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Dynamical conductivity of disordered quantum chains.

Shintaro Takayoshi1, Thierry Giamarchi2

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Summary
This summary is machine-generated.

We investigated quantum transport in disordered 1D systems. Our findings show interaction-dependent conductivity and localization length, consistent with field theory, offering insights for cold atom experiments.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Statistical Physics

Background:

  • Understanding transport properties in disordered quantum systems is crucial for condensed matter physics.
  • One-dimensional (1D) systems exhibit unique phenomena like Anderson localization.
  • Interactions can significantly alter the behavior of disordered quantum systems.

Purpose of the Study:

  • To numerically investigate the frequency-dependent conductivity of a 1D fermionic chain with nearest-neighbor interactions and a random potential.
  • To analyze the impact of interaction and disorder strengths on transport properties.
  • To compare numerical results with theoretical predictions, particularly bosonized field theory.

Main Methods:

  • Chebyshev matrix product state (CheMPS) method for numerical computation.
  • Exact diagonalization and analytical solutions for benchmarking.
  • Analysis of dynamical conductivity spectra and localization length.

Main Results:

  • The conductivity exhibits a power-law decay at high frequencies, with an exponent dependent on interaction strength.
  • A characteristic pinning frequency, related to the inverse localization length, was identified.
  • Localization length follows a power law of disorder strength, with interaction-dependent exponent, showing good agreement with field theory.
  • Low-frequency conductivity is consistent with the noninteracting case, irrespective of interaction strength.

Conclusions:

  • The CheMPS method provides reliable results for transport properties in interacting 1D disordered systems.
  • Numerical findings align with bosonized field theory predictions for conductivity and localization length.
  • Results have implications for experimental studies using cold atomic gases.