Logarithmic Superdiffusion in Two Dimensional Driven Lattice Gases

Krug, Joachim; Neiss, Robert Axel; Schadschneider, Andreas; Schmidt, Johannes

doi:10.1007/s10955-018-1995-z

“…Marginally irrelevant hydrodynamic fluctuations are common in d = 2 spatial dimensions, where the leading divergence (90) arises at one-loop; examples include regular fluid dynamics [67] (where α = 1/2), surface chiral metals [52] (where α = 2/3) as well as driven-dissipative systems (see e.g. [68,69]). Logarithmically-enhanced diffusion is also possible in d = 1 spatial dimensions, if the leading effect of hydrodynamic fluctuations arises at two-loops -a possibility realized for example in surface growth with reflection symmetry [70].…”

Section: A Theory With Logarithmically-enhanced Diffusionmentioning

confidence: 99%

Hydrodynamics in lattice models with continuous non-Abelian symmetries

Glorioso

¹

,

Delacrétaz

²

,

Chen

³

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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“…Marginally irrelevant hydrodynamic fluctuations are common in d = 2 spatial dimensions, where the leading divergence (5.1) arises at one-loop; examples include regular fluid dynamics [52] (where α = 1/2), surface chiral metals [53] (where α = 2/3) as well as driven-dissipative systems (see e.g. [54,55]). Logarithmically-enhanced diffusion is also possible in d = 1 spatial dimensions, if the leading effect of hydrodynamic fluctuations arises at two-loops -a possibility realized for example in surface growth with reflection symmetry [56].…”

Section: A Theory With Logarithmically-enhanced Diffusionmentioning

confidence: 99%

Hydrodynamics in lattice models with continuous non-Abelian symmetries

Glorioso,

Delacrétaz,

Chen

et al. 2020

Preprint

View full text Add to dashboard Cite

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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“…In fact, for a = 1 the stationary state is not Gaussian [19] but the RG analysis of [11] suggests that the behaviour should be the same as for a = 1, in particular the stationary state should be asymptotically Gaussian on large scales, as indicated by the simulations in [13]. Even though log corrections to diffusivity may look too tiny to be observed, we emphasise that the predicted (log t) 2/3 -effect in 2d driven diffusive models has been very recently numerically measured [26].…”

Section: Discussionmentioning

confidence: 54%