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arXiv:1903.05492 · Physical Review Letters

Quantum Critical Dynamics of a Heisenberg-Ising Chain in a Longitudinal Field: Many-Body Strings versus Fractional Excitations

Zhe Wang, M. Schmidt, Alois Loidl, Jianda Wu, Haiyuan Zou, Wang Yang, Chao Dong, Yoshimitsu Kohama, Koichi Kindo, Denis Ivanovich Gorbunov, Sandra K. Niesen, Oliver Breunig, Johannes Engelmayer, T. Lorenz

Published Aug 6, 2019• 48 citations
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Abstract

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.

DOI
10.1103/physrevlett.123.067202

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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.
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.
Quantum dynamics of strongly correlated systems is a challenging problem. Although the low energy fractional excitations of one-dimensional integrable models are often well understood, exploring quantum dynamics in these systems remains challenging in the gapless regime, especially at intermediate and high energies. Based on the algebraic Bethe ansatz formalism, we study spin dynamics in a representative one-dimensional strongly correlated model, i.e., the antiferromagnetic spin-12\frac{1}{2}21​ XXZ chain with the Ising anisotropy, via the form-factor formulas. Various excitations at different energy scales are identified crucial to the dynamic spin structure factors under the guidance of sum rules. At small magnetic polarizations, gapless excitations dominate the low energy spin dynamics arising from the magnetic-field-induced incommensurability. In contrast, spin dynamics at intermediate and high energies is characterized by the two- and three-string states, which are multiparticle excitations based on the commensurate N\'eel ordered background. Our work is helpful for experimental studies on spin dynamics in both condensed matter and cold atom systems beyond the low energy effective Luttinger liquid theory. Based on an intuitive physical picture, we speculate that the dynamic feature at high energies due to the multiparticle antibound state excitations can be generalized to nonintegrable spin systems.
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.
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.
Despite being predicted almost a century ago as the excitations of the spin-1/2 antiferromagnetic chain, Bethe strings were overshadowed by the more dominant multi-spinon-pair excitations and were only observed recently. Here we confirm their existence in the quasi-one-dimensional quantum antiferromagnet BaCo 2 V 2 O 8 using a magnetic field to separate them from the spinons. We find excellent quantitative agreement over an extended field range between these experimental results and our theoretical predictions based on the algebraic Bethe ansatz formalism. This work proves the existence of Bethe strings (multimagnon bound states) up to length-3 in BaCo 2 V 2 O 8 .
Combining inelastic neutron scattering and numerical simulations, we study the quasi-one-dimensional Ising anisotropic quantum antiferromagnet BaCo_{2}V_{2}O_{8} in a longitudinal magnetic field. This material shows a quantum phase transition from a Néel ordered phase at zero field to a longitudinal incommensurate spin density wave at a critical magnetic field of 3.8 T. Concomitantly, the excitation gap almost closes and a fundamental reconfiguration of the spin dynamics occurs. These experimental results are well described by the universal Tomonaga-Luttinger liquid theory developed for interacting spinless fermions in one dimension. We especially observe the rise of mainly longitudinal excitations, a hallmark of the unconventional low-field regime in Ising-like quantum antiferromagnetic chains.