Entanglement transitions in translation-invariant tensor networks

• URL: http://arxiv.org/abs/2605.04026v1
• Date: Tue, 05 May 2026 17:50:38 GMT
• Title: Entanglement transitions in translation-invariant tensor networks
• Abstract summary: The computational cost of row-by-row tensor network contraction is associated with the entanglement of the state of a row.<n>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.<n>Our results establish connections between contraction complexity, spectral properties of the transfer matrix, and purification under non-unitary dynamics.
• Score: 6.763845362393166
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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