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Dynamics in Systems with Modulated Symmetries.

Pablo Sala1,2, Julius Lehmann1,2, Tibor Rakovszky3

  • 1Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany.

Physical Review Letters
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This summary is machine-generated.

We introduce novel spatially modulated symmetries and explore their impact on system dynamics. Periodic modulations cause diffusive correlations in 1D, while exponential modulations create unique boundary and bulk behaviors.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Quantum Field Theory

Background:

  • Symmetries are fundamental in physics, governing conservation laws and system properties.
  • Existing notions of multipole and subsystem symmetries are extended to more general forms.
  • Spatially modulated symmetries represent a novel class of symmetry in physical systems.

Purpose of the Study:

  • To generalize multipole and subsystem symmetries to spatially modulated symmetries.
  • To investigate the long-time dynamics of systems exhibiting these novel symmetries.
  • To uncover new physical phenomena arising from exponential and quasiperiodic modulations.

Main Methods:

  • Development of microscopic models in 1, 2, and 3 dimensions.
  • Numerical simulation of a stochastic cellular automaton.
  • Analytical proof for one-dimensional systems.

Main Results:

  • Periodic modulations lead to diffusive correlations with finite microscopic momentum in 1D.
  • Higher-dimensional systems exhibit conserved momenta along lines/surfaces, causing exotic subdiffusion.
  • Exponential modulations result in infinitely long-lived boundary correlations and bulk exponential decay.

Conclusions:

  • Spatially modulated symmetries introduce rich and exotic dynamics in physical systems.
  • The nature of modulation (periodic vs. exponential) dictates distinct long-time behaviors.
  • These findings offer new insights into symmetry, dynamics, and emergent phenomena.