Stability of Superdiffusion in Nearly Integrable Spin Chains

Abstract

Superdiffusive finite-temperature spin or charge transport has been recently observed in a variety of integrable spin and Hubbard chains or ladders, with nonabelian global symmetries. While it is understood that such superdiffusive dynamics is caused by giant Goldstone-like quasiparticles stabilized by integrability, the type of transport in systems which are not perfectly integrable is still obscure. We here show that integrability-breaking perturbations that preserve the nonabelian symmetry couple weakly to these giant Goldstone-like quasiparticles, so they are long-lived and give divergent contributions to the low-frequency conductivity σ(ω). We find, perturbatively, that σ(ω) ∼ ω −1/3 for translation-invariant static perturbations that conserve energy, and σ(ω) ∼ | log ω| for noisy perturbations. The (presumable) crossover to regular diffusion appears to lie beyond perturbation theory. By contrast, integrability-breaking perturbations that break the nonabelian symmetry yield conventional diffusion. Numerical evidence supports the distinction between these two classes of perturbations.

Correlations and commuting transfer matrices in integrable unitary circuits

“…A similar construction was shown to hold for the calculation of out-of-time-order correlations. At long times, the correlations in integrable circuits with a nonabelian symmetry such as SU( 2) are expected to return Kardar-Parisi-Zhang (KPZ) dynamics [40,[42][43][44][45]. Unfortunately, the complicated Jordan block structure of the transfer matrix prevents a direct connection between the presented eigenstates and the long-time dynamics.…”

“…In fact, an extensive number of pseudo-vacuum states can be obtained by making use of the two-component structure of the transfer matrix, where the central unitary gates are related through hermitian conjugation. Making use of the unitarity, we observe that , (44) returning T m−1 from T m , such that any vacuum state for T m−1 can be used to construct a vacuum state for T m . This relation can be repeatedly applied, and a total number of m orthogonal pseudo-vacuum states can be defined as , (45) with n = 0, .…”

“…In the case of unitary circuits, Bethe ansatz techniques have been used to calculate the spectral form factor for randomized Floquet models with a conserved charge [41] and (quasi)local conservation laws have been identified [37]. Diffusive transport has been observed in the (anisotropic) XXZ case [38], whereas superdiffusion and Kardar-Parisi-Zhang scaling is expected in (isotropic) XXX models [40,[42][43][44][45].…”

Unbounded entanglement production via a dissipative impurity

“…Perturbative field-theoretical approaches are also available [17]. A promising direction is to extend the hydrodynamic framework to integrable systems subjected to dissipation [14,[18][19][20][21]. This is motivated by the tremendous success of Generalized Hydrodynamics (GHD) for integrable systems [22,23].…”

Absence of superdiffusion in certain random spin models

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The dynamics of spin at finite temperature in the spin-1/2 Heisenberg chain was found to be superdiffusive in numerous recent numerical and experimental studies. Theoretical approaches to this problem have emphasized the role of nonabelian SU (2) symmetry as well as integrability but the associated methods cannot be readily applied when integrability is broken.We examine spin transport in a spin-1/2 chain in which the exchange couplings fluctuate in space and time around a nonzero mean J, a model introduced by De Nardis et al [1]. We show that operator dynamics in the strong noise limit at infinite temperature can be analyzed using conventional perturbation theory as an expansion in J.

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