Solvable Nonunitary Fermionic Long-Range Model with Extended Symmetry.

We define and study a long-range version of the xx model, arising as the free-fermion point of the xxz-type Haldane-Shastry (HS) chain. It has a description via nonunitary fermions, based on the free-fermion Temperley-Lieb algebra, and may also be viewed as an alternating gl(1|1) spin chain. Even and odd lengths behave very differently; we focus on odd length.