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./Physical review. B

Fermionic quantum spin liquids: Exact results for parametric pumping

Andrei A. Zvyagin

Published Jul 12, 2019• 1 citation
Publisher

Abstract

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.

DOI
10.1103/physrevb.100.024413

Related papers

Parametric pumping of the two-dimensional quantum spin liquid

Andrei A. Zvyagin

With the help of the exact solution of the Kitaev model the parametric pumping of the two-dimensional quantum spin liquid under the action of the ac magnetic field is studied. In the dynamical regime the field produces oscillations of the magnetization with the field's frequency, modulated by the Rabi-like oscillations. In the steady-state regime, the Rabi-like oscillations are damped. The absorption of the ac field by the Kitaev spin model is finite and manifests resonance features. Such a behavior is generic for quantum spin liquids with fermionic excitations, and it is different from the linear spin-wave response of magnetically ordered systems to such a parametric pumping.

Physical review. B./Physical review. B•Feb 24, 2017•4 citations

Dynamics of a many-body quantum spin system caused by a sequence of pulses

Andrei A. Zvyagin

Exact results for time evolution of a many-body quantum system (a transverse field Ising spin chain) under the action of several pulses of an external field are obtained. Unlike the situation with a single pulse, the magnetization depends on time for the sequence of two pulses. For the two-pulse case the magnetization does not depend on the value of the time spacing between pulses, in sharp contrast with the standard spin echo cases. Modulated oscillations of magnetization with time do not decay if the energy of eigenstates of the system before pulses is $k$ independent $(k$ is the quasimomentum), while for $k$-dependent initial eigenstates the modulated oscillations of magnetization decay (without inclusion of the ``external'' relaxation) to the steady-state value, depending on the parameters of pulses; i.e., the oscillations reveal time irreversibility.

Physical review. B./Physical review. B•Aug 13, 2018•1 citation

Dynamics of a one-dimensional spinor Bose liquid: A phenomenological approach

Alex Kamenev, L. I. Glazman

The ground state of a spinor Bose liquid is ferromagnetic, while the softest excitation above the ground state is the magnon mode. The dispersion relation of the magnon in a one-dimensional liquid is periodic in the wave number $q$ with the period of $2\ensuremath{\pi}n$, determined by the density $n$ of the liquid. Dynamic correlation functions, such as, e.g., spin-spin correlation function, exhibit power-law singularities at the magnon spectrum, $\ensuremath{\omega}\ensuremath{\rightarrow}{\ensuremath{\omega}}_{m}(q,n)$. Without using any specific model of the interparticle interactions, we relate the corresponding exponents to independently measurable quantities $\ensuremath{\partial}{\ensuremath{\omega}}_{m}/\ensuremath{\partial}q$ and $\ensuremath{\partial}{\ensuremath{\omega}}_{m}/\ensuremath{\partial}n$.

arXiv:0808.0479•Physical Review A•Jul 16, 2009•59 citations

Dynamics of the Kitaev chain model under parametric pumping

Andrei A. Zvyagin

Dynamics of the Kitaev chain model under the effect of parametric pumping is studied. Two contributions to dynamical characteristics are considered: from the extended eigenstates and from the edge bound state (zero Majorana modes). It is shown that in the dynamical regime the frequencies of Rabi oscillations for zero Majorana modes are much larger than those related to gapped extended states. In the steady-state regime, the Rabi oscillations are blurred due to relaxation processes, and only oscillations of the characteristics of the model with the pumping frequency exist, producing absorption of the pumping power by extended states. Experimental realizations of the considered effect are discussed.

Physical Review B•Jul 18, 2014•11 citations

Degenerate parametric amplification with time-dependent pump amplitude and phase

Maurice T. Raiford

A quantum-statistical treatment of degenerate (single-mode) parametric amplification is given in which the pump is allowed to have time-dependent amplitude and phase. This relaxes earlier restrictions of a constant pump in exact resonance with the signal. Solutions are obtained for the case where the ratio of the time derivative of the pump phase to the coupling strength between pump and signal is constant. This includes the special case of simple offresonance, where the pump has a constant frequency differing from twice the signal frequency by a given amount (and has constant amplitude). The Wigner distribution for the signal mode is obtained (the $P$ distribution does not in general exist as a well-defined function beyond a finite time interval for this process) and is used to determine the time development of the expectation values of various field operators of interest, such as field strengths and fluctuations. A critical point exists in the solution for the photon annihilation operator such that the behavior of the solution and the resulting quantities which it determines is divided into an exponential region and an oscillatory region. The critical point defines, from the expectation value for the photon number, the condition for amplification. For the case of simple off-resonance, this gives the frequency range of amplification. A calculation without using the rotating-wave approximation is given in the Appendix which shows that, to first order, the same range is obtained as when the approximation is used. The effect of damping is given, showing, e.g., how it slows the growth rate of the signal (in the region of amplification) and how it narrows the frequency range of amplification. The effect of a time-dependent pump (and damping) on the breakdown of the $P$ distribution is also described.

