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Area of Science:

  • Condensed matter physics
  • Quantum field theory
  • Many-body physics

Background:

  • The Luttinger model describes interacting one-dimensional massless Dirac fermions, challenging Fermi liquid theory.
  • Discretizing this model on a lattice faces the fermion-doubling obstruction, hindering accurate simulations.
  • Existing methods either introduce spurious excitations or gap the Dirac point.

Purpose of the Study:

  • To overcome the fermion-doubling obstruction in discretizing the Luttinger model.
  • To develop a local Lagrangian for simulating helical Luttinger liquids with Hubbard interactions.
  • To enable quantum Monte Carlo simulations that preserve topological properties.

Main Methods:

  • Discretization of both space and time in the Luttinger model.
  • Formulation of a local Lagrangian for a helical Luttinger liquid.
  • Application of quantum Monte Carlo simulations.

Main Results:

  • A novel discretization scheme that circumvents the fermion-doubling obstruction.
  • Successful generation of a local Lagrangian for the interacting system.
  • Demonstration of preserved topological protection of the Dirac cone in simulations.

Conclusions:

  • The developed method provides a viable approach for discretizing interacting fermion systems.
  • This work enables robust quantum simulations of topological phenomena in one dimension.
  • It opens new avenues for studying strongly correlated electron systems.