Dynamics of the Ising Model near the Critical Point

We study the real-time domain-wall dynamics near a quantum critical point of the one-dimensional anisotropic ferromagnetic spin $1∕2$ chain. By numerical simulation, we find that the domain wall is dynamically stable in the Heisenberg-Ising model. Near the quantum critical point, the width of the domain wall diverges as ${(\ensuremath{\Delta}\ensuremath{-}1)}^{\ensuremath{-}1∕2}$.We study the real-time domain-wall dynamics near a quantum critical point of the one-dimensional anisotropic ferromagnetic spin $1∕2$ chain. By numerical simulation, we find that the domain wall is dynamically stable in the Heisenberg-Ising model. Near the quantum critical point, the width of the domain wall diverges as ${(\ensuremath{\Delta}\ensuremath{-}1)}^{\ensuremath{-}1∕2}$.

arXiv:0704.0193Physical Review BMay 16, 20078 citations

Quantum critical dynamics in the two-dimensional transverse Ising model

Chisa Hotta, Tempei Yoshida, Kenji Harada

In the vicinity of the quantum critical point (QCP), thermodynamic properties diverge toward zero temperature governed by universal exponents. Although this fact is well known, how it is reflected in quantum dynamics has not been addressed. The QCP of the transverse Ising model on a triangular lattice is an ideal platform to test the issue, since it has an experimental realization, the dielectrics being realized in an organic dimer Mott insulator, $\ensuremath{\kappa}\text{\ensuremath{-}}{\mathrm{ET}}_{2}X$, where a quantum electric dipole represents the Ising degrees of freedom. We track the Glauber-type dynamics of the model by constructing a kinetic protocol based on the quantum Monte Carlo method. The dynamical susceptibility takes the form of the Debye function and shows a significant peak narrowing in approaching a QCP due to the divergence of the relaxation timescale. It explains the anomaly of dielectric constants observed in the organic materials, indicating that the material is very near the ferroelectric QCP. We disclose how the dynamical and other critical exponents develop near QCP beyond the simple field theory.In the vicinity of the quantum critical point (QCP), thermodynamic properties diverge toward zero temperature governed by universal exponents. Although this fact is well known, how it is reflected in quantum dynamics has not been addressed. The QCP of the transverse Ising model on a triangular lattice is an ideal platform to test the issue, since it has an experimental realization, the dielectrics being realized in an organic dimer Mott insulator, $\ensuremath{\kappa}\text{\ensuremath{-}}{\mathrm{ET}}_{2}X$, where a quantum electric dipole represents the Ising degrees of freedom. We track the Glauber-type dynamics of the model by constructing a kinetic protocol based on the quantum Monte Carlo method. The dynamical susceptibility takes the form of the Debye function and shows a significant peak narrowing in approaching a QCP due to the divergence of the relaxation timescale. It explains the anomaly of dielectric constants observed in the organic materials, indicating that the material is very near the ferroelectric QCP. We disclose how the dynamical and other critical exponents develop near QCP beyond the simple field theory.

Physical Review ResearchMar 17, 20237 citations

We study the real-time domain-wall dynamics near a quantum critical point of the one-dimensional anisotropic ferromagnetic spin

1∕2

chain. By numerical simulation, we find that the domain wall is dynamically stable in the Heisenberg-Ising model. Near the quantum critical point, the width of the domain wall diverges as ${(\ensuremath{\Delta}\ensuremath{-}1)}^{\ensuremath{-}1∕2}$.