Finite-Entanglement Scaling of 2D Metals
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866911752837398528 |
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| author | Mortier, Quinten Li, Ming-Hao Haegeman, Jutho Bultinck, Nick |
| author_facet | Mortier, Quinten Li, Ming-Hao Haegeman, Jutho Bultinck, Nick |
| contents | We extend the study of finite-entanglement scaling from one-dimensional gapless models to two-dimensional systems with a Fermi surface. In particular, we show that the entanglement entropy of a contractible spatial region with linear size $L$ scales as $S\sim L\log[ξf(L/ξ)]$ in the optimal tensor network, and hence area-law entangled, state approximation to a metallic state, where $f(x)$ is a scaling function which depends on the shape of the Fermi surface and $ξ$ is a finite correlation length induced by the restricted entanglement. Crucially, the scaling regime can be realized with numerically tractable bond dimensions. We also discuss the implications of the Lieb-Schultz-Mattis theorem at fractional filling for tensor network state approximations of metallic states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_02091 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Finite-Entanglement Scaling of 2D Metals Mortier, Quinten Li, Ming-Hao Haegeman, Jutho Bultinck, Nick Strongly Correlated Electrons Statistical Mechanics We extend the study of finite-entanglement scaling from one-dimensional gapless models to two-dimensional systems with a Fermi surface. In particular, we show that the entanglement entropy of a contractible spatial region with linear size $L$ scales as $S\sim L\log[ξf(L/ξ)]$ in the optimal tensor network, and hence area-law entangled, state approximation to a metallic state, where $f(x)$ is a scaling function which depends on the shape of the Fermi surface and $ξ$ is a finite correlation length induced by the restricted entanglement. Crucially, the scaling regime can be realized with numerically tractable bond dimensions. We also discuss the implications of the Lieb-Schultz-Mattis theorem at fractional filling for tensor network state approximations of metallic states. |
| title | Finite-Entanglement Scaling of 2D Metals |
| topic | Strongly Correlated Electrons Statistical Mechanics |
| url | https://arxiv.org/abs/2305.02091 |