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Journal of Physics A Mathematical and Theoretical

Quantum spin dynamics of quasi-one-dimensional Heisenberg-Ising magnets in a transverse field: confined spinons, E 8 spectrum, and quantum phase transitions

Kirill Amelin, J. Viirok, U. Nagel, T. Rõõm, Johannes Engelmayer, T. Dey, Agustinus Agung Nugroho, T. Lorenz, Zhe Wang

Published Nov 29, 2022• 16 citations
Publisher

Abstract

Abstract We report on high-resolution terahertz spectroscopic studies of quantum spin dynamics in the quasi-one-dimensional Ising-like ferromagnet CoNb2O6 and antiferromagnet BaCo2V2O8 as a function of an applied transverse magnetic field. In the ordered phases stabilized by inter-chain couplings, we reveal characteristics for confined spinon excitations, E 8 dynamical spectrum, and field-induced quantum phase transitions. The connections between these characteristic dynamical features are found in the field-dependent evolution of the excitation spectra.

DOI
10.1088/1751-8121/aca6b8

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Abstract We report on high-resolution terahertz spectroscopic studies of quantum spin dynamics in the quasi-one-dimensional Ising-like ferromagnet CoNb2O6 and antiferromagnet BaCo2V2O8 as a function of an applied transverse magnetic field. In the ordered phases stabilized by inter-chain couplings, we reveal characteristics for confined spinon excitations, E 8 dynamical spectrum, and field-induced quantum phase transitions. The connections between these characteristic dynamical features are found in the field-dependent evolution of the excitation spectra.
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 E8{E}_{8}E8​ Lie algebra. Here we report on high-resolution terahertz spectroscopy of quantum spin dynamics in the ferromagnetic Ising-chain material CoNb2O6{\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}CoNb2​O6​. At 0.25 K in the magnetically ordered phase we identify characteristics of the first six E8{E}_{8}E8​ particles, m1{\mathrm{m}}_{1}m1​ to m6{\mathrm{m}}_{6}m6​, and the two-particle (m1+m2)({\mathrm{m}}_{1}+{\mathrm{m}}_{2})(m1​+m2​) continuum in an applied transverse magnetic field of Bc1D=4.75T{B}_{c}^{\text{1D}}=4.75 \mathrm{T}Bc1D​=4.75T, 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 (m3tom6)({\mathrm{m}}_{3} \mathrm{to} {\mathrm{m}}_{6})(m3​tom6​) above the low-energy two-particle continua features quantum many-body effects in the exotic dynamic spectrum.
We report a high-resolution terahertz spectroscopic study of quantum spin dynamics in the antiferromagnetic Heisenberg-Ising spin-chain compound BaCo_{2}V_{2}O_{8} as a function of temperature and longitudinal magnetic field. Confined spinon excitations are observed in an antiferromagnetic phase below T_{N}≃5.5 K. In a field-induced gapless phase above B_{c}=3.8 T, we identify many-body string excitations as well as low-energy fractional psinon or antipsinon excitations by comparing to Bethe ansatz calculations. In the vicinity of B_{c}, the high-energy string excitations are found to have a dominant contribution to the spin dynamics as compared with the fractional excitations.
We report on spectroscopy study of elementary magnetic excitations in an Ising-like antiferromagnetic chain compound SrCo2V2O8{\mathrm{SrCo}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}SrCo2​V2​O8​ as a function of temperature and applied transverse magnetic field up to 25 T. An optical as well as an acoustic branch of confined spinons, the elementary excitations at zero field, are identified in the antiferromagnetic phase below the N\'eel temperature of 5 K and described by a one-dimensional Schr\"odinger equation. The confinement can be suppressed by an applied transverse field and a quantum disordered phase is induced at 7 T. In this disordered paramagnetic phase, we observe three emergent fermionic excitations with different transverse-field dependencies. The nature of these modes is clarified by studying spin dynamic structure factor of a 1D transverse-field Heisenberg-Ising (XXZ)(XXZ)(XXZ) model using the method of infinite time evolving block decimation. Our work reveals emergent quantum phenomena and provides a concrete system for testifying theoretical predications of one-dimension quantum spin models.
We study the dynamics of the quasi-one-dimensional Ising-Heisenberg antiferromagnet BaCo2V2O8{\mathrm{BaCo}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}BaCo2​V2​O8​ 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 ggg 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.
Experimental Observation of High-Energy E8E_8E8​ Particles in the Ising Chain Ferromagnet CoNb2_22​O6_66​
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 E8E_8E8​ Lie algebra. Here we report on high-resolution terahertz spectroscopy of quantum spin dynamics in the ferromagnetic Ising-chain material CoNb2_22​O6_66​. At 0.25 K in the magnetically ordered phase we identify characteristics of the first six E8E_8E8​ particles, m1\mathbf{m}_1m1​ to m6\mathbf{m}_6m6​, and the two-particle (m1+m2\mathbf{m}_1+\mathbf{m}_2m1​+m2​) continuum in an applied transverse magnetic field of Bc1D=4.75B_c^{1D}=4.75Bc1D​=4.75 T, before the three-dimensional magnetic order is suppressed above Bc3D≈5.3B_c^{3D}\approx 5.3Bc3D​≈5.3 T. The observation of the higher-energy particles (m3\mathbf{m}_3m3​ to m6\mathbf{m}_6m6​) above the low-energy two-particle continua features quantum many-body effects in the exotic dynamic spectrum.
Near the transverse-field-induced quantum critical point of the Ising chain, an exotic dynamic spectrum consisting of exactly eight particles was predicted, which is uniquely described by an emergent quantum integrable field theory with the symmetry of the E8{E}_{8}E8​ Lie algebra, but rarely explored experimentally. Here we use high-resolution terahertz spectroscopy to resolve quantum spin dynamics of the quasi-one-dimensional Ising antiferromagnet BaCo2V2O8\mathrm{BaC}{\mathrm{o}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}BaCo2​V2​O8​ in an applied transverse field. By comparing to an analytical calculation of the dynamical spin correlations, we identify E8{E}_{8}E8​ particles as well as their two-particle excitations.