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:1910.11255 · Physical review. B./Physical review. B

Domain wall melting in spin-1 XXZ chains

Marko Medenjak, Jacopo De Nardis

Published Feb 19, 2020• 8 citations
arXivHTMLPDF

Abstract

We study the nonequilibrium spin dynamics in the nonintegrable spin-1 XXZ chains, emerging from inhomogeneous quenches, with two halves initialized in distinct maximally polarized states. Employing the time-dependent variational principle (TDVP) we are able to reach times that are inaccessible by standard time-dependent density matrix renormalization group methods. We identify three distinct phases depending on the anisotropy of the chain, corresponding to diffusive, logarithmic superdiffusive, and insulating. In the easy-axis regime we observe a transient ballistic behavior with a crossover time that diverges as the isotropic point is approached. This leads us to the conclusion that on the intermediate-large timescales the spin dynamics is well described by the integrable Landau-Lifshitz classical differential equation.

DOI
10.1103/physrevb.101.081411

Related papers

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

Real-time study of diffusive and ballistic transport in spin- 1 2 chains using the adaptive time-dependent density matrix renormalization group method

S. Langer, Fabian Heidrich‐Meisner, Jochen Gemmer B +2 more

Using the adaptive time-dependent density matrix renormalization group method, we numerically study the spin dynamics and transport in one-dimensional spin-1/2 systems at zero temperature. Instead of computing transport coefficients from linear-response theory, we study the real-time evolution of the magnetization starting from spatially inhomogeneous initial states. In particular, we are able to analyze systems far away from equilibrium with this setup. By computing the time dependence of the variance of the magnetization, we can distinguish diffusive from ballistic regimes, depending on model parameters. For the example of the anisotropic spin-1/2 chain and at half filling, we find the expected ballistic behavior in the easy-plane phase, while in the massive regime the dynamics of the magnetization is diffusive. Our approach allows us to tune the deviation of the initial state from the ground state and the qualitative behavior of the dynamics turns out to be valid even for highly perturbed initial states in the case of easy-plane exchange anisotropies. We further cover two examples of nonintegrable models, the frustrated chain and the two-leg spin ladder, and we encounter diffusive transport in all massive phases. In the former system, our results indicate ballistic behavior in the critical phase. We propose that the study of the time dependence of the spatial variance of particle densities could be instrumental in the characterization of the expansion of ultracold atoms in optical lattices as well.

arXiv:0812.4252•Physical Review B•Jun 9, 2009•118 citations

Magnon Theory of Domain Wall Wavefronts and the Ballistic Diffusive Crossover in the Classical Anisotropic Landau Lifshitz Spin Chain

Akash Sarkar

We study the far-from-equilibrium dynamics of domain-wall initial states in the integrable lattice Landau--Lifshitz spin chain. Building on the linear spin-wave description of domain-wall spreading, we derive the long-wavelength magnon dispersion directly from the microscopic integrable Hamiltonian and use it to characterize the propagation and broadening of the resulting wavefronts. The dispersion interpolates between a quadratic form at the isotropic point and a linear form in the easy-plane regime. In the isotropic limit, the quadratic dispersion leads to diffusive broadening, whereas in the easy-plane regime the domain-wall front propagates ballistically. Keeping the leading nonlinear correction to the linear dispersion gives a cubic dispersive term, which produces a characteristic $t^{1/3}$ broadening of the ballistic front. We further show that the sign of this cubic correction changes at a critical anisotropy, leading to a reversal of the dispersive wake from trailing to advancing. The resulting critical point occurs at $Δ_c=1/7$, corresponding to $γ_c\simeq 1.047$. Numerical simulations of the full nonlinear spin dynamics confirm the analytical scaling and demonstrate the coexistence of the amplitude-independent spin-wave front with amplitude-dependent nonlinear soliton propagation.

arXiv:2609.13474•Sep 11, 2026•0 citations

Dynamics of the spin- 12 Heisenberg chain initialized in a domain-wall state

Grégoire Misguich, Kirone Mallick, P. L. Krapivsky

We study the dynamics of an isotropic spin-$\frac{1}{2}$ Heisenberg chain starting in a domain-wall initial condition where the spins are initially up on the left half-line and down on the right half-line. We focus on the long-time behavior of the magnetization profile. We perform extensive time-dependent density-matrix renormalization-group simulations (up to $t=350$) and find that the data are compatible with a diffusive behavior. Subleading corrections decay slowly blurring the emergence of the diffusive behavior. We also compare our results with two alternative scenarios: superdiffusive behavior and enhanced diffusion with a logarithmic correction. We finally discuss the evolution of the entanglement entropy.

arXiv:1708.01843•Physical review. B./Physical review. B•Nov 27, 2017•86 citations

