Extracting the Speed of Light from Matrix Product States
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866917568303857664 |
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| author | Eberharter, Alexander A. Vanderstraeten, Laurens Verstraete, Frank Läuchli, Andreas M. |
| author_facet | Eberharter, Alexander A. Vanderstraeten, Laurens Verstraete, Frank Läuchli, Andreas M. |
| contents | We provide evidence that the spectrum of the local effective Hamiltonian and the transfer operator in infinite-system matrix product state simulations are identical up to a global rescaling factor, i.e.~the speed of light of the system, when the underlying system is described by a 1+1 dimensional CFT. We provide arguments for this correspondence based on a path integral point of view. This observation turns out to yield very precise estimates for the speed of light in practice, confirming exact results to high precision where available, but also allowing us to finally determine the speed of light of the non-integrable, critical $SU(2)$ Heisenberg chains with half-integer spin $S>1/2$ with unprecedented accuracy. We also show that the same technology applied to doped Hubbard ladders provides highly accurate velocities for a range of dopings. Combined with measurements of compressibilities we present new results for the Luttinger liquid parameter in the Luther-Emery regime of doped Hubbard ladders, outperforming earlier approaches based on the fitting of real-space correlation functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_00663 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Extracting the Speed of Light from Matrix Product States Eberharter, Alexander A. Vanderstraeten, Laurens Verstraete, Frank Läuchli, Andreas M. Strongly Correlated Electrons Quantum Gases High Energy Physics - Theory We provide evidence that the spectrum of the local effective Hamiltonian and the transfer operator in infinite-system matrix product state simulations are identical up to a global rescaling factor, i.e.~the speed of light of the system, when the underlying system is described by a 1+1 dimensional CFT. We provide arguments for this correspondence based on a path integral point of view. This observation turns out to yield very precise estimates for the speed of light in practice, confirming exact results to high precision where available, but also allowing us to finally determine the speed of light of the non-integrable, critical $SU(2)$ Heisenberg chains with half-integer spin $S>1/2$ with unprecedented accuracy. We also show that the same technology applied to doped Hubbard ladders provides highly accurate velocities for a range of dopings. Combined with measurements of compressibilities we present new results for the Luttinger liquid parameter in the Luther-Emery regime of doped Hubbard ladders, outperforming earlier approaches based on the fitting of real-space correlation functions. |
| title | Extracting the Speed of Light from Matrix Product States |
| topic | Strongly Correlated Electrons Quantum Gases High Energy Physics - Theory |
| url | https://arxiv.org/abs/2303.00663 |