%0 Electronic Article
%A Moussa, Adel Ben
%A Lamers, Jules
%A Serban, Didina
%A Toufik, Ayman
%T A solvable non-unitary fermionic long-range model with extended symmetry
%N DESY-24-051
%M PUBDB-2024-01386
%M DESY-24-051
%M arXiv:2404.10164
%D 2024
%Z 6+23 pages, 3 figs, 1 table
%X 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 simple realisation via non-unitary fermions, based on the free-fermion Temperley-Lieb algebra, and may also be viewed as an alternating \mathfrakgl(1|1) spin chain. Even and odd length behave very differently; we focus on odd length. The model is integrable, and we explicitly identify two commuting hamiltonians. While non-unitary, their spectrum is real by PT-symmetry. One hamiltonian is chiral and quadratic in fermions, while the other is parity-invariant and quartic. Their one-particle spectra have two linear branches, realising a massless relativistic dispersion on the lattice. The appropriate fermionic modes arise from 'quasi-translation' symmetry, which replaces ordinary translation symmetry. The model exhibits exclusion statistics, like for the isotropic HS chain, with even more 'extended symmetry' and larger degeneracies.
%K model, integrability (INSPIRE)
%K spin, chain (INSPIRE)
%K symmetry, translation (INSPIRE)
%K algebra, Temperley-Lieb (INSPIRE)
%K long-range (INSPIRE)
%K statistics (INSPIRE)
%K chiral (INSPIRE)
%K lattice (INSPIRE)
%K dispersion (INSPIRE)
%K PT symmetry (INSPIRE)
%K one-particle (INSPIRE)
%F PUB:(DE-HGF)25
%9 Preprint
%R 10.3204/PUBDB-2024-01386
%U https://bib-pubdb1.desy.de/record/605268