Dimensions of the possible

Won-Young Hwang

We discuss possibility of upper-bounding dimension of quantum states device-independently. Provided that the states are pure, it is possible to generate certain four states whose dimension is bounded by two.

Frances Y. Kuo, Ian H. Sloan, G.W. Wasilkowski +1 more

Noriaki Horiuchi

Urbashi Satpathi, Sumit Ghosh, Alak K. Ray +1 more

Possibility of electronic charge and spin separation leading to charge density wave and spin density wave is well established in one dimensional systems in presence and absence of Coulomb interaction. We start from quasi one dimension and show the possibility of such a transition in quasi one dimension as well as in two dimension by going to a regime where it can be shown for free electrons that just interact via Fermi statistics. Since Coulomb interaction can only facilitate the phenomenon, the purpose of our work is to show the phenomena unambiguously in the limit when Coulomb interaction can be ignored. Finally we also comment on dimensions greater than two and inclusion of Coulomb interactions.

Edp Sciences, Les Ulis

Particles possessing fractional statistics in two dimension have been dubbed anyons. We want to show how it is possible to extend this concept in the case of conformally invariant systems in one dimension, and reproduce the flux-tube attachment construction due to Wilczek. We will introduce a class of models describing 1D anyons, which has the great advantage over its 2D counterparts to be exactly solvable. The properties of these 1D anyons generalize those of a Luttinger liquid and yield a complete classification of 1D fixed points when time-reversal symmetry is broken. I HOW ANYONS MAY ARISE IN ONE DIMENSION Fractional statistics arises in two dimensions because the exchange of particle is encoded by the braid group BN rather than by the permutation group S N. This fractional exchange statistics is often thought to be possible only in two dimensions in contrast with for instance fractional exclusion statistics which is defined independently of the dimensionality. However already in their seminal paper Leinaas and hfyrheim investigated the possibility to define intermediate statistics in one dimension by considering generalized boundary conditions for wavefunctions

Josh Izaac, Jingbo B. Wang