Domain wall melting in the spin- 12 XXZ spin chain: Emergent Luttinger liquid with a fractal quasiparticle charge

Mario Collura, Andrea De Luca, Pasquale Calabrese +1 more

In spin chains with local unitary evolution preserving the magnetization ${S}^{\mathrm{z}}$, the domain-wall state $\left|\ensuremath{\cdots}\ensuremath{\uparrow}\ensuremath{\uparrow}\ensuremath{\uparrow}\ensuremath{\uparrow}\ensuremath{\uparrow}\ensuremath{\downarrow}\ensuremath{\downarrow}\ensuremath{\downarrow}\ensuremath{\downarrow}\ensuremath{\downarrow}\ensuremath{\cdots}\right\ensuremath{\rangle}$ typically ``melts.'' At large times, a nontrivial magnetization profile develops in an expanding region around the initial position of the domain wall. For nonintegrable dynamics, the melting is diffusive, with entropy production within a melted region of size $\sqrt{t}$. In contrast, when the evolution is integrable, ballistic transport dominates and results in a melted region growing linearly in time, with no extensive entropy production: The spin chain remains locally in states of zero entropy at any time. Here we show that, for the integrable spin-$1/2$ XXZ chain, low-energy quantum fluctuations in the melted region give rise to an emergent Luttinger liquid which, remarkably, differs from the equilibrium one. The striking feature of this emergent Luttinger liquid is its quasiparticle charge (or Luttinger parameter $K$), which acquires a fractal dependence on the XXZ chain anisotropy parameter $\mathrm{\ensuremath{\Delta}}$.

arXiv:2001.04948•Physical review. B./Physical review. B•Nov 23, 2020•54 citations

Real-time and real-space spin and energy dynamics in one-dimensional spin- 1 2 systems induced by local quantum quenches at finite temperatures

Christoph Karrasch, Joel E. Moore, Fabian Heidrich‐Meisner

We study the spin and energy dynamics in one-dimensional spin-$\frac{1}{2}$ systems induced by local quantum quenches at finite temperatures using a time-dependent density matrix renormalization group method. System sizes are chosen large enough to ensure that the time-dependent data for the accessible time scales represent the behavior in the thermodynamic limit. As a main result, we observe a ballistic spreading of perturbations of the energy density in the integrable spin-$\frac{1}{2}$ XXZ chain for all temperatures and exchange anisotropies, related to the divergent thermal conductivity in this model and the exact conservation of the energy current. In contrast, the spin dynamics is ballistic in the massless phase, but shows a diffusive behavior at high temperatures in the easy-axis phase in the case of a vanishing background spin density. We extract a quantitative estimate for the spin-diffusion constant from the time dependence of the spatial variance of the spin density, which agrees well with values obtained from current-current correlation functions using an Einstein relation. Interestingly, the diffusion constant approaches a constant value deep in the easy-axis regime. As an example for nonintegrable models, we consider two-leg ladders, for which we observe indications of diffusive energy and spin dynamics. The relevance of our results for recent experiments with quantum magnets and bosons in optical lattices is discussed.

