The q-deformed Haldane-Shastry chain at q=i with even length
Adel Ben Moussa, Jules Lamers, Didina Serban
TL;DR
This paper explores the properties of a long-range fermionic chain model at a special quantum deformation point, revealing unique algebraic structures and differences between even and odd system sizes.
Contribution
It extends previous work on the q=i Haldane-Shastry chain to even-length systems, uncovering nilpotent conserved charges and Jordan block structures.
Findings
Conserved charges are nilpotent for even N.
Presence of Jordan blocks in the algebraic structure.
Differences between even and odd N cases.
Abstract
In this note we announce some results extending our recent work with A. Toufik on the free-fermion point q=i of the Haldane-Shastry chain to the case with an even number N of sites. The resulting long-range version of the Heisenberg XX chain may be viewed as a model of fermions with extended gl(1|1) symmetry. Unlike for odd N, the conserved charges are nilpotent and exhibit Jordan blocks.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.