Entanglement transitions in translation-invariant tensor networks
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866909014759047168 |
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| author | Wang, Yi-Cheng Garratt, Samuel J. Altman, Ehud |
| author_facet | Wang, Yi-Cheng Garratt, Samuel J. Altman, Ehud |
| contents | We study the complexity of approximately contracting translation-invariant tensor networks. The computational cost of row-by-row tensor network contraction, which defines a discrete time evolution governed by a fixed transfer matrix, is associated with the entanglement of the state of a row. By analyzing a family of tensor networks whose transfer matrices interpolate between chaotic Floquet and strongly non-unitary limits, we uncover a transition between volume- and area-law entanglement in states evolved under the transfer matrix. We show that deep in the volume-law phase the spectrum of the transfer matrix in the complex plane consists of a dense ring with a sharp outer edge, reminiscent of behavior identified for non-unitary random matrices. At late times an evolving row state therefore has significant contributions from many eigenvectors with nearly degenerate eigenvalue magnitudes. In the area-law phase, there is instead a distinct leading eigenvalue. Our results establish connections between contraction complexity, spectral properties of the transfer matrix, and purification under non-unitary dynamics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_04026 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Entanglement transitions in translation-invariant tensor networks Wang, Yi-Cheng Garratt, Samuel J. Altman, Ehud Quantum Physics Statistical Mechanics We study the complexity of approximately contracting translation-invariant tensor networks. The computational cost of row-by-row tensor network contraction, which defines a discrete time evolution governed by a fixed transfer matrix, is associated with the entanglement of the state of a row. By analyzing a family of tensor networks whose transfer matrices interpolate between chaotic Floquet and strongly non-unitary limits, we uncover a transition between volume- and area-law entanglement in states evolved under the transfer matrix. We show that deep in the volume-law phase the spectrum of the transfer matrix in the complex plane consists of a dense ring with a sharp outer edge, reminiscent of behavior identified for non-unitary random matrices. At late times an evolving row state therefore has significant contributions from many eigenvectors with nearly degenerate eigenvalue magnitudes. In the area-law phase, there is instead a distinct leading eigenvalue. Our results establish connections between contraction complexity, spectral properties of the transfer matrix, and purification under non-unitary dynamics. |
| title | Entanglement transitions in translation-invariant tensor networks |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2605.04026 |