arXiv:1312.2938•Physical Review B•Feb 28, 2014•138 citations
We study the nonequilibrium spin dynamics in the nonintegrable spin-1 XXZ chains, emerging from inhomogeneous quenches, with two halves initialized in distinct maximally polarized states. Employing the time-dependent variational principle (TDVP) we are able to reach times that are inaccessible by standard time-dependent density matrix renormalization group methods. We identify three distinct phases depending on the anisotropy of the chain, corresponding to diffusive, logarithmic superdiffusive, and insulating. In the easy-axis regime we observe a transient ballistic behavior with a crossover time that diverges as the isotropic point is approached. This leads us to the conclusion that on the intermediate-large timescales the spin dynamics is well described by the integrable Landau-Lifshitz classical differential equation.
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.
Using the adaptive time-dependent density matrix renormalization group method, we numerically study the spin dynamics and transport in one-dimensional spin-1/2 systems at zero temperature. Instead of computing transport coefficients from linear-response theory, we study the real-time evolution of the magnetization starting from spatially inhomogeneous initial states. In particular, we are able to analyze systems far away from equilibrium with this setup. By computing the time dependence of the variance of the magnetization, we can distinguish diffusive from ballistic regimes, depending on model parameters. For the example of the anisotropic spin-1/2 chain and at half filling, we find the expected ballistic behavior in the easy-plane phase, while in the massive regime the dynamics of the magnetization is diffusive. Our approach allows us to tune the deviation of the initial state from the ground state and the qualitative behavior of the dynamics turns out to be valid even for highly perturbed initial states in the case of easy-plane exchange anisotropies. We further cover two examples of nonintegrable models, the frustrated chain and the two-leg spin ladder, and we encounter diffusive transport in all massive phases. In the former system, our results indicate ballistic behavior in the critical phase. We propose that the study of the time dependence of the spatial variance of particle densities could be instrumental in the characterization of the expansion of ultracold atoms in optical lattices as well.
We study the far-from-equilibrium dynamics of domain-wall initial states in the integrable lattice Landau--Lifshitz spin chain. Building on the linear spin-wave description of domain-wall spreading, we derive the long-wavelength magnon dispersion directly from the microscopic integrable Hamiltonian and use it to characterize the propagation and broadening of the resulting wavefronts. The dispersion interpolates between a quadratic form at the isotropic point and a linear form in the easy-plane regime. In the isotropic limit, the quadratic dispersion leads to diffusive broadening, whereas in the easy-plane regime the domain-wall front propagates ballistically. Keeping the leading nonlinear correction to the linear dispersion gives a cubic dispersive term, which produces a characteristic t1/3t^{1/3}t1/3 broadening of the ballistic front. We further show that the sign of this cubic correction changes at a critical anisotropy, leading to a reversal of the dispersive wake from trailing to advancing. The resulting critical point occurs at Δc=1/7Δ_c=1/7Δc​=1/7, corresponding to γc≃1.047γ_c\simeq 1.047γc​≃1.047. Numerical simulations of the full nonlinear spin dynamics confirm the analytical scaling and demonstrate the coexistence of the amplitude-independent spin-wave front with amplitude-dependent nonlinear soliton propagation.
We study the dynamics of an isotropic spin-12\frac{1}{2}21​ Heisenberg chain starting in a domain-wall initial condition where the spins are initially up on the left half-line and down on the right half-line. We focus on the long-time behavior of the magnetization profile. We perform extensive time-dependent density-matrix renormalization-group simulations (up to t=350t=350t=350) and find that the data are compatible with a diffusive behavior. Subleading corrections decay slowly blurring the emergence of the diffusive behavior. We also compare our results with two alternative scenarios: superdiffusive behavior and enhanced diffusion with a logarithmic correction. We finally discuss the evolution of the entanglement entropy.
In spin chains with local unitary evolution preserving the magnetization Sz{S}^{\mathrm{z}}Sz, the domain-wall state $\left|\ensuremath{\cdots}\ensuremath{\uparrow}\ensuremath{\uparrow}\ensuremath{\uparrow}\ensuremath{\uparrow}\ensuremath{\uparrow}\ensuremath{\downarrow}\ensuremath{\downarrow}\ensuremath{\downarrow}\ensuremath{\downarrow}\ensuremath{\downarrow}\ensuremath{\cdots}\right\ensuremath{\rangle}$ typically ``melts.'' At large times, a nontrivial magnetization profile develops in an expanding region around the initial position of the domain wall. For nonintegrable dynamics, the melting is diffusive, with entropy production within a melted region of size t\sqrt{t}t​. In contrast, when the evolution is integrable, ballistic transport dominates and results in a melted region growing linearly in time, with no extensive entropy production: The spin chain remains locally in states of zero entropy at any time. Here we show that, for the integrable spin-1/21/21/2 XXZ chain, low-energy quantum fluctuations in the melted region give rise to an emergent Luttinger liquid which, remarkably, differs from the equilibrium one. The striking feature of this emergent Luttinger liquid is its quasiparticle charge (or Luttinger parameter KKK), which acquires a fractal dependence on the XXZ chain anisotropy parameter $\mathrm{\ensuremath{\Delta}}$.
We study the spin and energy dynamics in one-dimensional spin-12\frac{1}{2}21​ systems induced by local quantum quenches at finite temperatures using a time-dependent density matrix renormalization group method. System sizes are chosen large enough to ensure that the time-dependent data for the accessible time scales represent the behavior in the thermodynamic limit. As a main result, we observe a ballistic spreading of perturbations of the energy density in the integrable spin-12\frac{1}{2}21​ XXZ chain for all temperatures and exchange anisotropies, related to the divergent thermal conductivity in this model and the exact conservation of the energy current. In contrast, the spin dynamics is ballistic in the massless phase, but shows a diffusive behavior at high temperatures in the easy-axis phase in the case of a vanishing background spin density. We extract a quantitative estimate for the spin-diffusion constant from the time dependence of the spatial variance of the spin density, which agrees well with values obtained from current-current correlation functions using an Einstein relation. Interestingly, the diffusion constant approaches a constant value deep in the easy-axis regime. As an example for nonintegrable models, we consider two-leg ladders, for which we observe indications of diffusive energy and spin dynamics. The relevance of our results for recent experiments with quantum magnets and bosons in optical lattices is discussed.