There has been considerable recent progress in identifying candidate materials for the transverse-field Ising chain (TFIC), a paradigmatic model for quantum criticality. Here, we study the local spin dynamical structure factor of different spin components in the quantum disordered region of the TFIC. We show that the low-frequency local dynamics of the spins in the Ising- and transverse-field directions have strikingly distinctive temperature dependencies. This leads to the thermal-activation gap for the secular term of the nuclear magnetic resonance $1/{T}_{2}^{\ensuremath{'}}$ relaxation rate to be half of that for the $1/{T}_{1}$ relaxation rate. Our findings reveal a surprise in the nonzero-temperature dynamics of the venerable TFIC model and uncover a means to evince the material realization of the TFIC universality.There has been considerable recent progress in identifying candidate materials for the transverse-field Ising chain (TFIC), a paradigmatic model for quantum criticality. Here, we study the local spin dynamical structure factor of different spin components in the quantum disordered region of the TFIC. We show that the low-frequency local dynamics of the spins in the Ising- and transverse-field directions have strikingly distinctive temperature dependencies. This leads to the thermal-activation gap for the secular term of the nuclear magnetic resonance $1/{T}_{2}^{\ensuremath{'}}$ relaxation rate to be half of that for the $1/{T}_{1}$ relaxation rate. Our findings reveal a surprise in the nonzero-temperature dynamics of the venerable TFIC model and uncover a means to evince the material realization of the TFIC universality.

arXiv:2111.15107Physical review. B./Physical review. BSep 29, 202210 citations

From the transverse field Ising chain to the quantum E8 integrable model

Xiao Wang, Jiahao Yang, Jianda Wu

This review reports a series of theoretical and experimental progress on researches of the transverse field Ising chain (TFIC) and the quantum E8 integrable model. For the TFIC, on one hand, a unique exotic quantum critical behavior of Grüneisen ratio (a ratio from magnetic or thermal expansion coefficient to specific heat) is theoretically established; on the other hand microscopic models can accommodate the TFIC universality class are substantially expanded. These progresses successfully promote a series of experiments collaborations to first-time realize the TFIC universality class in quasi one-dimensional anti-ferromagnetic material BaCo2V2O8 and SrCo2V2O8. For the quantum E8 integrable model, the low temperature local dynamics and the dynamical structure factor with zero transfer momentum of this system are analytically determined, where a cascade of edge singularities with power-law divergences are obtained in the continuum region of the dynamical structure factor. After combining with detailed quantum critical scaling behaviors analysis and large scale iTEBD calculation, it successfully facilitates a series of experiments, including THz spectrum measurements, inelastic neutron scattering and NMR experiments, to realize the quantum E8 integrable model in BaCo2V2O8 for the first time. The experimental realization of the quantum E8 integrable model substantially extends the frontiers of studying quantum integrable models in real materials. The series of progress and developments on the TFIC and the quantum E8 integrable model lay down a concrete ground to go beyond quantum integrability, and can inspire studies in condensed matter systems, cold atom systems, statistical field theory and conformal field theory.This review reports a series of theoretical and experimental progress on researches of the transverse field Ising chain (TFIC) and the quantum E8 integrable model. For the TFIC, on one hand, a unique exotic quantum critical behavior of Grüneisen ratio (a ratio from magnetic or thermal expansion coefficient to specific heat) is theoretically established; on the other hand microscopic models can accommodate the TFIC universality class are substantially expanded. These progresses successfully promote a series of experiments collaborations to first-time realize the TFIC universality class in quasi one-dimensional anti-ferromagnetic material BaCo2V2O8 and SrCo2V2O8. For the quantum E8 integrable model, the low temperature local dynamics and the dynamical structure factor with zero transfer momentum of this system are analytically determined, where a cascade of edge singularities with power-law divergences are obtained in the continuum region of the dynamical structure factor. After combining with detailed quantum critical scaling behaviors analysis and large scale iTEBD calculation, it successfully facilitates a series of experiments, including THz spectrum measurements, inelastic neutron scattering and NMR experiments, to realize the quantum E8 integrable model in BaCo2V2O8 for the first time. The experimental realization of the quantum E8 integrable model substantially extends the frontiers of studying quantum integrable models in real materials. The series of progress and developments on the TFIC and the quantum E8 integrable model lay down a concrete ground to go beyond quantum integrability, and can inspire studies in condensed matter systems, cold atom systems, statistical field theory and conformal field theory.

Acta Physica SinicaJan 1, 20211 citation

1/{T}_{1}

relaxation rate. Our findings reveal a surprise in the nonzero-temperature dynamics of the venerable TFIC model and uncover a means to evince the material realization of the TFIC universality.