Solvable Nonunitary Fermionic Long-Range Model with Extended Symmetry

Moussa, Adel Ben; Serban, Didina; Lamers, Jules; Toufik, Ayman

doi:10.1103/PhysRevLett.134.046503

Journal Article

PUBDB-2025-04489

Solvable Nonunitary Fermionic Long-Range Model with Extended Symmetry

Moussa, A. B. ; Lamers, J. (Corresponding author)DESY* ; Serban, D. ; Toufik, A.

2025
APS College Park, Md.

Physical review letters 134(4), 046503 (2025) [10.1103/PhysRevLett.134.046503]

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Please use a persistent id in citations: doi:10.1103/PhysRevLett.134.046503 doi:10.3204/PUBDB-2025-04489

Report No.: DESY-24-051; arXiv:2404.10164

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 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. The model is integrable, and we explicitly identify two commuting Hamiltonians. While nonunitary, 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, realizing 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 the isotropic HS chain, with even more “extended symmetry” and larger degeneracies.

Keyword(s): model: integrability ; spin: chain ; algebra: Temperley-Lieb ; long-range ; chiral ; lattice ; PT symmetry ; XXZ model ; GL(1|1)

Classification:

ddc:530

Note: Phys Rev Lett 134 (2025) 046503. v1: 6+23 pages, 3 figs, 1 table. v2: various minor improvements; 6+27 pages, 1+3 figs, 1 table. v3: further impovements, 6+28 pages, 1+3 figs, 1 table. v4: accepted for publication

Contributing Institute(s):

Theorie-Gruppe (T)

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Experiment(s):

No specific instrument

Appears in the scientific report 2025

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Medline

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