Undular Diffusion in Nonlinear Sigma Models

Krajnik, Žiga; Ilievski, Enej; Prosen, Tomaž

doi:10.1103/physrevlett.125.240607

Cited by 6 publications

(22 citation statements)

References 64 publications

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“…In particular, signatures of symmetry breaking persist to infinite temperature. As demonstrated in a recent study 250 , two-point dynamical correlation functions amongst different components of G-invariant Noether charges show two different types of behavior: while longitudinal correlators lying in the unbroken symmetry sector exhibit normal diffusive behavior (with Gaussian asymptotic scaling profiles) as expected, the transversal (i.e. symmetry-broken) sector reveals another type of anomalous transport law characterized by (i) diffusive dynamical exponent z = 2 and (ii) oscillatory stationary scaling profiles-hence the name undular diffusion 250 .…”

Section: Undular Diffusion In Nonabelian Systemssupporting

confidence: 57%

“…This is not quite what is observed in the transverse sector. While charge dynamics in the symmetry-broken sector exhibits a diffusion-like spreading with a normal dynamical exponent z = 2, the stationary Gaussian scaling profiles are characterized by a complexvalued "diffusion constant" 250 . This law is thus to be distinguished from normal diffusion (i.e.…”

Section: Undular Diffusion In Nonabelian Systemsmentioning

confidence: 99%

“…To this end, it is convenient to introduce complex fields S ± = S x ± iS y . As a direct consequence of U (1) symmetry, it is clear that both S ± (x, t)S ± (0, 0) µ and S z (x, t)S ± (0, 0) µ vanish 250 . This leaves two nontrivial correlators, namely S ± (x, t)S ∓0 c µ .…”

Section: Undular Diffusion In Nonabelian Systemsmentioning

confidence: 99%

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Superdiffusion in spin chains

Bulchandani,

Gopalakrishnan,

Ilievski

2021

Preprint

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This review summarizes recent advances in our understanding of anomalous transport in spin chains, viewed through the lens of integrability. Numerical advances, based on tensor-network methods, have shown that transport in many canonical integrable spin chains-most famously the Heisenberg model-is anomalous. Concurrently, the framework of generalized hydrodynamics has been extended to explain some of the mechanisms underlying anomalous transport. We present what is currently understood about these mechanisms, and discuss how they resemble (and differ from) the mechanisms for anomalous transport in other contexts. We also briefly review potential transport anomalies in systems where integrability is an emergent or approximate property. We survey instances of anomalous transport and dynamics that remain to be understood.

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Section: Undular Diffusion In Nonabelian Systemssupporting

confidence: 57%

Section: Undular Diffusion In Nonabelian Systemsmentioning

confidence: 99%

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Superdiffusion in spin chains

Bulchandani,

Gopalakrishnan,

Ilievski

2021

Preprint

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“…with D = σ/(β 0 χ 0 ) and A = 2μ 0 λ/(β 2 0 χ 0 ) [8,55]. See also the recent discussion in [56]. We shall now perform a scale analysis.…”

Section: Adding Energy Conservationmentioning

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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“…This is despite the fact that the heuristic linear-response argument requires this, or otherwise involves the Kubo-Mori-Bogoliubov inner product [40,87] (but we expect the same results to hold using this inner product). The question of how non-abelian charges affect hydrodynamics has been discussed in the literature, see the recent viewpoints given in [88,89], and in particular their connection with super-diffusion [90].…”

Section: The Problem Of Finite-dimensionality Is Nontrivial In Non-integrable Models Perhapsmentioning

confidence: 99%

Hydrodynamic Projections and the Emergence of Linearised Euler Equations in One-Dimensional Isolated Systems

Doyon

2022

Commun. Math. Phys.

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One of the most profound questions of mathematical physics is that of establishing from first principles the hydrodynamic equations in large, isolated, strongly interacting many-body systems. This involves understanding relaxation at long times under reversible dynamics, determining the space of emergent collective degrees of freedom (the ballistic waves), showing that projection occurs onto them, and establishing their dynamics (the hydrodynamic equations). We make progress in these directions, focussing for simplicity on one-dimensional systems. Under a model-independent definition of the complete space of extensive conserved charges, we show that hydrodynamic projection occurs in Euler-scale two-point correlation functions. A fundamental ingredient is a property of relaxation: we establish ergodicity of correlation functions along almost every direction in space and time. We further show that to every extensive conserved charge with a local density is associated a local current and a continuity equation; and that Euler-scale two-point correlation functions of local conserved densities satisfy a hydrodynamic equation. The results are established rigorously within a general framework based on Hilbert spaces of observables. These spaces occur naturally in the $$C^*$$ C ∗ algebra description of statistical mechanics by the Gelfand–Naimark–Segal construction. Using Araki’s exponential clustering and the Lieb–Robinson bound, we show that the results hold, for instance, in every nonzero-temperature Gibbs state of short-range quantum spin chains. Many techniques we introduce are generalisable to higher dimensions. This provides a precise and universal theory for the emergence of ballistic waves at the Euler scale and how they propagate within homogeneous, stationary states.

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Undular Diffusion in Nonlinear Sigma Models

Cited by 6 publications

References 64 publications

Superdiffusion in spin chains

Superdiffusion in spin chains

Hydrodynamics in lattice models with continuous non-Abelian symmetries

Hydrodynamic Projections and the Emergence of Linearised Euler Equations in One-Dimensional Isolated Systems

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