Long-Time Dynamics in Quantum Spin Lattices: Ergodicity and Hydrodynamic Projections at All Frequencies and Wavelengths

TY - JOUR

T1 - Long-Time Dynamics in Quantum Spin Lattices

T2 - Ergodicity and Hydrodynamic Projections at All Frequencies and Wavelengths

AU - Ampelogiannis, Dimitrios

AU - Doyon, Benjamin

N1 - Funding Information: We are grateful to Berislav Buça and Olalla Castro Alvaredo for insightful comments and a current collaboration on related aspects. We also thank Abhishek Dhar for sharing a draft of [] and for related discussions on ergodicity. BD was supported by EPSRC under the grant “Emergence of hydrodynamics in many-body systems: new rigorous avenues from functional analysis”, Ref. EP/W000458/1. DA is supported by a studentship from the Engineering and Physical Sciences Research Council. Publisher Copyright: © 2023, The Author(s).

PY - 2023/5/5

Y1 - 2023/5/5

N2 - Obtaining rigorous and general results about the non-equilibrium dynamics of extended many-body systems is a difficult task. In quantum lattice models with short-range interactions, the Lieb–Robinson bound tells us that the spatial extent of operators grows at most linearly in time. But what happens within this light-cone? We discuss rigorous results on ergodicity and the emergence of the Euler hydrodynamic scale in correlation functions, which establish fundamental principles at the root of non-equilibrium physics. One key idea of the present work is that general structures of Euler hydrodynamics, obtained under ballistic scaling, follow independently from the details of the microscopic dynamics, and in particular do not necessitate chaos; they are consequences of “extensivity”. Another crucial observation is that these apply at arbitrary frequencies and wavelengths. That is, long-time, persistent oscillations of correlation functions over ballistic regions of spacetime, which may be of microscopic frequencies and wavelengths, are predicted by a general Euler-hydrodynamic theory that takes the same form as that for smoothed-out correlation functions. This involves a natural extension of notions of conserved quantities and hydrodynamic projection and shows that the Euler hydrodynamic paradigm covers the full frequency-wavelength plane.

AB - Obtaining rigorous and general results about the non-equilibrium dynamics of extended many-body systems is a difficult task. In quantum lattice models with short-range interactions, the Lieb–Robinson bound tells us that the spatial extent of operators grows at most linearly in time. But what happens within this light-cone? We discuss rigorous results on ergodicity and the emergence of the Euler hydrodynamic scale in correlation functions, which establish fundamental principles at the root of non-equilibrium physics. One key idea of the present work is that general structures of Euler hydrodynamics, obtained under ballistic scaling, follow independently from the details of the microscopic dynamics, and in particular do not necessitate chaos; they are consequences of “extensivity”. Another crucial observation is that these apply at arbitrary frequencies and wavelengths. That is, long-time, persistent oscillations of correlation functions over ballistic regions of spacetime, which may be of microscopic frequencies and wavelengths, are predicted by a general Euler-hydrodynamic theory that takes the same form as that for smoothed-out correlation functions. This involves a natural extension of notions of conserved quantities and hydrodynamic projection and shows that the Euler hydrodynamic paradigm covers the full frequency-wavelength plane.

UR - http://www.scopus.com/inward/record.url?scp=85158138468&partnerID=8YFLogxK

U2 - 10.1007/s00023-023-01304-2

DO - 10.1007/s00023-023-01304-2

M3 - Article

AN - SCOPUS:85158138468

SN - 1424-0637

VL - 25

SP - 65

EP - 123

JO - Annales Henri Poincare

JF - Annales Henri Poincare

ER -