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arXiv:1708.08050 · Physical review. B./Physical review. B

Semiclassical dynamics of spin density waves

Gia-Wei Chern, Kipton M. Barros, Zhentao Wang, Hidemaro Suwa, Cristian D. Batista

Published Jan 10, 2018• 38 citations
arXivHTMLPDF

Abstract

Spin density waves (SDW) provide a canonical example of quantum states with spontaneously broken symmetries. The dynamics of SDWs in Mott insulators is described by the well-known Holstein-Primakoff Hamiltonian, which is equivalent to the semiclassical Landau-Lifshitz equation. Based on a real-space formulation of the time-dependent Hartree-Fock method, the authors demonstrate how to extend the semiclassical dynamics description to the case of itinerant magnets or Mott systems with a moderate charge gap. They further show that, within the adiabatic approximation, the SDW dynamics is governed by a generalized quantum Landau-Lifshitz equation.

DOI
10.1103/physrevb.97.035120

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Spin density waves (SDW) provide a canonical example of quantum states with spontaneously broken symmetries. The dynamics of SDWs in Mott insulators is described by the well-known Holstein-Primakoff Hamiltonian, which is equivalent to the semiclassical Landau-Lifshitz equation. Based on a real-space formulation of the time-dependent Hartree-Fock method, the authors demonstrate how to extend the semiclassical dynamics description to the case of itinerant magnets or Mott systems with a moderate charge gap. They further show that, within the adiabatic approximation, the SDW dynamics is governed by a generalized quantum Landau-Lifshitz equation.
The transverse dynamical susceptibility and the spin-wave stiffness constant of spin-density-wave (SDW) states in itinerant-electron systems are studied. The Hamiltonian is transformed by using a transformation which rotates the spin coordinate system locally, so that the new zzz direction lies in the direction of the local spin. For this transformed Hamiltonian, a self-consistent many-body theory developed by Fedro and Wilson and extended by Kishore is exploited to derive an exact expression for the transverse dynamical susceptibility. From the long-wavelength limit of the spin-wave spectrum, given by the poles of the transverse dynamical susceptibility, an exact formula for the spin-wave stiffness constant is obtained. Within the Hartree-Fock approximation, it reduces to the Fisher's formula for antiferromagnets.
In order to clarify the physics of the crossover from a spin-density-wave (SDW) Mott insulator to a charge-density-wave (CDW) Peierls insulator in one-dimensional (1D) systems, we investigate the Hubbard-Holstein Hamiltonian at half filling within a density matrix renormalisation group (DMRG) approach. Determining the spin and charge correlation exponents, the momentum distribution function, and various excitation gaps, we confirm that an intervening metallic phase expands the SDW-CDW transition in the weak-coupling regime.
We present the magnetic phase diagram of the $\ensuremath{\nu}=2$ quantum Hall system on the whole (rs,EZ)({r}_{s},{E}_{Z})(rs​,EZ​) plane. We fix the phase boundaries of the paramagnetic and ferromagnetic states by looking for a softening of spin-density excitations in the time-dependent Hartree-Fock theory. A nontrivial phase is obtained in the self-consistent Hartree-Fock theory for ${r}_{s}\ensuremath{\sim}2$ and ${E}_{Z}\ensuremath{\lesssim}0.06\ensuremath{\hbar}{\ensuremath{\omega}}_{c}$, where both the paramagnetic and ferromagnetic states show spin instability. We show that the obtained phase is the spin-density wave (SDW) state, and explain the mechanism how the SDW stabilizes.
We present the magnetic phase diagram of the ν = 2 quantum Hall system on the whole (rs, EZ ) plane.We fix the phase boundaries of the paramagnetic and ferromagnetic states by looking for a softening of spin density excitations (SDE) in the time-dependent Hartree-Fock theory.A new phase is obtained in the self-consistent Hartree-Fock theory for rs ∼ 2 and EZ 0.06 ωc, where both the paramagnetic and ferromagnetic states show spin instability.We show that the new phase is the spin density wave (SDW) state, and explain the mechanism how the SDW stabilizes.
The dynamics of solitons in spin-density-wave systems is studied numerically using the one-dimensional Hubbard model. The motion of solitons is induced by an electric field, which is introduced into the model in the form of a time-dependent vector potential. The unrestricted Hartree-Fock approximation is used. An improved method of the decomposition of exponential operator is used to solve the time-dependent Hartree-Fock equation. First, the motion of a single soliton is studied, with emphasis on discrete lattice effects. It is found that the discreteness effects reduce the soliton saturation velocity which was found in a previous paper. Second, processes of collisions between a soliton and an antisoliton are studied. The states after the collision are quite different between the cases with a charge soliton pair and with a neutral soliton pair. In the case of the charged soliton pair, the solitons repel each other and reflect to opposite directions. In the case of the neutral soliton pair. In the case of the charged soliton pair, the solitons repel each other and reflect to opposite directions. In the case of the neutral soliton pair, the solitons attract each other to make a dynamical bound state.