Approaching off-diagonal long-range order for 1+1 -dimensional relativistic anyons

Abstract

We construct and study relativistic anyons in 1+1 dimensions generalizing well-known models of Dirac fermions. First, a model of free anyons is constructed and then extended in two ways: (i) By adding density-density interactions, as in the Luttinger model. (ii) By coupling the free anyons to a U(1)-gauge field, as in the Schwinger model. Second, physical properties of these extensions are studied. By investigating off-diagonal long-range order (ODLRO) at zero temperature, we show that anyonic statistics allows one to get arbitrarily close to ODLRO but that this possibility is destroyed by the gauge coupling. The latter is due to a non-zero effective mass generated by gauge invariance, which we show also implies the presence of screening, independently of the anyonic statistics.

Anyons in a tight wave-guide and the Tonks-Girardeau gas

“…In 1D there does not seem to be a unique agreed-upon model for anyonic exchange statistics. Depending on how one proceeds to quantization, they have historically been described [1,[12][13][14]64] as ordinary particles with either contact interactions (Lieb-Liniger model) or inverse-square interactions (Calogero-Sutherland model) but other formalisms exist [15][16][17][18]. In particular, the chiral BF/Kundu model [19][20][21][22] and the anyon-Hubbard model [23][24][25] have attracted attention recently.…”