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

Physical review. B, Condensed matter

Parametric sound pumping in thes=1/2 spin chain

Andrei A. Zvyagin

Published Jun 1, 1992• 2 citations
Publisher

Abstract

The parametric sound excitation of the spin s=1/2 chain is considered theoretically. The equation for the sound absorption shows that there is no parametric instability of spins in resonance for this one-dimensional system. The sound excitation takes place in a nonthreshold manner.
DOI
10.1103/physrevb.45.12917

Related papers

Nonlinear spin excitations in finite Heisenberg chains

Shakhnoza Rakhmanova, D. L. Mills

In the recent literature, there have been discussions of nonlinear spin excitations in one-dimensional, anisotropic Heisenberg spin chains. These have the character of localized excitations, which emerge from the time-dependent classical equations of motion. We show that for a given frequency, in a finite spin chain one has a hierarchy of nonlinear excitations, whose envelopes have the appearance of a one soliton, two soliton,..., states. Also, we consider the nature of these nonlinear excitations in an applied magnetic field of frequency \ensuremath{\omega}, and explore aspects of the transient behavior of the system in response to a time varying external field. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matter•Oct 1, 1996•48 citations

Anomalous parametric resonance in a spin-1/2 chain: dynamical effects of nontrivial topology

Mahmoud T. Elewa, M. I. Dykman

Resonant parametric modulation is a major tool of studying magnetic systems. For a spin-1/2 chain in a strong magnetic field, the resulting excitations can be mapped on fermionic excitations in the Kitaev chain. We show that the response to turning on the modulation reveals dynamical bulk aspects of the nontrivial topology of the closed chain. In the topological regime, depending on the turn-on rate, the system displays an absence of frequency dispersion of the time-averaged magnetization and an absence or a suppression of its spatial correlations near resonance. The transition between the topological and trivial regimes is controlled by the modulation frequency.

cond-mat.mes-hallCross-listedarXiv:2511.10891•Physical review. B./Physical review. B•Nov 17, 2025•0 citations

Fermionic quantum spin liquids: Exact results for parametric pumping

Andrei A. Zvyagin

The time dependence of the response of the quantum spin liquid with fermionic excitations to parametric pumping has been calculated exactly for the special case of periodic pumping, the steplike periodic field, without using the resonance approximation, and for any value of the pumping magnitude. In the closed regime each mode (related to each eigenstate of the system) oscillates with time. The oscillations persist about the steady-state values, which are determined by the parameters of the pumping. The magnitude of the oscillations is finite for any value of the magnitude of the pumping. Those features drastically differ from the well-known resonance parametric pumping of magnons in magnetically ordered system, where the number of resonance magnons grows exponentially in time. The interference of infinitely many modes generically yields only decaying-in-time modulated oscillations of the total number of quasiparticles per mode even in the closed regime. For the fermionic system only one mode is in resonance, while others are out of resonance. It is totally different from the bosonic behavior of magnons under parametric pumping, where all modes can exist in resonance. The inclusion of the linear relaxation in the open regime for that quantum spin liquid produces the decay of oscillations to the initial state.

Physical review. B./Physical review. B•Jul 12, 2019•1 citation

Excitations for the one-dimensional S = 1 pseudo-Heisenberg antiferromagnetic chain

E. V. Orlenko, Fedor E. Orlenko, George G. Zegrya

We are interested in the anisotropic S=1 antiferromagnetic chain. System of particles with an arbitrary spin is described directly from the first principles, based on the symmetry law. The ground state of the one-dimensional S=1 pseudo-Heisenberg antiferromagnet with single-ion anisotropy is calculated. Excitations of the chain in the form of nonlinear spin waves and, in particular, the possibility of a soliton solution is considered.

