Parent Hamiltonian Construction of Generalized Calogero-Sutherland Models
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908959661621248 |
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| author | Borutta, Hari Feuerpfeil, Andreas Iqbal, Yasir |
| author_facet | Borutta, Hari Feuerpfeil, Andreas Iqbal, Yasir |
| contents | The Calogero-Sutherland model is a paradigmatic integrable system describing one-dimensional non-relativistic particles with inverse-square interactions. At interaction strength $λ=2$, the CSM exhibits a deep connection to anyon physics, featuring the Laughlin-Jastrow polynomial as its exact ground state. Motivated by this structure, we develop a general reverse-engineering construction of positive semi-definite continuum parent Hamiltonians for trial states admitting a rational conformal field theory description with central charge $c<1$. By leveraging the null-vector structure of the underlying primary fields and the associated Belavin-Polyakov-Zamolodchikov equations, we derive corresponding many-body annihilation operators. We then apply this construction explicitly to the Moore-Read and $k=3$ Read-Rezayi states - relating to Ising and Fibonacci anyons, respectively - obtaining continuum Hamiltonians for which these Jack-polynomial states are exact zero modes. We emphasize, however, that our construction does not by itself establish ground-state uniqueness or determine the nature of the excitation spectrum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_11074 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Parent Hamiltonian Construction of Generalized Calogero-Sutherland Models Borutta, Hari Feuerpfeil, Andreas Iqbal, Yasir Strongly Correlated Electrons Other Condensed Matter Mathematical Physics The Calogero-Sutherland model is a paradigmatic integrable system describing one-dimensional non-relativistic particles with inverse-square interactions. At interaction strength $λ=2$, the CSM exhibits a deep connection to anyon physics, featuring the Laughlin-Jastrow polynomial as its exact ground state. Motivated by this structure, we develop a general reverse-engineering construction of positive semi-definite continuum parent Hamiltonians for trial states admitting a rational conformal field theory description with central charge $c<1$. By leveraging the null-vector structure of the underlying primary fields and the associated Belavin-Polyakov-Zamolodchikov equations, we derive corresponding many-body annihilation operators. We then apply this construction explicitly to the Moore-Read and $k=3$ Read-Rezayi states - relating to Ising and Fibonacci anyons, respectively - obtaining continuum Hamiltonians for which these Jack-polynomial states are exact zero modes. We emphasize, however, that our construction does not by itself establish ground-state uniqueness or determine the nature of the excitation spectrum. |
| title | Parent Hamiltonian Construction of Generalized Calogero-Sutherland Models |
| topic | Strongly Correlated Electrons Other Condensed Matter Mathematical Physics |
| url | https://arxiv.org/abs/2604.11074 |