Subdiffusive hydrodynamics of nearly-integrable anisotropic spin chains

De Nardis, Jacopo; Gopalakrishnan, Sarang; Vasseur, Romain; Ware, Brayden

doi:10.48550/arxiv.2109.13251

Cited by 5 publications

(8 citation statements)

References 45 publications

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“…As we will discuss, this anomalous FCS is related to a breakdown of the central limit theorem due to strong correlations between successive scattering events [38]. Our results generalize to nonintegrable systems with hardcore kinetic constraints; there, they give subdiffusion [39,40] with the same universal FCS [41].…”

mentioning

confidence: 68%

“…While we used results from integrability, in fact the main phenomenological features survive even in the absence of integrability, at large ∆, because they only rely on the stability of magnons. When integrability is broken at large ∆, there is a parametrically large time window (polynomial in 1/∆ [40]) for which magnons are diffusive but stable; in this time window, one expects subdiffusion [39,40] with anomalous counting statistics. In this regime, the universal skewed distribution (7) once again arises asymptotically; however, its width is now set by t 1/4 rather than t 1/2 [41].…”

Section: T E Z D P I B B a = " >mentioning

confidence: 99%

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Theory of anomalous full counting statistics in anisotropic spin chains

Gopalakrishnan¹,

Morningstar²,

Vasseur³

et al. 2022

Preprint

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We present an analytic theory of the full counting statistics of spin transport in the anisotropic one-dimensional XXZ spin chain. We consider a setup in which the left and right half of the chain are initially created at different magnetization densities, and consider the probability distribution of the magnetization transferred between the two half-chains. We derive a closed-form expression for the probability distribution of the magnetization transfer, in terms of random walks on the halfline. Although the magnetization transfer is diffusive on average, its distribution has a universal non-gaussian form at late times. We show that this distribution strongly violates the large-deviation principle, and explain the physical origin of this violation. We discuss the crossovers that occur as the initial state is brought closer to global equilibrium. Our predictions can directly be tested in experiments using quantum gas microscopes or superconducting qubit arrays.

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confidence: 68%

Section: T E Z D P I B B a = " >mentioning

confidence: 99%

Theory of anomalous full counting statistics in anisotropic spin chains

Gopalakrishnan¹,

Morningstar²,

Vasseur³

et al. 2022

Preprint

Self Cite

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“…A version of the folded XXZ model in which integrability is broken by noise was recently studied in Ref. [88], concluding z = 4 as well.…”

Section: Discussionmentioning

confidence: 99%

Emergent tracer dynamics in constrained quantum systems

Feldmeier,

Witczak-Krempa,

Knap

2022

Preprint

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We show how the tracer motion of tagged, distinguishable particles can effectively describe transport in various homogeneous quantum many-body systems with constraints. We consider systems of spinful particles on a one-dimensional lattice subjected to constrained spin interactions, such that some or even all multipole moments of the effective spin pattern formed by the particles are conserved. On the one hand, when all moments-and thus the entire spin pattern-are conserved, dynamical spin correlations reduce to tracer motion identically, generically yielding a subdiffusive dynamical exponent z = 4. This provides a common framework to understand the dynamics of several constrained lattice models, including models with XNOR or tJz -constraints. We consider random unitary circuit dynamics with such a conserved spin pattern and use the tracer picture to obtain exact expressions for their late-time dynamical correlations. Our results can also be extended to integrable quantum many-body systems that feature a conserved spin pattern but whose dynamics is insensitive to the pattern, which includes for example the folded XXZ spin chain. On the other hand, when only a finite number of moments of the pattern are conserved, the dynamics is described by a convolution of the internal hydrodynamics of the spin pattern with a tracer distribution function. As a consequence, we find that the tracer universality is robust in generic systems if at least the quadrupole moment of the pattern remains conserved. In cases where only total magnetization and dipole moment of the pattern are constant, we uncover an intriguing coexistence of two processes with equal dynamical exponent but different scaling functions, which we relate to phase coexistence at a first order transition.

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“…In this Letter, we investigate the effect of weak IBP of strength g on the high-T diffusion in the XXZ model, with the main conclusion that the dc diffusion constant D, appearing at nonzero g > 0 is unrelated to the dissipationless diffusion D I in the integrable system, as previously hinted [25,31] and recently also suggested in Ref. [32]. As a consequence, the generalized Einstein relation D = σ 0 /χ 0 , which relates σ 0 and the spin susceptibility χ 0 (T → ∞) ∼ 1/(4T ) (taking k B = 1) with diffusion constant is not valid for integrable XXZ model.…”

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confidence: 99%

From dissipationless to normal diffusion in easy-axis Heisenberg spin chain

P.¹,

S.²,

Lenarčič³

et al. 2022

Preprint

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The anomalous spin diffusion of the integrable easy-axis Heisenberg chain originates in the ballistic transport of symmetry sectors with nonzero magnetization. Ballistic transport is replaced by normal dissipative transport in all magnetization sectors upon introducing the integrability-breaking perturbations, including external driving. Such behavior implies that the diffusion constant obtained for the integrable model is relevant for the spread of spin excitations but not for the spin conductivity. We present numerical results for closed systems and driven open systems, indicating that the diffusion constant shows a discontinuous variation as the function of perturbation strength.

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Subdiffusive hydrodynamics of nearly-integrable anisotropic spin chains

Cited by 5 publications

References 45 publications

Theory of anomalous full counting statistics in anisotropic spin chains

Theory of anomalous full counting statistics in anisotropic spin chains

Emergent tracer dynamics in constrained quantum systems

From dissipationless to normal diffusion in easy-axis Heisenberg spin chain

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