Natural Science•Jan 1, 2010•1 citation

Sound pumping in an alternating quantum spin chain

Andrei A. Zvyagin, G. A. Zvyagina

The pumping of the energy of a longitudinal sound by a quantum spin chain with the alternation of coupling constants is studied theoretically. It is shown that the power of the sound wave, absorbed by the dimerized spin chain, is zero in the dynamical regime, i.e., at times, smaller than relaxation times. In the steady-state regime, for times, larger than the relaxation time, the dimerized quantum spin chain can absorb the power of the sound. We have shown that the absorption of the sound exists when the frequency of the wave is between two threshold values, related to two critical fields, at which quantum phase transitions take place. Contrary, the calculated magnetic field dependence of the absorbed power of the sound does not clearly manifest two critical fields. Nevertheless, we have shown that it is possible to extract the information about the value of the field, at which the spin gap of low-lying excitations is closed, from the temperature dependence of the absorption of the longitudinal sound.

Physical Review B•Mar 16, 2006•0 citations

Resonance in a Quantum Chain

Eytan Barouch

A resonance of a magnetic impurity with a quantum spin‐chain is studied. A Fresnel diffraction pattern is found.

Studies in Applied Mathematics•Apr 1, 1977•1 citation
In the recent literature, there have been discussions of nonlinear spin excitations in one-dimensional, anisotropic Heisenberg spin chains. These have the character of localized excitations, which emerge from the time-dependent classical equations of motion. We show that for a given frequency, in a finite spin chain one has a hierarchy of nonlinear excitations, whose envelopes have the appearance of a one soliton, two soliton,..., states. Also, we consider the nature of these nonlinear excitations in an applied magnetic field of frequency \ensuremath{\omega}, and explore aspects of the transient behavior of the system in response to a time varying external field. \textcopyright{} 1996 The American Physical Society.
Resonant parametric modulation is a major tool of studying magnetic systems. For a spin-1/2 chain in a strong magnetic field, the resulting excitations can be mapped on fermionic excitations in the Kitaev chain. We show that the response to turning on the modulation reveals dynamical bulk aspects of the nontrivial topology of the closed chain. In the topological regime, depending on the turn-on rate, the system displays an absence of frequency dispersion of the time-averaged magnetization and an absence or a suppression of its spatial correlations near resonance. The transition between the topological and trivial regimes is controlled by the modulation frequency.
The time dependence of the response of the quantum spin liquid with fermionic excitations to parametric pumping has been calculated exactly for the special case of periodic pumping, the steplike periodic field, without using the resonance approximation, and for any value of the pumping magnitude. In the closed regime each mode (related to each eigenstate of the system) oscillates with time. The oscillations persist about the steady-state values, which are determined by the parameters of the pumping. The magnitude of the oscillations is finite for any value of the magnitude of the pumping. Those features drastically differ from the well-known resonance parametric pumping of magnons in magnetically ordered system, where the number of resonance magnons grows exponentially in time. The interference of infinitely many modes generically yields only decaying-in-time modulated oscillations of the total number of quasiparticles per mode even in the closed regime. For the fermionic system only one mode is in resonance, while others are out of resonance. It is totally different from the bosonic behavior of magnons under parametric pumping, where all modes can exist in resonance. The inclusion of the linear relaxation in the open regime for that quantum spin liquid produces the decay of oscillations to the initial state.
The pumping of the energy of a longitudinal sound by a quantum spin chain with the alternation of coupling constants is studied theoretically. It is shown that the power of the sound wave, absorbed by the dimerized spin chain, is zero in the dynamical regime, i.e., at times, smaller than relaxation times. In the steady-state regime, for times, larger than the relaxation time, the dimerized quantum spin chain can absorb the power of the sound. We have shown that the absorption of the sound exists when the frequency of the wave is between two threshold values, related to two critical fields, at which quantum phase transitions take place. Contrary, the calculated magnetic field dependence of the absorbed power of the sound does not clearly manifest two critical fields. Nevertheless, we have shown that it is possible to extract the information about the value of the field, at which the spin gap of low-lying excitations is closed, from the temperature dependence of the absorption of the longitudinal sound.