Exactly solvable model with interaction of particles of different kinds

Sagar Vijay, Jeongwan Haah, Liang Fu

Exactly solvable models often provide valuable insights in theoretical studies of topological phases. Here the authors introduce exactly solvable models of interacting Majorana fermions each with extensive topological ground-state degeneracy and a hierarchy of pointlike, topological excitations that are only free to move within submanifolds of the full lattice. These very different models make up a new kind of topological quantum order.

Miki Wadati, Yuko Akutsu

Martin Hallnäs, Edwin Langmann A, Cornelius Paufler

As is well known, there exists a four-parameter family of local interactions in 1D. We interpret these parameters as coupling constants of delta-type interactions which include different kinds of momentum-dependent terms, and determine all cases leading to many-body systems of distinguishable particles which are exactly solvable by the coordinate Bethe ansatz. We find two such families of systems, one with two independent coupling constants deforming the well-known delta-interaction model to non-identical particles, and the other with a particular one-parameter combination of the delta and (the so-called) delta-prime interaction. We also find that the model of non-identical particles gives rise to a somewhat unusual solution of the Yang–Baxter relations. For the other model we write down explicit formulae for all eigenfunctions.

van Diejen, Jan

N. N. Bogolyubov, A. G. Shumovskaya, A. S. Shumovskiǐ

Martin A. Hallnäs, Edwin Langmann A, Cornelius Paufler

As is well known, there exists a four-parameter family of local interactions in 1D. We interpret these parameters as coupling constants of delta-type interactions which include different kinds of momentum-dependent terms, and determine all cases leading to many-body systems of distinguishable particles which are exactly solvable by the coordinate Bethe ansatz. We find two such families of systems, one with two independent coupling constants deforming the well-known delta-interaction model to non-identical particles, and the other with a particular one-parameter combination of the delta and (the so-called) delta-prime interaction. We also find that the model of non-identical particles gives rise to a somewhat unusual solution of the Yang–Baxter relations. For the other model we write down explicit formulae for all eigenfunctions.