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:0704.0193 · Physical Review B

Domain-wall dynamics near a quantum critical point

Shengjun Yuan, Hans A. De Raedt, Seiji Miyashita

Published May 16, 2007• 8 citations
arXivHTMLPDF

Abstract

We study the real-time domain-wall dynamics near a quantum critical point of the one-dimensional anisotropic ferromagnetic spin $1∕2$ chain. By numerical simulation, we find that the domain wall is dynamically stable in the Heisenberg-Ising model. Near the quantum critical point, the width of the domain wall diverges as ${(\ensuremath{\Delta}\ensuremath{-}1)}^{\ensuremath{-}1∕2}$.

DOI
10.1103/physrevb.75.184305

Related papers

Anisotropic Ferromagnetic Quantum Domains

Francisco Castilho Alcaraz, Silvio R. A. Salinas, Walter Felipe Wreszinski

We study a model for anisotropic ferromagnetic quantum domain walls. The large degeneracy of the ground state in the extreme anisotropic (Ising) limit, associated with the translational invariance of the ``kink center,'' is lifted in the quantum system in a peculiar way. The critical point, at which the Hamiltonian is invariant under the quantum group ${\mathrm{U}}_{q}$ [SU(2)], is exactly determined by a cluster method. We also find the ground state wave function at the critical point. Some generalizations of these results for arbitrary spin and dimension are obtained.

Physical Review Letters•Jul 31, 1995•80 citations

Semiclassical dynamics of domain walls in the one-dimensional Ising ferromagnet in a transverse field

Boris A. Ivanov, H.-J. Mikeska

We investigate analytically and numerically the dynamics of domain walls in a spin chain with ferromagnetic Ising interaction and subject to an external magnetic field perpendicular to the easy magnetization axis (transverse field Ising model). The analytical results obtained within the continuum approximation and numerical simulations performed for the discrete classical model are used to analyze the quantum properties of domain walls using the semiclassical approximation. We show that the domain wall spectrum shows a band structure consisting of $2S$ nonintersecting zones.

arXiv:cond-mat/0404014•Physical Review B•Nov 10, 2004•16 citations

Critical domain-wall dynamics of model B

R. H. Dong, B. Zheng, Ningxu Zhou

With Monte Carlo methods, we simulate the critical domain-wall dynamics of model B, taking the two-dimensional Ising model as an example. In the macroscopic short-time regime, a dynamic scaling form is revealed. Due to the existence of the quasirandom walkers, the magnetization shows intrinsic dependence on the lattice size L . An exponent which governs the L dependence of the magnetization is measured to be sigma=0.243(8) .

arXiv:1209.0360•Physical Review E•May 22, 2009•1 citation

Entanglement and quantum phases in the anisotropic ferromagnetic Heisenberg chain in the presence of domain walls

Francisco Castilho Alcaraz, A. Saguia, M. S. Sarandy

We discuss entanglement in the spin-1∕2 anisotropic ferromagnetic Heisenberg chain in the presence of a boundary magnetic field generating domain walls. By increasing the magnetic field, the model undergoes a first-order quantum phase transition from a ferromagnetic to a kink-type phase, which is associated to a jump in the content of entanglement available in the system. Above the critical point, pairwise entanglement is shown to be nonvanishing and independent of the boundary magnetic field for large chains. Based on this result, we provide an analytical expression for the entanglement between arbitrary spins. Moreover, the effects of the quantum domains on the gapless region and for antiferromagnetic anisotropy are numerically analyzed. Finally multiparticle entanglement properties are considered, from which we establish a characterization of the critical anisotropy separating the gapless regime from the kink-type phase.

arXiv:quant-ph/0312039•Physical Review A•Sep 30, 2004•39 citations

Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point

Grégoire Misguich, Nicolas Pavloff, Vincent Pasquier

We study the dynamics of a spin- \frac{1}{2} 1 2 XXZ chain which is initially prepared in a domain-wall state. We compare the results of time-dependent Density Matrix Renormalization Group simulations with those of an effective description in terms of a classical anisotropic Landau-Lifshitz (LL) equation. Numerous quantities are analyzed: magnetization ( x x , y y and z z components), energy density, energy current, but also some spin-spin correlation functions or entanglement entropy in the quantum chain. Without any adjustable parameter a quantitative agreement is observed between the quantum and the LL problems in the long time limit, when the models are close to the isotropic point. This is explained as a consequence of energy conservation. At the isotropic point the mapping between the LL equation and the nonlinear Schrödinger equation is used to construct a variational solution capturing several aspects of the problem.

