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Lattice models with N=2 supersymmetry.

Paul Fendley1, Kareljan Schoutens, Jan de Boer

  • 1Department of Physics, University of Virginia, Charlottesville, Virginia 22904-4714, USA. fendley@virginia.edu

Physical Review Letters
|April 12, 2003
PubMed
Summary

We developed lattice models with N=2 supersymmetry, offering a new framework for quantum physics. These models regulate quantum field theories, connecting lattice structures to continuous models like the Thirring model.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Field Theory
  • High Energy Physics

Background:

  • Supersymmetry (SUSY) is a theoretical framework relating bosons and fermions.
  • Lattice models are crucial for studying quantum systems numerically and analytically.
  • Understanding interacting quantum systems is a fundamental challenge in physics.

Purpose of the Study:

  • Introduce novel lattice models with explicit N=2 supersymmetry.
  • Develop a supersymmetric lattice regulator for quantum field theories.
  • Explore the connection between lattice models and continuous quantum field theories.

Main Methods:

  • Construction of lattice models with N=2 supersymmetry generators.
  • Analysis using conformal field theory (CFT).
  • Application of the Bethe ansatz and cohomology for model analysis.

Main Results:

  • The Hamiltonian H=(Q(+),Q(-)) is derived for interacting lattice models.
  • Degrees of freedom can be represented as hard-core fermions or quantum dimers.
  • The simplest model acts as a supersymmetric lattice regulator for the massless (1+1)-dimensional Thirring (Luttinger) model.

Conclusions:

  • The introduced lattice models provide a powerful tool for studying supersymmetry in quantum systems.
  • These models bridge the gap between lattice discretizations and continuous quantum field theories.
  • Generalizations, such as the quantum monomer-dimer model, open new research avenues.

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