Domain-wall dynamics in the Landau-Lifshitz magnet and the classical-quantum correspondence for spin transport

Gamayun, Oleksandr; Yuan, Miao; Ilievski, Enej

doi:10.1103/physrevb.99.140301

Cited by 52 publications

(95 citation statements)

References 74 publications

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“…By separation of scales, the microscopic quasiparticle degrees of freedom couple to Ω as a local bath. This class of hydrodynamic states includes the tunable z-polarized domain walls ρ ∝ (1 + µσ z ) N/2 ⊗ (1 − µσ z ) N/2 that have frequently been considered in the literature 12,18,[39][40][41][42][43][44][45] . In the continuum limit N → ∞, the hydrodynamic state is determined as above, leading to a uniform initial condition for the quasiparticle mode occupancies and a domain wall initial condition for the pseudovacuum gauge field.…”

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confidence: 99%

Kardar-Parisi-Zhang universality from soft gauge modes

Bulchandani

2020

Phys. Rev. B

121

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The emergence of superdiffusive spin dynamics in integrable classical and quantum magnets is well established by now, but there is no generally valid theoretical explanation for this phenomenon. A fundamental difficulty is that the hydrodynamic fluctuations of conserved quasiparticle modes are purely diffusive. We propose a "hydrodynamic Higgs mechanism" in isotropic integrable magnets, which generates soft gauge modes that are decoupled from the quasiparticle sector. We show that the coarse-grained time evolution of these modes lies in the Kardar-Parisi-Zhang universality class of dynamics.

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confidence: 99%

Kardar-Parisi-Zhang universality from soft gauge modes

Bulchandani

2020

Phys. Rev. B

121

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“…[15] for additional data corroborating this conjecture for higher spin integrable quantum models with higher rank nonabelian symmetries. Since low energy regimes of non-integrable lattice models are often described by integrable field theories, one could then apply such results also to non-integrable SO(3) symmetric lattice models at low temperatures [18] or integrable SO(3) symmetric field theories [19].…”

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confidence: 99%

Kardar–Parisi–Zhang Physics in Integrable Rotationally Symmetric Dynamics on Discrete Space–Time Lattice

Krajnik

Prosen

2020

J Stat Phys

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We introduce a deterministic SO(3) invariant dynamics of classical spins on a discrete space-time lattice and prove its complete integrability by explicitly finding a related non-constant (baxterized) solution of the set-theoretic quantum Yang-Baxter equation over the 2-sphere. Equipping the algebraic structure with the corresponding Lax operator we derive an infinite sequence of conserved quantities with local densities. The dynamics depend on a single continuous spectral parameter and reduce to a (lattice) Landau-Lifshitz model in the limit of a small parameter which corresponds to the continuous time limit. Using quasiexact numerical simulations of deterministic dynamics and Monte Carlo sampling of initial conditions corresponding to a maximum entropy equilibrium state we determine spin-spin spatio-temporal (dynamical) correlation functions with relative accuracy of three orders of magnitude. We demonstrate that in the equilibrium state with a vanishing total magnetization the correlation function precisely follow Kardar-Parisi-Zhang scaling hence the spin transport belongs to the universality class with dynamical exponent z = 3/2, in accordance to recent related simulations in discrete and continuous time quantum Heisenberg spin 1/2 chains.

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“…In a recent paper Gamayun el al. [27] (we also mention [28]) considered the domain wall problem in a different model, which is a classical ferromagnetic chain in the continuum limit. There, the magnetization M is a classical unit vector which depends on time and on a continuous space variable r, and its (precession) dynamics is described by the celebrated anisotropic Landau Lifshitz (LL) equation.…”

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confidence: 99%

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

2019

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We study the dynamics of a spin-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, y and 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.

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Domain-wall dynamics in the Landau-Lifshitz magnet and the classical-quantum correspondence for spin transport

Cited by 52 publications

References 74 publications

Kardar-Parisi-Zhang universality from soft gauge modes

Kardar-Parisi-Zhang universality from soft gauge modes

Kardar–Parisi–Zhang Physics in Integrable Rotationally Symmetric Dynamics on Discrete Space–Time Lattice

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

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