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Area of Science:

  • Condensed matter physics
  • Quantum mechanics
  • Many-body systems

Background:

  • Quantum particles with long-range potentials exhibit complex ground-state phases.
  • The transition from Coulombic to linear confinement potentials is crucial for understanding these phases.
  • Disorder's role in these quantum systems is a key area of investigation.

Purpose of the Study:

  • Investigate ground-state properties of quantum particles with tunable long-range potentials.
  • Determine the impact of disorder on the Wigner crystal phase.
  • Characterize the emergent phases, such as the Mott glass.

Main Methods:

  • Bosonization techniques to map fermionic systems to bosonic ones.
  • Nonperturbative functional renormalization group (FRG) for analyzing interacting quantum systems.
  • Analysis of ground-state properties including compressibility and conductivity.

Main Results:

  • In the absence of disorder, a Wigner crystal forms for potentials with σ ≤ 0.
  • Disorder suppresses Wigner crystallization for -3/2 < σ ≤ 0, leading to a Mott glass.
  • For σ < -3/2, the Wigner crystal state persists even with disorder.

Conclusions:

  • Disorder plays a critical role in determining the ground state of quantum particles with long-range interactions.
  • The study identifies a transition from Wigner crystal to Mott glass phases driven by disorder.
  • The findings provide insights into quantum phase transitions in disordered systems.