Diagrammatic Monte Carlo for Fermionic Rényi Entanglement Entropy
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918515634601984 |
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| author | Shi, Boyuan |
| author_facet | Shi, Boyuan |
| contents | We develop a direct diagrammatic Monte Carlo framework for the Renyi entanglement entropy of interacting lattice fermions. The method starts from the fermionic graded-swap representation of Z_n[A]=Tr_Aρ_A^n, which converts the entropy problem into a replicated path integral with mixed temporal boundary conditions on the entangling region. In this representation the replica momenta are half-shifted, q_m=(2m+1)π/n, and the interaction expansion has a determinant form suitable for connected-determinant summation. We combine this expansion with a many-configuration Markov-chain Monte Carlo sampler to obtain order-by-order corrections for very large systems to very high orders. As a benchmark, we compare the order-by-order coefficients of a 3*3 Hubbard cluster with exact diagonalization. We then report a production calculation for a large periodic lattice with a square subregions. The dominant system-size limitation is therefore memory rather than a conventional auxiliary-field sign problem. The results provide a step toward diagrammatic calculations of fermionic entanglement observables in regimes where direct quantum Monte Carlo sampling is costly or sign-problem limited. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_21632 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Diagrammatic Monte Carlo for Fermionic Rényi Entanglement Entropy Shi, Boyuan Strongly Correlated Electrons Computational Physics We develop a direct diagrammatic Monte Carlo framework for the Renyi entanglement entropy of interacting lattice fermions. The method starts from the fermionic graded-swap representation of Z_n[A]=Tr_Aρ_A^n, which converts the entropy problem into a replicated path integral with mixed temporal boundary conditions on the entangling region. In this representation the replica momenta are half-shifted, q_m=(2m+1)π/n, and the interaction expansion has a determinant form suitable for connected-determinant summation. We combine this expansion with a many-configuration Markov-chain Monte Carlo sampler to obtain order-by-order corrections for very large systems to very high orders. As a benchmark, we compare the order-by-order coefficients of a 3*3 Hubbard cluster with exact diagonalization. We then report a production calculation for a large periodic lattice with a square subregions. The dominant system-size limitation is therefore memory rather than a conventional auxiliary-field sign problem. The results provide a step toward diagrammatic calculations of fermionic entanglement observables in regimes where direct quantum Monte Carlo sampling is costly or sign-problem limited. |
| title | Diagrammatic Monte Carlo for Fermionic Rényi Entanglement Entropy |
| topic | Strongly Correlated Electrons Computational Physics |
| url | https://arxiv.org/abs/2605.21632 |