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Emergent Hydrodynamics in Nonequilibrium Quantum Systems.

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Density matrix truncation (DMT) accurately models Floquet systems, revealing prethermalization and heating dynamics. This novel tool also captures hydrodynamics in quantum spin chains, enabling energy diffusion coefficient extraction.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Dynamics
  • Statistical Mechanics

Background:

  • Periodically driven many-body systems, known as Floquet systems, are a key area of research.
  • Understanding their late-time dynamics, including prethermalization and heating, is crucial but computationally challenging.

Purpose of the Study:

  • To introduce and validate a novel numerical tool, density matrix truncation (DMT), for studying large-scale Floquet systems.
  • To investigate the interplay between Floquet heating and transport phenomena.
  • To demonstrate DMT's capability in analyzing static Hamiltonians and extracting transport coefficients.

Main Methods:

  • Development and application of density matrix truncation (DMT), a novel numerical technique.
  • Simulation of large-scale Floquet systems with both homogeneous and spatially inhomogeneous drives.
  • Simulation of large-scale quantum spin chains (up to L=100) with static Hamiltonians.

Main Results:

  • DMT accurately captures key Floquet physics: prethermalization and late-time heating to infinite temperature.
  • An interplay between Floquet heating and diffusive transport is identified as critical for system dynamics under inhomogeneous drives.
  • DMT quantitatively captures the emergence of hydrodynamics in static systems, allowing direct extraction of the energy diffusion coefficient.

Conclusions:

  • Density matrix truncation (DMT) is a powerful and accurate numerical tool for large-scale quantum systems.
  • DMT provides new insights into Floquet physics and the emergence of hydrodynamics.
  • The method facilitates the quantitative study of energy diffusion in quantum spin chains.