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Dynamic structure factor of the Calogero-Sutherland model.

Michael Pustilnik1

  • 1School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA.

Physical Review Letters
|August 16, 2006
PubMed
Summary

We studied the dynamic structure factor in a quantum model with inverse-square interaction. We found power-law singularities at frequency interval borders, similar to Fermi-edge singularities.

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Area of Science:

  • Quantum mechanics
  • Condensed matter physics
  • Statistical mechanics

Background:

  • The Calogero-Sutherland model is a key one-dimensional quantum system.
  • Understanding dynamic structure factors is crucial for characterizing quantum many-body systems.
  • Fermi-edge singularities provide insights into electron interactions in metals.

Purpose of the Study:

  • To evaluate the dynamic structure factor S(q, omega) for the one-dimensional quantum Hamiltonian with inverse-square interaction.
  • To analyze the behavior of S(q, omega) at small momentum transfers (q).
  • To investigate the nature of singularities in the dynamic structure factor.

Main Methods:

  • Analytical evaluation of the dynamic structure factor S(q, omega).
  • Analysis of the frequency spectrum for a fixed small momentum q.
  • Identification and characterization of power-law singularities.

Main Results:

  • For small q, S(q, omega) is non-zero within a finite frequency interval (deltaomega proportional to q^2/m).
  • Power-law singularities are observed at the frequency interval boundaries.
  • The exponents of these singularities depend on the interaction strength.

Conclusions:

  • The dynamic structure factor exhibits unique behavior in the Calogero-Sutherland model.
  • The observed singularities share similarities with Fermi-edge singularities in X-ray absorption spectra.
  • This study provides a deeper understanding of quantum interactions in one-dimensional systems.

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