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Hydrodynamic nonlinear response of interacting integrable systems.

Michele Fava1, Sounak Biswas2, Sarang Gopalakrishnan3

  • 1Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, Oxford OX1 3PU, United Kingdom; michele.fava@physics.ox.ac.uk.

Proceedings of the National Academy of Sciences of the United States of America
|September 8, 2021
PubMed
Summary
This summary is machine-generated.

We developed a new method to calculate the nonlinear response of interacting integrable systems. This approach accurately describes systems in the hydrodynamic limit and distinguishes them from noninteracting ones.

Keywords:
generalized hydrodynamicsintegrable systemsnonlinear response

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Area of Science:

  • Condensed matter physics
  • Quantum many-body systems
  • Statistical mechanics

Background:

  • Understanding the nonlinear response of quantum systems is crucial for characterizing their dynamics.
  • Integrable systems offer a unique platform to study many-body interactions due to their exact solvability.
  • Distinguishing between interacting and noninteracting integrable systems is key to understanding emergent phenomena.

Purpose of the Study:

  • To develop a general formalism for computing the nonlinear response of interacting integrable systems.
  • To provide a method for calculating finite-temperature Drude weights.
  • To identify and characterize nonperturbative regimes in nonlinear response.

Main Methods:

  • Development of a theoretical formalism for nonlinear response calculations.
  • Asymptotic analysis in the hydrodynamic limit.
  • Application to specific models like the Lieb-Liniger gas and the XXZ spin chain.
  • Comparison with numerical evaluations.

Main Results:

  • A formalism for asymptotically exact nonlinear response in the hydrodynamic limit.
  • Spatially resolved nonlinear response as a signature distinguishing interacting from noninteracting integrable systems.
  • A prescription for computing finite-temperature Drude weights of arbitrary order.
  • Identification of intrinsically nonperturbative regimes.

Conclusions:

  • The developed formalism provides a powerful tool for studying nonlinear phenomena in integrable systems.
  • The study highlights the importance of spatially resolved measurements for characterizing quantum systems.
  • The findings offer new insights into the behavior of interacting quantum matter.