Entanglement Hamiltonian and orthogonal polynomials
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866908623554215936 |
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| author | Bernard, Pierre-Antoine Bonsignori, Riccarda Eisler, Viktor Parez, Gilles Vinet, Luc |
| author_facet | Bernard, Pierre-Antoine Bonsignori, Riccarda Eisler, Viktor Parez, Gilles Vinet, Luc |
| contents | We study the entanglement Hamiltonian for free-fermion chains with a particular form of inhomogeneity. The hopping amplitudes and chemical potentials are chosen such that the single-particle eigenstates are related to discrete orthogonal polynomials of the Askey scheme. Due to the bispectral properties of these functions, one can construct an operator which commutes exactly with the entanglement Hamiltonian and corresponds to a linear or parabolic deformation of the physical one. We show that this deformation is interpreted as a local inverse temperature and can be obtained in the continuum limit via methods of conformal field theory. Using this prediction, the properly rescaled eigenvalues of the commuting operator are found to provide a very good approximation of the entanglement spectrum and entropy. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_12021 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Entanglement Hamiltonian and orthogonal polynomials Bernard, Pierre-Antoine Bonsignori, Riccarda Eisler, Viktor Parez, Gilles Vinet, Luc Statistical Mechanics High Energy Physics - Theory Mathematical Physics Quantum Physics We study the entanglement Hamiltonian for free-fermion chains with a particular form of inhomogeneity. The hopping amplitudes and chemical potentials are chosen such that the single-particle eigenstates are related to discrete orthogonal polynomials of the Askey scheme. Due to the bispectral properties of these functions, one can construct an operator which commutes exactly with the entanglement Hamiltonian and corresponds to a linear or parabolic deformation of the physical one. We show that this deformation is interpreted as a local inverse temperature and can be obtained in the continuum limit via methods of conformal field theory. Using this prediction, the properly rescaled eigenvalues of the commuting operator are found to provide a very good approximation of the entanglement spectrum and entropy. |
| title | Entanglement Hamiltonian and orthogonal polynomials |
| topic | Statistical Mechanics High Energy Physics - Theory Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2412.12021 |