© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:1512.00731 · Physical review. B./Physical review. B

Nonequilibrium dynamics of the Ising chain in a fluctuating transverse field

Gergő Roósz, Róbert Juhász, Ferenc Iglói

Published Apr 6, 2016• 14 citations

Abstract

We study nonequilibrium dynamics of the quantum Ising chain at zero temperature when the transverse field is varied stochastically. In the equivalent fermion representation, the equation of motion of Majorana operators is derived in the form of a one-dimensional, continuous-time quantum random walk with stochastic, time-dependent transition amplitudes. This type of external noise gives rise to decoherence in the associated quantum walk and the semiclassical wave packet generally has a diffusive behavior. As a consequence, in the quantum Ising chain, the average entanglement entropy grows in time as ${t}^{1/2}$ and the logarithmic average magnetization decays in the same form. In the case of a dichotomous noise, when the transverse field is changed in discrete time steps, $\ensuremath{\tau}$, there can be excitation modes, for which coherence is maintained, provided their energy satisfies ${\ensuremath{\epsilon}}_{k}\ensuremath{\tau}\ensuremath{\approx}n\ensuremath{\pi}$ with a positive integer $n$. If the dispersion of ${\ensuremath{\epsilon}}_{k}$ is quadratic, the long-time behavior of the entanglement entropy and the logarithmic magnetization is dominated by these ballistically traveling coherent modes and both will have a ${t}^{3/4}$ time dependence.

DOI: 10.1103/physrevb.93.134305

Related papers

Nonequilibrium Dynamics due to Magnetization Transport in Transverse Ising Chain

Sirshendu Bhattacharyya, Subinay Dasgupta

We study the dynamics caused by transport of transverse magnetization in one dimensional transverse Ising chain at zero temperature. We observe that a class of initial states in fermionic momentum-space produce spatial variation in transverse magnetization. Starting from such a state, we obtain the transverse magnetization analytically and then observe its dynamics in presence of a homogeneous constant field $\Gamma$. In contradiction with general expectation, whatever be the strength of the field, the magnetization of the system does not become homogeneous even after infinite time. In each site, the dynamics is associated with oscillations having two different timescales. The envelope of the larger timescale oscillation decays algebraically having an exponent which is universal for the entire class of such initial states. Signature of quantum criticality is also embedded in the dynamics in two aspects : Behavioral change shown by the frequency of large timescale oscillation at any site and the corresponding magnetization at infinity when they cross the quantum critical point.

•Dec 13, 2016•0 citations

Dynamical quantum phase transitions following a noisy quench

Rouhollah Jafari, A. Langari, Sebastian Eggert +1 more

We study how time-dependent energy fluctuations impact the dynamical quantum phase transitions (DQPTs) following a noisy ramped quench of the transverse magnetic field in a quantum Ising chain. By numerically solving the stochastic Schrödinger equation of the mode-decoupled fermionic Hamiltonian of the problem, we identify two generic scenarios: Depending on the amplitude of the noise and the rate of the ramp, the expected periodic sequence of noiseless DQPTs may either be uniformly shifted in time or else replaced by a disarray of closely spaced DQPTs. Guided by an exact noise master equation, we trace the phenomenon to the interplay between noise-induced excitations which accumulate during the quench and the near-adiabatic dynamics of the massive modes of the system. Our analysis generalizes to any one-dimensional fermionic two-band model subject to a noisy quench. Published by the American Physical Society 2024

arXiv:2310.13337•Physical review. B./Physical review. B•May 23, 2024•20 citations

Quantum dynamics of an Ising spin chain in a random transverse field

Xun Jia, Sudip Chakravarty

We consider an Ising spin chain in a random transverse magnetic field and compute the zero temperature wave vector and frequency dependent dynamic structure factor numerically by using Jordan-Wigner transformation. Two types of distributions of magnetic fields are introduced. For a rectangular distribution, a dispersing branch is observed, and disorder tends to broaden the dispersion peak and close the excitation gap. For a binary distribution, a nondispersing branch at almost zero energy is obtained, in addition to a dispersing branch. We discuss the relationship of our work to the neutron scattering measurement in $\mathrm{Li}\mathrm{Ho}{\mathrm{F}}_{4}$.

arXiv:cond-mat/0607703•Physical Review B•Nov 30, 2006•13 citations

Non-equilibrium quench dynamics in quantum quasicrystals

Ferenc Iglói, Gergő Roósz, Yu‐Cheng Lin

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.

arXiv:1210.7328•New Journal of Physics•Feb 25, 2013•23 citations

Relaxation, prethermalization, and diffusion in a noisy quantum Ising chain

Jamir Marino, Alessandro Silva

We study the dynamics of thermalization resulting from a time-dependent noise in a quantum Ising chain subject to a sudden quench of the transverse magnetic field. For weak noise the dynamics shows a prethermalized state at intermediate time scales, eventually drifting towards an asymptotic infinite temperature steady state characterized by diffusive behavior. By computing analytically the density of kinks, as well as the transverse and longitudinal magnetic field correlators, we characterize these two regimes, their observability, and their signatures in the various physical quantities.

arXiv:1203.2108•Physical Review B•Aug 22, 2012•85 citations

Nonequilibrium Steady State in a Quantum System: One-Dimensional Transverse Ising Model with Energy Current

