Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2408.13725 · Physical review. B./Physical review. B

Magnetization oscillations in a periodically driven transverse field Ising chain

Xiao Wang, Masaki Oshikawa, Márton Kormos, Jianda Wu

Published Nov 1, 2024• 6 citations
arXivHTMLPDF

Abstract

We investigate the nonequilibrium dynamics of the magnetization in an Ising chain subjected to a slowly rotating transverse field. The magnetization oscillations are found to be explained by the contributions from different particle excitations in the quantum ${E}_{8}$ model. We study the magnetization in the frequency domain in detail, uncovering a series of singular peaks for the $z$ (Ising) component. These singular peaks are split into two sets for the magnetization along the $x$ and $y$ directions with frequency shifts set by the rotational-field frequency. The peaks include both $\ensuremath{\delta}$-function type and edge-singularity type peaks. The $\ensuremath{\delta}$-function peaks can be attributed to particle excitations involving an ${E}_{8}$ particle with either the vacuum or a different particle. The edge-singularity peaks are contributed by particle excitations of two ${E}_{8}$ particles with either the vacuum or another particle, or by particle excitations that contain two sets of two particles with each set including at least a particle of the same type. We propose a Rydberg qubit array for possible experimental investigation.

DOI
10.1103/physrevb.110.195101

Related papers

Quasi-Periodically Driven Quantum Ising Chains

Dhruvil Doshi

Understanding the equilibration of isolated quantum systems under unitary dynamics is an interesting topic. In this paper, we look at the early time behaviour of periodically and quasi-periodically driven Transverse field Ising chains when and their corresponding dynamical free energies. We study the system under different frequencies and observe how the system evolves with changes in the field amplitudes in both types of oscillations.

arXiv:2208.12331•Aug 25, 2022•0 citations

Dynamical phase transition in the transverse field Ising chain characterized by the transverse magnetization spectral function

G. Piccitto, Alessandro Silva

We study the response of a quantum Ising chain to transverse field oscillations in the asymptotic state attained after a quantum quench. We show that for quenches across a quantum phase transition, the dissipative part of the response at low frequencies is negative, corresponding to energy emission up to a critical frequency ${\ensuremath{\omega}}^{*}$. The latter is found to be connected to the time period ${t}^{*}$ of the singularities in the Loschmidt echo $({t}^{*}=2\ensuremath{\pi}/{\ensuremath{\omega}}^{*})$ signaling the presence of a dynamical quantum phase transition. This result suggests that a linear-response experiment can be used to detect this kind of phenomenon.

arXiv:1903.03439•Physical review. B./Physical review. B•Oct 28, 2019•10 citations

Cascade of singularities in the spin dynamics of a perturbed quantum critical Ising chain

Xiao Wang, Haiyuan Zou, Kristóf Hódsági +3 more

When the quantum critical transverse-field Ising chain is perturbed by a longitudinal field, a quantum integrable model emerges in the scaling limit with massive excitations described by the exceptional ${E}_{8}$ Lie algebra. Using the corresponding analytical form factors of the quantum ${E}_{8}$ integrable model, we systematically study the spin dynamic structure factor of the perturbed quantum critical Ising chain, where particle channels with total energy up to $5{m}_{1}$ (${m}_{1}$ being the mass of the lightest ${E}_{8}$ particle) are exhausted. In addition to the significant single-particle contributions to the dynamic spectrum, each two-particle channel with different masses is found to exhibit an edge singularity at the threshold of the total mass and decays with an inverse square root of energy, which is attributed to the singularity of the two-particle density of states at the threshold. The singularity is absent for particles with equal masses due to a cancellation mechanism involving the structure of the form factors. As a consequence, the dynamic structure factor displays a cascade of bumping peaks in the continuum region with clear singular features which can serve as a solid guidance for the material realization of the quantum ${E}_{8}$ model.

arXiv:2103.09128•Physical review. B./Physical review. B•Jun 10, 2021•22 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

