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

Wang, Zhe; Schmidt, Michael; Loidl, A.; Wu, Jianda; Zou, Haiyuan; Wang, Yang; Dong, Chao; Kohama, Yoshimitsu; Kindo, Koichi; Gorbunov, D. I.; Niesen, Sandra; Breunig, Oliver; Engelmayer, Johannes; Lorenz, T.

doi:10.1103/physrevlett.123.067202

Cited by 49 publications

(65 citation statements)

References 56 publications

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“…2 as a function of ζ i , the negative zeros of the Airy function Ai(−ζ i ) = 0. The linear dependence on ζ i reflects the spinon confinement in a linear confining potential [8,31], which is set up by the interchain couplings in the magnetically ordered phase [15,18,24,[27][28][29]35]. Above M 7 one can see a broader peak around 0.49 THz (labeled 2M 1 ) and a broad continuum at higher energy (labeled M 1 + M 1 ), consistent with the observation in Ref.…”

Section: Resultssupporting

confidence: 88%

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

et al. 2020

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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 CoNb 2 O 6. At 0.25 K in the magnetically ordered phase we identify characteristics of the first six E 8 particles, m 1 to m 6 , and the two-particle (m 1 + m 2) continuum in an applied transverse magnetic field of B 1D c = 4.75 T, before the three-dimensional magnetic order is suppressed above B 3D c ≈ 5.3 T. The observation of the higher-energy particles (m 3 to m 6) above the low-energy two-particle continua features quantum many-body effects in the exotic dynamic spectrum.

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Section: Resultssupporting

confidence: 88%

“…1). The transverse-field Ising-chain quantum critical point is characterized by a peculiar thermodynamic property: With decreasing temperature at the critical field, the Grüneisen parameter converges [29,37,38], in contrast to the divergent behavior for a generic quantum critical point [39].…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2020

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“…These studies on spin ladders were partially motivated by Haldane's prediction of a gap in the excitation spectrum for integer-S antiferromagnets [20], as well as by the work of Shiba [21] who suggested that a weak inter-chain coupling between two spin 1/2 Heisenberg chain can explain the occurrence of discrete lines in the Raman spectrum of CsCoCl 3 and CsCoBr 3 [22,23]. Consequently, quasi one-dimensional spin ladders experienced an increasing research activity and the occurrence of confinement in these models has been intensively studied [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40], finally leading to remarkable observations through neutron scattering and high-resolution terahertz spectroscopy [41][42][43][44][45][46][47].…”

Section: Introductionmentioning

confidence: 99%

Confinement in the spectrum of a Heisenberg–Ising spin ladder

Lagnese¹,

Surace²,

Kormos³

et al. 2020

J. Stat. Mech.

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We consider the quantum quench dynamics of a Heisenberg-Ising spin ladder which is an archetypal model in which confinement of elementary excitations is triggered by internal interactions rather than an external field. We show that the confinement strongly affects the light cone structure of correlation functions providing signatures of the velocities of the mesons of the model. We also show that the meson masses can be measured from the real time analysis of the evolution of the order parameter.

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“…Due to collective quantum fluctuations, exotic states of matter can emerge near a quantum critical point (QCP) in quantum many-body systems [1][2][3][4][5][6], which have been attracting intensive research [7][8][9][10][11][12][13][14][15][16]. One such paradigmatic system is the transverse field Ising chain (TFIC) in the presence of a longitudinal field.…”

Section: Introductionmentioning

confidence: 99%

Cascade of singularities in the spin dynamics of a perturbed quantum critical Ising chain

et al. 2021

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When the quantum critical transverse-field Ising chain is perturbed by a longitudinal field, a quantum integrable model emerges in the scaling limit with massive excitations described by the exceptional E8 Lie algebra. Using the corresponding analytical form factors of the quantum E8 integrable model, we systematically study the spin dynamic structure factor of the perturbed quantum critical Ising chain, where particle channels with total energy up to 5m1 (m1 being the mass of the lightest E8 particle) are exhausted. In addition to the significant single-particle contributions to the dynamic spectrum, each two-particle channel with different masses is found to exhibit an edge singularity at the threshold of the total mass and decays with an inverse square root of energy, which is attributed to the singularity of the two-particle density of states at the threshold. The singularity is absent for particles with equal masses due to a cancellation mechanism involving the structure of the form factors. As a consequence, the dynamic structure factor displays a cascade of bumping peaks in the continuum region with clear singular features which can serve as a solid guidance for the material realization of the quantum E8 model.

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

Cited by 49 publications

References 56 publications

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

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

Confinement in the spectrum of a Heisenberg–Ising spin ladder

Cascade of singularities in the spin dynamics of a perturbed quantum critical Ising chain

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