Finite temperature spin dynamics in a perturbed quantum critical Ising chain with an $E_8$ symmetry

Abstract

A spectrum exhibiting $E_8$ symmetry is expected to arise when a small longitudinal field is introduced in the transverse-field Ising chain at its quantum critical point. Evidence for this spectrum has recently come from neutron scattering measurements in cobalt niobate, a quasi one-dimensional Ising ferromagnet. Unlike its zero-temperature counterpart, the finite-temperature dynamics of the model has not yet been determined. We study the dynamical spin structure factor of the model at low frequencies and nonzero temperatures, using the form factor method. Its frequency dependence is singular, but differs from the diffusion form. The temperature dependence of the nuclear magnetic resonance (NMR) relaxation rate has an activated form, whose prefactor we also determine. We propose NMR experiments as a means to further test the applicability of the $E_8$ description for CoNb${}_2$O${}_6$.

arXiv comment5 pages 2 figures - Supplementary Material 11 pages

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Cited by in corpus (27)

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• $E_8$ Spectra of Quasi-one-dimensional Antiferromagnet BaCo${}_2$V${}_2$O${}_8$ under Transverse Field
• Observation of E8 Particles in an Ising Chain Antiferromagnet
• From confined spinons to emergent fermions: Observation of elementary magnetic excitations in a transverse-field Ising chain
• Experimental Observation of Quantum Many-Body Excitations of $E_8$ Symmetry in the Ising Chain Ferromagnet CoNb${}_2$O${}_6$
• Crossovers and critical scaling in the one-dimensional transverse-field Ising model
• One-dimensional Quantum Spin Dynamics of Bethe String States
• Cascade of singularities in the spin dynamics of a perturbed quantum critical Ising chain
• Phase diagram and quantum criticality of Heisenberg spin chains with Ising-like interchain couplings -- Implication to YbAlO${}_3$
• Exact finite volume expectation values of local operators in excited states
• Magnetic excitations in the one-dimensional Heisenberg-Ising model with external fields and their experimental realizations
• Local dynamics and thermal activation in the transverse-field Ising chain
• Quantum criticality of bosonic systems with the Lifshitz dispersion
• Quantum Supercritical Regime with Universal Magnetocaloric Scaling in Ising Magnets
• Field-induced antiferromagnetism and Tomonaga-Luttinger liquid behavior in the quasi-one-dimensional Ising-Antiferromagnet SrCo2V2O8
• Universality of Heisenberg-Ising chain in external fields
• Magnetization oscillations in a periodically driven transverse field Ising chain
• Exact Spin Correlators of Integrable Quantum Circuits from Algebraic Geometry
• Mesons in a quantum Ising ladder
• Truncated string state space approach and its application to nonintegrable spin-$\frac{1}{2}$ Heisenberg chain
• Quantum critical dynamics for a prototype class of insulating antiferromagnets
• 1/5 and 1/3 magnetization plateaux in the spin 1/2 chain system YbAlO3
• Spin dynamics and dark particle in a weak-coupled quantum Ising ladder with ${\mathcal{D}}_8^{(1)}$ spectrum
• Thermally activated detection of dark particles in a weakly coupled quantum Ising ladder
• Quantum Supercritical Crossover with Dynamical Singularity
• Thermodynamics of a Quantum Ising system coupled to a spin bath: Zero Temperature Results