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Variable-Range Hopping through Marginally Localized Phonons.

Sumilan Banerjee1, Ehud Altman1

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Summary
This summary is machine-generated.

Anderson localized particles coupled to phonons in one dimension do not exhibit standard hopping. Instead, a many-body phonon process suppresses hopping, preventing many-body localization at low temperatures.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Disordered Systems

Background:

  • Anderson localization describes the absence of diffusion in disordered systems.
  • Phonons are quantized lattice vibrations crucial for electron transport.
  • Many-body localization (MBL) is a quantum phenomenon preventing thermalization in interacting disordered systems.

Purpose of the Study:

  • Investigate the conditions for many-body localization in a one-dimensional system of Anderson localized particles coupled to phonons.
  • Analyze the impact of phonon-mediated hopping on the transport properties of such coupled systems.

Main Methods:

  • Analysis of phonon-mediated hopping transport in both weak and strong coupling regimes.
  • Theoretical modeling of electron-phonon and ultracold fermion-phonon interactions in disordered systems.

Main Results:

  • The standard variable-range hopping mechanism is ineffective at low temperatures due to bath discreteness.
  • System thermalization occurs via a many-body process involving a diverging number of phonons.
  • This process leads to a singular prefactor in Mott's formula, strongly suppressing hopping rates.

Conclusions:

  • The investigated one-dimensional coupled system does not achieve many-body localization under the studied conditions.
  • The findings highlight a novel thermalization mechanism in disordered quantum systems.
  • Potential implications for higher-dimensional electron-phonon coupled systems are suggested.