-energy dispersion has an incommensurate nature and has a local minimum at an irrational wave number due to the applied transverse field.