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@ARTICLE{Moussa:605268,
      author       = {Moussa, Adel Ben and Lamers, Jules and Serban, Didina and
                      Toufik, Ayman},
      title        = {{A} solvable non-unitary fermionic long-range model with
                      extended symmetry},
      reportid     = {PUBDB-2024-01386, DESY-24-051. arXiv:2404.10164},
      year         = {2024},
      note         = {6+23 pages, 3 figs, 1 table},
      abstract     = {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 $\mathfrak{gl}(1|1)$ 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.},
      keywords     = {model, integrability (INSPIRE) / spin, chain (INSPIRE) /
                      symmetry, translation (INSPIRE) / algebra, Temperley-Lieb
                      (INSPIRE) / long-range (INSPIRE) / statistics (INSPIRE) /
                      chiral (INSPIRE) / lattice (INSPIRE) / dispersion (INSPIRE)
                      / PT symmetry (INSPIRE) / one-particle (INSPIRE)},
      cin          = {T},
      cid          = {I:(DE-H253)T-20120731},
      pnm          = {611 - Fundamental Particles and Forces (POF4-611) /
                      BrokenSymmetries - Exact Results from Broken Symmetries
                      (101044226)},
      pid          = {G:(DE-HGF)POF4-611 / G:(EU-Grant)101044226},
      experiment   = {EXP:(DE-MLZ)NOSPEC-20140101},
      typ          = {PUB:(DE-HGF)25},
      eprint       = {2404.10164},
      howpublished = {arXiv:2404.10164},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2404.10164;\%\%$},
      doi          = {10.3204/PUBDB-2024-01386},
      url          = {https://bib-pubdb1.desy.de/record/605268},
}