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000639395 0247_ $$2ISSN$$a1079-7114
000639395 0247_ $$2arXiv$$aarXiv:2404.10164
000639395 0247_ $$2datacite_doi$$a10.3204/PUBDB-2025-04489
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000639395 1001_ $$0P:(DE-HGF)0$$aMoussa, Adel Ben$$b0
000639395 245__ $$aSolvable Nonunitary Fermionic Long-Range Model with Extended Symmetry
000639395 260__ $$aCollege Park, Md.$$bAPS$$c2025
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000639395 500__ $$aPhys 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
000639395 520__ $$aWe define and study a long-range version of the xx model, arising as the free-fermion point of the xxz-type Haldane-Shastry (HS) chain. It has a description via nonunitary fermions, based on the free-fermion Temperley-Lieb algebra, and may also be viewed as an alternating gl(1|1) spin chain. Even and odd lengths behave very differently; we focus on odd length. The model is integrable, and we explicitly identify two commuting Hamiltonians. While nonunitary, their spectrum is real by PT symmetry. One Hamiltonian is chiral and quadratic in fermions, while the other is parity invariant and quartic. Their one-particle spectra have two linear branches, realizing a massless relativistic dispersion on the lattice. The appropriate fermionic modes arise from “quasi-translation” symmetry, which replaces ordinary translation symmetry. The model exhibits exclusion statistics, like the isotropic HS chain, with even more “extended symmetry” and larger degeneracies.
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000639395 536__ $$0G:(EU-Grant)101044226$$aBrokenSymmetries - Exact Results from Broken Symmetries (101044226)$$c101044226$$fERC-2021-COG$$x1
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000639395 650_7 $$2INSPIRE$$amodel: integrability
000639395 650_7 $$2INSPIRE$$aspin: chain
000639395 650_7 $$2INSPIRE$$aalgebra: Temperley-Lieb
000639395 650_7 $$2INSPIRE$$along-range
000639395 650_7 $$2INSPIRE$$achiral
000639395 650_7 $$2INSPIRE$$alattice
000639395 650_7 $$2INSPIRE$$aPT symmetry
000639395 650_7 $$2INSPIRE$$aXXZ model
000639395 650_7 $$2INSPIRE$$aGL(1|1)
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000639395 7001_ $$0P:(DE-H253)PIP1028527$$aLamers, Jules$$b1$$eCorresponding author
000639395 7001_ $$0P:(DE-HGF)0$$aSerban, Didina$$b2
000639395 7001_ $$0P:(DE-HGF)0$$aToufik, Ayman$$b3
000639395 773__ $$0PERI:(DE-600)1472655-5$$a10.1103/PhysRevLett.134.046503$$gVol. 134, no. 4, p. 046503$$n4$$p046503$$tPhysical review letters$$v134$$x0031-9007$$y2025
000639395 7870_ $$0PUBDB-2024-01386$$aMoussa, Adel Ben et.al.$$d2024$$iIsParent$$rDESY-24-051 ; arXiv:2404.10164$$tA solvable non-unitary fermionic long-range model with extended symmetry
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