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

Quantum quench in a driven Ising chain

Neil J. Robinson, Isaac Pérez Castillo, Edgar Guzmán-González

We consider the Ising chain driven by oscillatory transverse magnetic fields. For certain parameter regimes, we reveal a hidden integrable structure in the problem, which allows access to the exact time evolution in this driven quantum system. We compute time-evolved one- and two-point functions following a quench that activates the driving. It is shown that this model does not heat up to infinite temperature, despite the absence of energy conservation, and we further discuss the generalization to a family of driven Hamiltonians that do not appear to suffer heating to infinite temperature, despite the absence of integrability and disorder. The particular model studied in detail also presents a route for realizing exotic physics (in this case, signatures of the ${E}_{8}$ structure associated with perturbing a critical quantum Ising chain with a small longitudinal magnetic field) by suitably tuning the driving frequency. In particular, we numerically confirm that the ratio of the masses of the two lowest meson excitations is given by the golden ratio.

arXiv:2011.14345•Physical review. B./Physical review. B•Apr 19, 2021•4 citations
We investigate the nonequilibrium dynamics of the magnetization in an Ising chain subjected to a slowly rotating transverse field. The magnetization oscillations are found to be explained by the contributions from different particle excitations in the quantum E8{E}_{8}E8​ model. We study the magnetization in the frequency domain in detail, uncovering a series of singular peaks for the zzz (Ising) component. These singular peaks are split into two sets for the magnetization along the xxx and yyy directions with frequency shifts set by the rotational-field frequency. The peaks include both \ensuremathδ\ensuremath{\delta}\ensuremathδ-function type and edge-singularity type peaks. The \ensuremathδ\ensuremath{\delta}\ensuremathδ-function peaks can be attributed to particle excitations involving an E8{E}_{8}E8​ particle with either the vacuum or a different particle. The edge-singularity peaks are contributed by particle excitations of two E8{E}_{8}E8​ particles with either the vacuum or another particle, or by particle excitations that contain two sets of two particles with each set including at least a particle of the same type. We propose a Rydberg qubit array for possible experimental investigation.
We study the response of a quantum Ising chain to transverse field oscillations in the asymptotic state attained after a quantum quench. We show that for quenches across a quantum phase transition, the dissipative part of the response at low frequencies is negative, corresponding to energy emission up to a critical frequency ${\ensuremath{\omega}}^{*}$. The latter is found to be connected to the time period t∗{t}^{*}t∗ of the singularities in the Loschmidt echo $({t}^{*}=2\ensuremath{\pi}/{\ensuremath{\omega}}^{*})$ signaling the presence of a dynamical quantum phase transition. This result suggests that a linear-response experiment can be used to detect this kind of phenomenon.
When the quantum critical transverse-field Ising chain is perturbed by a longitudinal field, a quantum integrable model emerges in the scaling limit with massive excitations described by the exceptional E8{E}_{8}E8​ Lie algebra. Using the corresponding analytical form factors of the quantum E8{E}_{8}E8​ integrable model, we systematically study the spin dynamic structure factor of the perturbed quantum critical Ising chain, where particle channels with total energy up to 5m15{m}_{1}5m1​ (m1{m}_{1}m1​ being the mass of the lightest E8{E}_{8}E8​ particle) are exhausted. In addition to the significant single-particle contributions to the dynamic spectrum, each two-particle channel with different masses is found to exhibit an edge singularity at the threshold of the total mass and decays with an inverse square root of energy, which is attributed to the singularity of the two-particle density of states at the threshold. The singularity is absent for particles with equal masses due to a cancellation mechanism involving the structure of the form factors. As a consequence, the dynamic structure factor displays a cascade of bumping peaks in the continuum region with clear singular features which can serve as a solid guidance for the material realization of the quantum E8{E}_{8}E8​ model.
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 LiHoF4\mathrm{Li}\mathrm{Ho}{\mathrm{F}}_{4}LiHoF4​.
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 Γ\GammaΓ. 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 consider the Ising chain driven by oscillatory transverse magnetic fields. For certain parameter regimes, we reveal a hidden integrable structure in the problem, which allows access to the exact time evolution in this driven quantum system. We compute time-evolved one- and two-point functions following a quench that activates the driving. It is shown that this model does not heat up to infinite temperature, despite the absence of energy conservation, and we further discuss the generalization to a family of driven Hamiltonians that do not appear to suffer heating to infinite temperature, despite the absence of integrability and disorder. The particular model studied in detail also presents a route for realizing exotic physics (in this case, signatures of the E8{E}_{8}E8​ structure associated with perturbing a critical quantum Ising chain with a small longitudinal magnetic field) by suitably tuning the driving frequency. In particular, we numerically confirm that the ratio of the masses of the two lowest meson excitations is given by the golden ratio.