Preprint

PUBDB-2024-01386

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png A solvable non-unitary fermionic long-range model with extended symmetry

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

2024

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Please use a persistent id in citations: doi:10.3204/PUBDB-2024-01386

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 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.

Keyword(s): model, integrability ; spin, chain ; symmetry, translation ; algebra, Temperley-Lieb ; long-range ; statistics ; chiral ; lattice ; dispersion ; PT symmetry ; one-particle

Note: 6+23 pages, 3 figs, 1 table

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Contributing Institute(s):

1. Theorie-Gruppe (T)

Research Program(s):

1. 611 - Fundamental Particles and Forces (POF4-611) (POF4-611)
2. BrokenSymmetries - Exact Results from Broken Symmetries (101044226) (101044226)

Experiment(s):

1. No specific instrument

Appears in the scientific report 2024

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Database coverage:

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