Tibor Antal A, Zoltàn Ràcz, L. Sasvári

We study the nonequilibrium steady states of an Ising chain in a transverse field $h$ by investigating the effect of a field $\ensuremath{\lambda}$, which drives the current of energy. The zero-temperature, $h$- $\ensuremath{\lambda}$ phase diagram is determined exactly, and it is found that the energy current appears continuously above a threshold $\ensuremath{\lambda}>{\ensuremath{\lambda}}_{c}(h)$. The long-range magnetic order (present for $h<{h}_{c},\ensuremath{\lambda}<{\ensuremath{\lambda}}_{c}$) is destroyed in the current-carrying state where the correlations are characterized by power-law, oscillatory decay. The mechanism which generates the power-law correlations in the current-carrying state is discussed.

arXiv:cond-mat/9612047•Physical Review Letters•Jan 13, 1997•72 citations

We study nonequilibrium dynamics of the quantum Ising chain at zero temperature when the transverse field is varied stochastically. In the equivalent fermion representation, the equation of motion of Majorana operators is derived in the form of a one-dimensional, continuous-time quantum random walk with stochastic, time-dependent transition amplitudes. This type of external noise gives rise to decoherence in the associated quantum walk and the semiclassical wave packet generally has a diffusive behavior. As a consequence, in the quantum Ising chain, the average entanglement entropy grows in time as

{t}^{1/2}

and the logarithmic average magnetization decays in the same form. In the case of a dichotomous noise, when the transverse field is changed in discrete time steps,

\ensuremath{\tau}

, there can be excitation modes, for which coherence is maintained, provided their energy satisfies

{\ensuremath{\epsilon}}_{k}\ensuremath{\tau}\ensuremath{\approx}n\ensuremath{\pi}

with a positive integer

n

. If the dispersion of

{\ensuremath{\epsilon}}_{k}

is quadratic, the long-time behavior of the entanglement entropy and the logarithmic magnetization is dominated by these ballistically traveling coherent modes and both will have a

{t}^{3/4}

time dependence.

We study the dynamics caused by transport of transverse magnetization in one dimensional transverse Ising chain at zero temperature. We observe that a class of initial states in fermionic momentum-space produce spatial variation in transverse magnetization. Starting from such a state, we obtain the transverse magnetization analytically and then observe its dynamics in presence of a homogeneous constant field

\Gamma

. In contradiction with general expectation, whatever be the strength of the field, the magnetization of the system does not become homogeneous even after infinite time. In each site, the dynamics is associated with oscillations having two different timescales. The envelope of the larger timescale oscillation decays algebraically having an exponent which is universal for the entire class of such initial states. Signature of quantum criticality is also embedded in the dynamics in two aspects : Behavioral change shown by the frequency of large timescale oscillation at any site and the corresponding magnetization at infinity when they cross the quantum critical point.

We study how time-dependent energy fluctuations impact the dynamical quantum phase transitions (DQPTs) following a noisy ramped quench of the transverse magnetic field in a quantum Ising chain. By numerically solving the stochastic Schrödinger equation of the mode-decoupled fermionic Hamiltonian of the problem, we identify two generic scenarios: Depending on the amplitude of the noise and the rate of the ramp, the expected periodic sequence of noiseless DQPTs may either be uniformly shifted in time or else replaced by a disarray of closely spaced DQPTs. Guided by an exact noise master equation, we trace the phenomenon to the interplay between noise-induced excitations which accumulate during the quench and the near-adiabatic dynamics of the massive modes of the system. Our analysis generalizes to any one-dimensional fermionic two-band model subject to a noisy quench. Published by the American Physical Society 2024

We consider an Ising spin chain in a random transverse magnetic field and compute the zero temperature wave vector and frequency dependent dynamic structure factor numerically by using Jordan-Wigner transformation. Two types of distributions of magnetic fields are introduced. For a rectangular distribution, a dispersing branch is observed, and disorder tends to broaden the dispersion peak and close the excitation gap. For a binary distribution, a nondispersing branch at almost zero energy is obtained, in addition to a dispersing branch. We discuss the relationship of our work to the neutron scattering measurement in

\mathrm{Li}\mathrm{Ho}{\mathrm{F}}_{4}

.

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 dynamics of thermalization resulting from a time-dependent noise in a quantum Ising chain subject to a sudden quench of the transverse magnetic field. For weak noise the dynamics shows a prethermalized state at intermediate time scales, eventually drifting towards an asymptotic infinite temperature steady state characterized by diffusive behavior. By computing analytically the density of kinks, as well as the transverse and longitudinal magnetic field correlators, we characterize these two regimes, their observability, and their signatures in the various physical quantities.

We study the nonequilibrium steady states of an Ising chain in a transverse field

h

by investigating the effect of a field $\ensuremath{\lambda}$, which drives the current of energy. The zero-temperature,

h

- $\ensuremath{\lambda}$ phase diagram is determined exactly, and it is found that the energy current appears continuously above a threshold $\ensuremath{\lambda}>{\ensuremath{\lambda}}_{c}(h)$. The long-range magnetic order (present for $h<{h}_{c},\ensuremath{\lambda}<{\ensuremath{\lambda}}_{c}$) is destroyed in the current-carrying state where the correlations are characterized by power-law, oscillatory decay. The mechanism which generates the power-law correlations in the current-carrying state is discussed.