A solvable non-unitary fermionic long-range model with extended symmetry
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916643459825664 |
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| author | Moussa, Adel Ben Lamers, Jules Serban, Didina Toufik, Ayman |
| author_facet | Moussa, Adel Ben Lamers, Jules Serban, Didina Toufik, Ayman |
| contents | 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 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 the isotropic HS chain, with even more 'extended symmetry' and larger degeneracies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10164 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A solvable non-unitary fermionic long-range model with extended symmetry Moussa, Adel Ben Lamers, Jules Serban, Didina Toufik, Ayman Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems 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 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 the isotropic HS chain, with even more 'extended symmetry' and larger degeneracies. |
| title | A solvable non-unitary fermionic long-range model with extended symmetry |
| topic | Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2404.10164 |