Macroscopic Diffusive Transport in a Microscopically Integrable Hamiltonian System

Prosen, Tomaž; Žunkovič, Bojan

doi:10.1103/physrevlett.111.040602

Cited by 88 publications

(150 citation statements)

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“…Specifically, studying dynamical correlations in quantum Heisenberg (XXX) chain of spins 1/2 at vanishing magnetization (or zero magnetic field), it has been demonstrated that the sole contribution to transport comes from the heat-peak with the sound-peaks being absent, but that the former broadens with a perfect KPZ scaling [9] over several orders of magnitude. This result is consistent with earlier observations [10] of z ∼ 1.5 in the integrable lattice Landau-Lifshitz (LLL) chain of classical spins [11] which can be thought of as an integrable classical version of the XXX model. More recently, these numerical experiments have been refined, confirming also the precise KPZ scaling profile of the heat-peak [12].…”

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confidence: 93%

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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confidence: 93%

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

Krajnik

Prosen

2020

J Stat Phys

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“…Intimately related to this question is the distinction between integrable and nonintegrable models. On the one hand, integrable models are characterized by a macroscopic number of (quasi)local conservation laws which can lead to anomalous thermalization [11,12] and ballistic transport [13][14][15]. As a consequence, diffusion is generally not expected to occur in these systems.…”

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confidence: 99%

Magnetization dynamics in clean and disordered spin-1 XXZ chains

et al. 2019

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We study spin transport in the one-dimensional anisotropic S = 1 Heisenberg model. Particular emphasis is given to dynamics at infinite temperature, where current autocorrelations and spatiotemporal correlation functions are obtained by means of an efficient pure-state approach based on the concept of typicality. Our comprehensive numerical analysis unveils that high-temperature spin transport is diffusive in the easy-axis regime for strong exchange anisotropies. This finding is based on the combination of numerous signatures, such as (i) Gaussian spreading of correlations, (ii) a time-independent diffusion coefficient, (iii) power-law decay of equal-site correlations, (iv) exponentially decaying long-wavelength modes, and (v) Lorentzian line shapes of the dynamical structure factor. Moreover, we provide evidence that some of these signatures are not exclusively restricted to the infinite-temperature limit, but can persist at lower temperatures as well, where we complement our results by additional quantum Monte Carlo simulations of large systems. In contrast to the easy-axis regime, we show that in the case of an isotropic chain, the signatures (i) -(v) are much less pronounced or even entirely absent, suggesting the existence of anomalous spin transport despite the nonintegrability of the model. Eventually, upon introducing a random on-site magnetic field, we observe a breakdown of diffusion and distinctly slower dynamics. In particular, our results exhibit qualitative similarities to disordered spin-1/2 chains and might be consistent with the onset of many-body localization in the S = 1 model for sufficiently strong disorder.

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“…We have shown that a redundancy of description in the thermal states of isotropic integrable models, corresponding to the direction of the magnetization vector, gives rise to soft gauge modes at the level of hydrodynamics, which are decoupled from the quasiparticle sector and provide a channel for superdiffusive spin transport. We have further demonstrated that the dynamics of these modes reduces to a propagating torsional degree of freedom, whose coarsed-grained timeevolution is described by the stochastic Burgers equation, explaining the numerical observation of KPZ scaling in such models [16][17][18][19][20][21][22] .…”

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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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Macroscopic Diffusive Transport in a Microscopically Integrable Hamiltonian System

Cited by 88 publications

References 29 publications

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

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

Magnetization dynamics in clean and disordered spin-1 XXZ chains

Kardar-Parisi-Zhang universality from soft gauge modes

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