Helical Luttinger Liquid on a Space-Time Lattice

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.