Physical Review A•May 1, 1974•45 citations

New fermionic description of quantum spin liquid state

Alexei M. Tsvelik

A novel approach to S=1/2 antiferromagnets with strong quantum fluctuations based on the representation of spin-1/2 operators as bilinear forms of real (Majorana) fermions is suggested. This representation does not contain unphysical states and thus does not require the imposition of constraints on the fermionic Hilbert space. This property allows one to construct a simple and effective mean field theory of the spin liquid state. As an example illustrating the basic properties of this state I consider a model of Kondo lattice. It is shown that this model has a singlet ground state; elementary excitations have a spectral gap and are S=1 real (Majorana) fermions.

arXiv:cond-mat/9206007•Physical Review Letters•Oct 5, 1992•88 citations
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.
With the help of the exact solution of the Kitaev model the parametric pumping of the two-dimensional quantum spin liquid under the action of the ac magnetic field is studied. In the dynamical regime the field produces oscillations of the magnetization with the field's frequency, modulated by the Rabi-like oscillations. In the steady-state regime, the Rabi-like oscillations are damped. The absorption of the ac field by the Kitaev spin model is finite and manifests resonance features. Such a behavior is generic for quantum spin liquids with fermionic excitations, and it is different from the linear spin-wave response of magnetically ordered systems to such a parametric pumping.
Exact results for time evolution of a many-body quantum system (a transverse field Ising spin chain) under the action of several pulses of an external field are obtained. Unlike the situation with a single pulse, the magnetization depends on time for the sequence of two pulses. For the two-pulse case the magnetization does not depend on the value of the time spacing between pulses, in sharp contrast with the standard spin echo cases. Modulated oscillations of magnetization with time do not decay if the energy of eigenstates of the system before pulses is kkk independent (k(k(k is the quasimomentum), while for kkk-dependent initial eigenstates the modulated oscillations of magnetization decay (without inclusion of the ``external'' relaxation) to the steady-state value, depending on the parameters of pulses; i.e., the oscillations reveal time irreversibility.
The ground state of a spinor Bose liquid is ferromagnetic, while the softest excitation above the ground state is the magnon mode. The dispersion relation of the magnon in a one-dimensional liquid is periodic in the wave number qqq with the period of $2\ensuremath{\pi}n$, determined by the density nnn of the liquid. Dynamic correlation functions, such as, e.g., spin-spin correlation function, exhibit power-law singularities at the magnon spectrum, $\ensuremath{\omega}\ensuremath{\rightarrow}{\ensuremath{\omega}}_{m}(q,n)$. Without using any specific model of the interparticle interactions, we relate the corresponding exponents to independently measurable quantities $\ensuremath{\partial}{\ensuremath{\omega}}_{m}/\ensuremath{\partial}q$ and $\ensuremath{\partial}{\ensuremath{\omega}}_{m}/\ensuremath{\partial}n$.
Dynamics of the Kitaev chain model under the effect of parametric pumping is studied. Two contributions to dynamical characteristics are considered: from the extended eigenstates and from the edge bound state (zero Majorana modes). It is shown that in the dynamical regime the frequencies of Rabi oscillations for zero Majorana modes are much larger than those related to gapped extended states. In the steady-state regime, the Rabi oscillations are blurred due to relaxation processes, and only oscillations of the characteristics of the model with the pumping frequency exist, producing absorption of the pumping power by extended states. Experimental realizations of the considered effect are discussed.
A quantum-statistical treatment of degenerate (single-mode) parametric amplification is given in which the pump is allowed to have time-dependent amplitude and phase. This relaxes earlier restrictions of a constant pump in exact resonance with the signal. Solutions are obtained for the case where the ratio of the time derivative of the pump phase to the coupling strength between pump and signal is constant. This includes the special case of simple offresonance, where the pump has a constant frequency differing from twice the signal frequency by a given amount (and has constant amplitude). The Wigner distribution for the signal mode is obtained (the PPP distribution does not in general exist as a well-defined function beyond a finite time interval for this process) and is used to determine the time development of the expectation values of various field operators of interest, such as field strengths and fluctuations. A critical point exists in the solution for the photon annihilation operator such that the behavior of the solution and the resulting quantities which it determines is divided into an exponential region and an oscillatory region. The critical point defines, from the expectation value for the photon number, the condition for amplification. For the case of simple off-resonance, this gives the frequency range of amplification. A calculation without using the rotating-wave approximation is given in the Appendix which shows that, to first order, the same range is obtained as when the approximation is used. The effect of damping is given, showing, e.g., how it slows the growth rate of the signal (in the region of amplification) and how it narrows the frequency range of amplification. The effect of a time-dependent pump (and damping) on the breakdown of the PPP distribution is also described.
A novel approach to S=1/2 antiferromagnets with strong quantum fluctuations based on the representation of spin-1/2 operators as bilinear forms of real (Majorana) fermions is suggested. This representation does not contain unphysical states and thus does not require the imposition of constraints on the fermionic Hilbert space. This property allows one to construct a simple and effective mean field theory of the spin liquid state. As an example illustrating the basic properties of this state I consider a model of Kondo lattice. It is shown that this model has a singlet ground state; elementary excitations have a spectral gap and are S=1 real (Majorana) fermions.