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Related Experiment Videos

Duality between the weak and strong interaction limits for randomly interacting fermions.

Philippe Jacquod1, Imre Varga

  • 1Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands.

Physical Review Letters
|September 13, 2002
PubMed
Summary

We found a duality transformation for interacting fermions, showing similar statistical properties at weak and strong interactions. This reveals a duality point where eigenstates exhibit identical spreading, persisting with more particles.

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Area of Science:

  • Condensed matter physics
  • Quantum mechanics

Background:

  • Understanding interacting fermion systems is crucial in condensed matter physics.
  • Characterizing the behavior of eigenstates under varying interaction strengths is a key challenge.

Purpose of the Study:

  • To establish a duality transformation for generic models of interacting fermions.
  • To investigate the statistical properties of eigenstates at weak and strong interactions.
  • To identify a duality point and characterize the intermediate regime.

Main Methods:

  • Analysis of interacting fermion models with two-body interactions.
  • Comparison of eigenstate properties in different interaction bases (U=0 and U=infinity).
  • Application of scaling arguments.

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Main Results:

  • Demonstrated a duality transformation for interacting fermions.
  • Showcased similar statistical properties of eigenstates at weak (U=0) and strong (U=infinity) interactions.
  • Identified a duality point U(d) with identical eigenstate spreading and a finite-width intermediate regime characterized by non-Lorentzian strength function spreading.

Conclusions:

  • The existence of a duality transformation simplifies the understanding of interacting fermion systems.
  • The identified duality point and intermediate regime offer new insights into quantum phase transitions.
  • Scaling arguments suggest the robustness of this intermediate regime with increasing particle numbers.