Bosonic Continuum Theory of One-Dimensional Lattice Anyons

Area of Science:

• Condensed Matter Physics
• Quantum Gases
• Many-Body Physics

Background:

• Anyons with tunable exchange phases are realized in 1D lattices of ultracold gases.
• Existing continuum theories fail to accurately describe these 1D lattice anyons.
• A theoretical framework is needed to connect lattice anyon behavior to continuum models.

Purpose of the Study:

• To derive the continuum limit of 1D lattice anyons.
• To establish a theoretical framework that accurately describes anyon behavior in 1D.
• To provide a mapping between experimental observations, lattice anyon models, and continuum theories.

Main Methods:

• Derivation of the continuum limit using interacting boson theory.
• Analysis of exchange phase periodicity analogous to 2D anyons.
• Numerical estimation of the Luttinger parameter as a function of exchange angle.

Main Results:

• A novel continuum theory for 1D lattice anyons is established.
• The theory fully preserves the exchange phase periodicity characteristic of 2D anyons.
• The Kundu anyon model is identified as a special case with natural regularization.
• Numerical analysis reveals the dependence of the Luttinger parameter on the exchange angle.
• Predictions of differing velocities for left- and right-moving collective excitations are made.

Conclusions:

• The derived continuum theory provides a robust framework for understanding 1D lattice anyons.
• This work establishes a crucial link between theoretical models and experimental realizations.
• The findings offer insights into the long-range properties and collective dynamics of anyonic systems.