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Physical review. B./Physical review. B

Quasiparticle dynamics in a quasiperiodic Ising model with temporally fluctuating transverse fields

Kohei Ohgane, Yusuke Masaki, Hiroaki Matsueda

Published Apr 11, 2023• 4 citations
Publisher

Abstract

We study quasiparticle dynamics in a quasiperiodic Ising model with temporally fluctuating transverse fields. Specifically, we calculate the dynamical exponents of the standard deviation of a quasiparticle spreading under a field chosen randomly from binary values $\ifmmode\pm\else\textpm\fi{}h$ at every time interval. We find that the short-time behavior of the dynamical exponents depends on the interval of the temporally fluctuating fields. We also reveal how the quasiparticle dynamics affects the relaxation of spin-spin correlation functions. The dynamics can be explained via the overlap between the eigenvectors of a Hamiltonian with $\ifmmode\pm\else\textpm\fi{}h$.

DOI
10.1103/physrevb.107.134201

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We study quasiparticle dynamics in a quasiperiodic Ising model with temporally fluctuating transverse fields. Specifically, we calculate the dynamical exponents of the standard deviation of a quasiparticle spreading under a field chosen randomly from binary values \ifmmode±\else\textpm\fih\ifmmode\pm\else\textpm\fi{}h\ifmmode±\else\textpm\fih at every time interval. We find that the short-time behavior of the dynamical exponents depends on the interval of the temporally fluctuating fields. We also reveal how the quasiparticle dynamics affects the relaxation of spin-spin correlation functions. The dynamics can be explained via the overlap between the eigenvectors of a Hamiltonian with \ifmmode±\else\textpm\fih\ifmmode\pm\else\textpm\fi{}h\ifmmode±\else\textpm\fih.
We study quasi-particle dynamics in a quasi-periodic Ising model with temporally fluctuating transverse fields. Specifically, we calculate the dynamical exponents of the standard deviation of a quasi-particle spreading under a field chosen randomly from binary values ±h\pm h±h at every time interval. We find that the short-time behavior of the dynamical exponents depends on the interval of the temporally fluctuating fields. We also reveal how the quasi-particle dynamics affects the relaxation of spin-spin correlation functions. The dynamics can be explained via the overlap between the eigenvectors of a Hamiltonian with ±h\pm h±h.
The effects of Gaussian disorder on the dynamics of the one-dimensional spin-1/2 random transverse Ising model are studied in the high-temperature limit by the recursion method. Both spin autocorrelation functions and the corresponding spectral densities are calculated for three types of disordered cases. It is found that when the standard deviation ${\ensuremath{\sigma}}_{J}$ of the exchange coupling (or the standard deviation ${\ensuremath{\sigma}}_{B}$ of the random transverse field) is small, the dynamics of the system undergoes two crossovers in sequence as the mean value of the exchange coupling (or the random transverse field) varies: from a central-peak behavior to a collective-mode one, and then to the precession of free spins in an external transverse magnetic field. However, when ${\ensuremath{\sigma}}_{J}$ or ${\ensuremath{\sigma}}_{B}$ are large enough, there is no crossover, i.e., the dynamics of the system shows a central-peak behavior and a disordered behavior, respectively.
We study the non-equilibrium dynamics of a quasiperiodic quantum Ising chain after a sudden change in the strength of the transverse field at zero temperature. In particular, we consider the dynamics of the entanglement entropy and the relaxation of the magnetization. The entanglement entropy increases with time as a power law, and the magnetization is found to exhibit stretched-exponential relaxation. These behaviors are explained in terms of anomalously diffusing quasiparticles, which are studied in a wave packet approach. The non-equilibrium magnetization is shown to have a dynamical phase transition.
We study the time dependent behavior of the four-spin interactions Ising chain in the presence of a disordered transverse magnetic field. In order to analyze the effects of field randomness in the dynamical behavior of the system we calculate the time-dependent correlation function and the longitudinal relaxation function of the infinite chain. We consider a bi-modal distribution for the field energy strength, where one of its values equals the exchange coupling energy while the other value can be lower or higher than the coupling energy. We find that an increasing concentration of weaker fields produces an enhancement of the central mode behavior. However, when the concentration of stronger fields increases, the system undergoes a crossover from central mode to collective-type dynamics.
We study the time evolution of the one-dimensional random-bond transverse Ising model with four-spin interactions. We calculate the time-dependent correlation function as well as the longitudinal relaxation function of the infinite chain. We analyze how the presence of disorder affect the dynamical behavior of the system in comparison with the pure model. We find that the main effect of disorder is to produce a crossover from a central mode to a collective-mode type of dynamics, as the concentration of weaker bonds is enhanced. Such crossover is also present in the case of an increase in bond dilution.