arXiv:1905.08756•SciPost Physics•Aug 29, 2019•48 citations

Nonuniversal critical dynamical behavior in 1D spin systems

Eduardo Lage

Recent results concerning non-universality in the dynamical critical behavior of the one-dimensional Ising model, are generalised to several formulations of the Potts model, using arguments based on domain wall motion. By applying real-space renormalisation group methods, the authors also study the dynamical Ising model, with single flips, both for a period distribution of nearest-neighbor exchanges and for the random chain (with nonzero couplings). They show that the critical dynamical exponent is z=1+J M /J m where J M (J m ) is the greatest (smallest) of the exchanges.

Journal of Physics C Solid State Physics•Sep 10, 1987•14 citations
We study the real-time domain-wall dynamics near a quantum critical point of the one-dimensional anisotropic ferromagnetic spin 1∕21∕21∕2 chain. By numerical simulation, we find that the domain wall is dynamically stable in the Heisenberg-Ising model. Near the quantum critical point, the width of the domain wall diverges as (\ensuremathΔ\ensuremath−1)\ensuremath−1∕2{(\ensuremath{\Delta}\ensuremath{-}1)}^{\ensuremath{-}1∕2}(\ensuremathΔ\ensuremath−1)\ensuremath−1∕2.
We study a model for anisotropic ferromagnetic quantum domain walls. The large degeneracy of the ground state in the extreme anisotropic (Ising) limit, associated with the translational invariance of the ``kink center,'' is lifted in the quantum system in a peculiar way. The critical point, at which the Hamiltonian is invariant under the quantum group Uq{\mathrm{U}}_{q}Uq​ [SU(2)], is exactly determined by a cluster method. We also find the ground state wave function at the critical point. Some generalizations of these results for arbitrary spin and dimension are obtained.
We investigate analytically and numerically the dynamics of domain walls in a spin chain with ferromagnetic Ising interaction and subject to an external magnetic field perpendicular to the easy magnetization axis (transverse field Ising model). The analytical results obtained within the continuum approximation and numerical simulations performed for the discrete classical model are used to analyze the quantum properties of domain walls using the semiclassical approximation. We show that the domain wall spectrum shows a band structure consisting of 2S2S2S nonintersecting zones.
We discuss entanglement in the spin-1∕2 anisotropic ferromagnetic Heisenberg chain in the presence of a boundary magnetic field generating domain walls. By increasing the magnetic field, the model undergoes a first-order quantum phase transition from a ferromagnetic to a kink-type phase, which is associated to a jump in the content of entanglement available in the system. Above the critical point, pairwise entanglement is shown to be nonvanishing and independent of the boundary magnetic field for large chains. Based on this result, we provide an analytical expression for the entanglement between arbitrary spins. Moreover, the effects of the quantum domains on the gapless region and for antiferromagnetic anisotropy are numerically analyzed. Finally multiparticle entanglement properties are considered, from which we establish a characterization of the critical anisotropy separating the gapless regime from the kink-type phase.
We study the dynamics of a spin- \frac{1}{2} 1 2 XXZ chain which is initially prepared in a domain-wall state. We compare the results of time-dependent Density Matrix Renormalization Group simulations with those of an effective description in terms of a classical anisotropic Landau-Lifshitz (LL) equation. Numerous quantities are analyzed: magnetization ( x x , y y and z z components), energy density, energy current, but also some spin-spin correlation functions or entanglement entropy in the quantum chain. Without any adjustable parameter a quantitative agreement is observed between the quantum and the LL problems in the long time limit, when the models are close to the isotropic point. This is explained as a consequence of energy conservation. At the isotropic point the mapping between the LL equation and the nonlinear Schrödinger equation is used to construct a variational solution capturing several aspects of the problem.
Recent results concerning non-universality in the dynamical critical behavior of the one-dimensional Ising model, are generalised to several formulations of the Potts model, using arguments based on domain wall motion. By applying real-space renormalisation group methods, the authors also study the dynamical Ising model, with single flips, both for a period distribution of nearest-neighbor exchanges and for the random chain (with nonzero couplings). They show that the critical dynamical exponent is z=1+J M /J m where J M (J m ) is the greatest (smallest) of the exchanges.