Spin diffusion in classical Heisenberg magnets with uniform, alternating, and random exchange

Srivastava, Niraj; Liu, Jianmin; Viswanath, V. S.; Müller, Gerhard

doi:10.1063/1.356842

Cited by 24 publications

(23 citation statements)

References 8 publications

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“…Our main motivation for revisiting the derivation above is recent literature on classical and quantum spin chains with SU(2) symmetry in d = 1 [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] (Section 6). In fact, we were inspired to carry out this effective field theory computation in part by papers arguing that the infinite temperature classical Heisenberg model does not have conventional spin diffusion [16,24,32], as predicted and obtained by many other authors [18,21,30]. In particular, [32] argues that the spin diffusion constant scales as D(t) ∼ log 4/3 t.…”

Section: Introductionmentioning

confidence: 99%

Hydrodynamics in lattice models with continuous non-Abelian symmetries

et al. 2021

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We develop a systematic effective field theory of hydrodynamics for many-body systems on the lattice with global continuous non-Abelian symmetries. Models with continuous non-Abelian symmetries are ubiquitous in physics, arising in diverse settings ranging from hot nuclear matter to cold atomic gases and quantum spin chains. In every dimension and for every flavor symmetry group, the low energy theory is a set of coupled noisy diffusion equations. Independence of the physics on the choice of canonical or microcanonical ensemble is manifest in our hydrodynamic expansion, even though the ensemble choice causes an apparent shift in quasinormal mode spectra. We use our formalism to explain why flavor symmetry is qualitatively different from hydrodynamics with other non-Abelian conservation laws, including angular momentum and charge multipoles.As a significant application of our framework, we study spin and energy diffusion in classical one-dimensional SU(2)-invariant spin chains, including the Heisenberg model along with multiple generalizations. We argue based on both numerical simulations and our effective field theory framework that non-integrable spin chains on a lattice exhibit conventional spin diffusion, in contrast to some recent predictions that diffusion constants grow logarithmically at late times. We show that the apparent enhancement of diffusion is due to slow equilibration caused by (non-Abelian) hydrodynamic fluctuations.

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Section: Introductionmentioning

confidence: 99%

Hydrodynamics in lattice models with continuous non-Abelian symmetries

et al. 2021

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“…Even in the classical limit S → +∞, where spin operators in Eq. (3) are replaced by standard unit vectors, identifying whether spin diffusion is normal or anomalous has a long-standing history [51][52][53][54][55][56][57][58]. The issue was settled by doing a systematic finite-size analysis in Ref.…”

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confidence: 99%

Universal spin dynamics in infinite-temperature one-dimensional quantum magnets

Dupont

Moore

2020

Phys. Rev. B

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We address the nature of spin dynamics in various integrable and non-integrable, isotropic and anisotropic quantum spin-S chains, beyond the paradigmatic S = 1/2 Heisenberg model. In particular, we investigate the algebraic long-time decay ∝ t −1/z of the spin-spin correlation function at infinite temperature, using state-of-the-art simulations based on tensor network methods. We identify three universal regimes for the spin transport, independent of the exact microscopic model: (i) superdiffusive with z = 3/2, as in the Kardar-Parisi-Zhang universality class, when the model is integrable with extra symmetries such as spin isotropy that drive the Drude weight to zero, (ii) ballistic with z = 1 when the model is integrable with a finite Drude weight, and (iii) diffusive with z = 2 with easy-axis anisotropy or without integrability, at variance with previous observations.

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“…Although the phenomenology of spin diffusion is an old concept [3,4], its validity in classical Heisenberg model has been vigourously debated in recent times. Although much effort [13][14][15][16][17][18][19][20] has been devoted to understand whether spin diffusion in this system is normal or anomalous, a convincing conclusion is yet to be reached. Settling this question is not only conceptually important e.g., in understanding transport properties of spin systems, but also has direct implications in routinely performed experiments e.g., NMR and ESR in magnetic compounds [5][6][7][8][9].…”

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confidence: 99%

“…The authors of Ref. [19] suggested that spin diffusion appears to be diffusive for the alternate coupling case, whereas, for random coupling, it is probably non-diffusive. However, for both the cases we find a clear t −1/2 behavior at late times.…”

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confidence: 99%

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Spin diffusion in the one-dimensional classical Heisenberg model

Bagchi

2013

Phys. Rev. B

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The problem of spin diffusion is studied numerically in one-dimensional classical Heisenberg model using a deterministic odd even spin precession dynamics. We demonstrate that spin diffusion in this model, like energy diffusion, is normal and one obtains a long time diffusive tail in the decay of autocorrelation function (ACF). Some variations of the model with different coupling schemes and with anisotropy are also studied and we find normal diffusion in all of them. A systematic finite size analysis of the Heisenberg model also suggests diffusive spreading of fluctuation, contrary to previous claims of anomalous diffusion.The classical Heisenberg model [1,2] has been extensively studied, both analytically and numerically, for several decades and has become a prototypical model for magnetic insulators. However, one important question that still awaits a conclusive answer is regarding the time dependent behavior of the spins, particularly at very high temperature. In the hydrodynamic limit, the dominant mode of fluctuation spreading in this system is believed to obey of the standard diffusion phenomenology. In absence of any microscopic theoretical formalism, studies were mostly numerical, generally involving calculation of time correlation functions. Although the phenomenology of spin diffusion is an old concept [3,4], its validity in classical Heisenberg model has been vigourously debated in recent times. Although much effort [13][14][15][16][17][18][19][20] has been devoted to understand whether spin diffusion in this system is normal or anomalous, a convincing conclusion is yet to be reached. Settling this question is not only conceptually important e.g., in understanding transport properties of spin systems, but also has direct implications in routinely performed experiments e.g., NMR and ESR in magnetic compounds [5][6][7][8][9]. In the following, we present a brief outline of the diffusion phenomenology and review some of the earlier studies in this direction.Let us consider a one-dimensional chain containing Heisenberg spins { S i } (three dimensional unit vectors) where, i = 1, 2, . . . , N with periodic boundary conditions, i.e., S N +1 ≡ S 1 . The Hamiltonian is given by,where K i is the interaction strength between the spins S i and S i+1 ; the spin-spin coupling is ferromagnetic for K i > 0 and anti-ferromagnetic if K i < 0. The microscopic equation of motion can be written as, is the local molecular field experienced by the spin at site i. Clearly, Eq. (2) conserves (i) the total energy, and (ii) the total spin S = i S i . Since there is no long range order in this system at any finite temperature and because of the conservation of total spin, the spin fluctuation in the hydrodynamic limit is expected to follow a continuity (diffusion) equation ∂ t S q (t) = −D s q 2 S q (t), where S q (t) is the (discrete) Fourier transform of S i (t) and D s is the spin diffusion constant. A similar equation holds for the energy density (since total energy is also a constant of motion). The continuity equation im...

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Spin diffusion in classical Heisenberg magnets with uniform, alternating, and random exchange

Cited by 24 publications

References 8 publications

Hydrodynamics in lattice models with continuous non-Abelian symmetries

Hydrodynamics in lattice models with continuous non-Abelian symmetries

Universal spin dynamics in infinite-temperature one-dimensional quantum magnets

Spin diffusion in the one-dimensional classical Heisenberg model

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