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• W4386316813 abstract "The complexity of quantum many-body systems is manifested in the vast diversity of their correlations, making it challenging to distinguish the generic from the atypical features. This can be addressed by analyzing correlations through ensembles of random states, chosen to faithfully embody the relevant physical properties. Here, we focus on spins with local interactions, whose correlations are extremely well captured by tensor network states. Adopting an operational perspective, we define ensembles of random tensor network states in one and two spatial dimensions that admit a sequential generation. As such, they directly correspond to outputs of quantum circuits with a sequential architecture and random gates. In one spatial dimension, the ensemble explores the entire family of matrix product states, while in two spatial dimensions, it corresponds to random isometric tensor network states. We extract the scaling behavior of the average correlations between two subsystems as a function of their distance. Using elementary concentration results, we then deduce the typical case for measures of correlation such as the von Neumann mutual information and a measure arising from the Hilbert-Schmidt norm. We find for all considered cases that the typical behavior is an exponential decay (for both one and two spatial dimensions). We observe the consistent emergence of a correlation length that depends only on the underlying spatial dimension and not the considered measure. Remarkably, increasing the bond dimension leads to a higher correlation length in one spatial dimension but has the opposite effect in two spatial dimensions.Received 23 January 2023Revised 1 July 2023Accepted 20 July 2023DOI:https://doi.org/10.1103/PRXQuantum.4.030330Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum correlations in quantum informationQuantum entanglementQuantum information theoryTechniquesMatrix product statesProjected entangled pair statesTensor network methodsTransfer matrix calculationsQuantum InformationCondensed Matter, Materials & Applied PhysicsStatistical Physics" @default.
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• W4386316813 date "2023-08-31" @default.
• W4386316813 modified "2023-10-04" @default.
• W4386316813 title "Typical Correlation Length of Sequentially Generated Tensor Network States" @default.
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• W4386316813 doi "https://doi.org/10.1103/prxquantum.4.030330" @default.
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