TY  - EJOUR
AU  - Moussa, Adel Ben
AU  - Lamers, Jules
AU  - Serban, Didina
AU  - Toufik, Ayman
TI  - A solvable non-unitary fermionic long-range model with extended symmetry
IS  - DESY-24-051
M1  - PUBDB-2024-01386
M1  - DESY-24-051
M1  - arXiv:2404.10164
PY  - 2024
N1  - 6+23 pages, 3 figs, 1 table
AB  - 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.
KW  - model, integrability (INSPIRE)
KW  - spin, chain (INSPIRE)
KW  - symmetry, translation (INSPIRE)
KW  - algebra, Temperley-Lieb (INSPIRE)
KW  - long-range (INSPIRE)
KW  - statistics (INSPIRE)
KW  - chiral (INSPIRE)
KW  - lattice (INSPIRE)
KW  - dispersion (INSPIRE)
KW  - PT symmetry (INSPIRE)
KW  - one-particle (INSPIRE)
LB  - PUB:(DE-HGF)25
DO  - DOI:10.3204/PUBDB-2024-01386
UR  - https://bib-pubdb1.desy.de/record/605268
ER  -