Effective short distance interaction in Calogero-Sutherland quantum fluids
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915088558981120 |
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| author | Bottesi, Federico L. Zemba, Guillermo R. |
| author_facet | Bottesi, Federico L. Zemba, Guillermo R. |
| contents | We consider the effective conformal field theory with symmetry W-infinity x W-infinity that describes the thermodynamic limit of the Calogero-Sutherland model. In the repulsive regime of the free fermion formulation, we identify an attractive interaction between opposite moving particle-hole pairs that dominates the short distance behavior and that is proposed as responsible for the destabilization of the ground state, leading to a new one of bosonic nature. The process is described by a Bogoliubov transformation of the free fermion bilinear operators into bosonic ones, preserving the form of the W-infinity algebra but decoupling the opposite chirality terms in the hamiltonian, as expected in the low energy limit. In coordinate space this interaction has a short range component that arises due to the quantum regularization of the theory. The described dynamical process may be considered as a mechanism of the emergence of the known charge and quantum statistics fractionalization of the low lying excitations of the theory, as predicted in both first and second quantization studies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_03153 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Effective short distance interaction in Calogero-Sutherland quantum fluids Bottesi, Federico L. Zemba, Guillermo R. High Energy Physics - Theory Mesoscale and Nanoscale Physics Mathematical Physics We consider the effective conformal field theory with symmetry W-infinity x W-infinity that describes the thermodynamic limit of the Calogero-Sutherland model. In the repulsive regime of the free fermion formulation, we identify an attractive interaction between opposite moving particle-hole pairs that dominates the short distance behavior and that is proposed as responsible for the destabilization of the ground state, leading to a new one of bosonic nature. The process is described by a Bogoliubov transformation of the free fermion bilinear operators into bosonic ones, preserving the form of the W-infinity algebra but decoupling the opposite chirality terms in the hamiltonian, as expected in the low energy limit. In coordinate space this interaction has a short range component that arises due to the quantum regularization of the theory. The described dynamical process may be considered as a mechanism of the emergence of the known charge and quantum statistics fractionalization of the low lying excitations of the theory, as predicted in both first and second quantization studies. |
| title | Effective short distance interaction in Calogero-Sutherland quantum fluids |
| topic | High Energy Physics - Theory Mesoscale and Nanoscale Physics Mathematical Physics |
| url | https://arxiv.org/abs/2406.03153 |