Anyons abound in 1D quantum gases

Yan Li, Zhi He

Жу, Ren-Gui, Wang +1 more

Martin Bonkhoff, Kevin Jägering, Sebastian Eggert +3 more

Anyons with arbitrary exchange phases exist on 1D lattices in ultracold gases. Yet, known continuum theories in 1D do not match. We derive the continuum limit of 1D lattice anyons via interacting bosons. The theory maintains the exchange phase periodicity fully analogous to 2D anyons. This provides a mapping between experiments, lattice anyons, and continuum theories, including Kundu anyons with a natural regularization as a special case. We numerically estimate the Luttinger parameter as a function of the exchange angle to characterize long-range signatures of the theory and predict different velocities for left- and right-moving collective excitations.

J. I. Cirac

G. Rosenberg, Babak Seradjeh, Conan Weeks +1 more

Anjan Kundu

Applying braided Yang-Baxter equation quantum integrable and Bethe ansatz solvable 1D anyonic lattice and field models are constructed.Along with known models we discover novel lattice anyonic and q-anyonic models as well as nonlinear Schrödinger equation (NLS) and the derivative NLS quantum field models involving anyonic operators, N -particle sectors of which yield the well known anyon gases, interacting through δ and derivative δ-function potentials.