Domain wall dynamics of the spin- $\frac{1}{2}$ Ising-like antiferromagnetic chain in presence of Dzyaloshinskii-Moriya interactionsDomain wall dynamics of the spin- $\frac{1}{2}$ Ising-like antiferromagnetic chain in presence of Dzyaloshinskii-Moriya interactions

Asim Kumar Ghosh

The European Physical Journal BJun 22, 20112 citations

Domain Walls in the Heisenberg-Ising Spin-1/2 Chain

Axel Saenz, Craig A. Tracy, Harold Widom

In this paper we obtain formulas for the distribution of the left-most up-spin in the Heisenberg-Ising spin-1/2 chain with anisotropy parameter $Δ$ , also known as the XXZ spin-1/2 chain, on the one-dimensional lattice $\mathbb{Z}$ with domain wall initial conditions. We use the Bethe Ansatz to solve the Schr $ö$ dinger equation and a recent antisymmetrization identity of Cantini, Colomo, and Pronko (arXiv:1906.07636) to simplify the marginal distribution of the left-most up-spin. In the $Δ=0$ case, the distribution $F_2$ arises. In the $Δ\neq 0$ case, we propose a conjectural series expansion type formula based on a saddle point analysis. The conjectural formula turns out to be a Fredholm series expansion in the $Δ\rightarrow 0$ limit and recovers the result for $Δ= 0$ .In this paper we obtain formulas for the distribution of the left-most up-spin in the Heisenberg-Ising spin-1/2 chain with anisotropy parameter $Δ$, also known as the XXZ spin-1/2 chain, on the one-dimensional lattice $\mathbb{Z}$ with domain wall initial conditions. We use the Bethe Ansatz to solve the Schr$ö$dinger equation and a recent antisymmetrization identity of Cantini, Colomo, and Pronko (arXiv:1906.07636) to simplify the marginal distribution of the left-most up-spin. In the $Δ=0$ case, the distribution $F_2$ arises. In the $Δ\neq 0$ case, we propose a conjectural series expansion type formula based on a saddle point analysis. The conjectural formula turns out to be a Fredholm series expansion in the $Δ\rightarrow 0$ limit and recovers the result for $Δ= 0$.

arXiv:2202.07695Feb 15, 20220 citations

The Ising Model and the Heisenberg Spin Chain

Horaƫiu Năstase

Cambridge University Press eBooksSep 21, 20170 citations

Domain-wall dynamics near a quantum critical point

Shengjun Yuan, Hans A. De Raedt, Seiji Miyashita

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 ${(\ensuremath{\Delta}\ensuremath{-}1)}^{\ensuremath{-}1∕2}$.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 ${(\ensuremath{\Delta}\ensuremath{-}1)}^{\ensuremath{-}1∕2}$.

arXiv:0704.0193Physical Review BMay 16, 20078 citations

Quantum domain walls in the one-dimensional Ising model in a transverse field

Peter Prelovšek, Igor Sega

Physics Letters AFeb 1, 19817 citations

Domain Walls in the Heisenberg-Ising Spin-

\frac {1}{2}

Chain

Domain wall dynamics of the spin-

\frac{1}{2}

Ising-like antiferromagnetic chain in presence of Dzyaloshinskii-Moriya interactions

In this paper we obtain formulas for the distribution of the left-most up-spin in the Heisenberg-Ising spin-1/2 chain with anisotropy parameter

Δ

, also known as the XXZ spin-1/2 chain, on the one-dimensional lattice

\mathbb{Z}

with domain wall initial conditions. We use the Bethe Ansatz to solve the Schr

ö

dinger equation and a recent antisymmetrization identity of Cantini, Colomo, and Pronko (arXiv:1906.07636) to simplify the marginal distribution of the left-most up-spin. In the

Δ=0

case, the distribution

F_2

arises. In the

Δ\neq 0

case, we propose a conjectural series expansion type formula based on a saddle point analysis. The conjectural formula turns out to be a Fredholm series expansion in the

Δ\rightarrow 0

limit and recovers the result for

Δ= 0

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 ${(\ensuremath{\Delta}\ensuremath{-}1)}^{\ensuremath{-}1∕2}$.