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Entanglement and its relation to energy variance for local one-dimensional Hamiltonians

Author(s): Banuls, Mari Carmen; Huse, David A; Cirac, J Ignacio

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Abstract: We explore the relation between the entanglement of a pure state and its energy variance for a local one-dimensional Hamiltonian, as the system size increases. In particular, we introduce a construction which creates a matrix product state of arbitrarily small energy variance delta(2) for N spins, with bond dimension scaling as root ND01/delta, where D-0 > 1 is a constant. This implies that a polynomially increasing bond dimension is enough to construct states with energy variance that vanishes with the inverse of the logarithm of the system size. We run numerical simulations to probe the construction on two different models and compare the local reduced density matrices of the resulting states to the corresponding thermal equilibrium. Our results suggest that the spatially homogeneous states with logarithmically decreasing variance, which can be constructed efficiently, do converge to the thermal equilibrium in the thermodynamic limit, while the same is not true if the variance remains constant.
Publication Date: 1-Apr-2020
Electronic Publication Date: 28-Apr-2020
Citation: Banuls, Mari Carmen, Huse, David A, Cirac, J Ignacio. (2020). Entanglement and its relation to energy variance for local one-dimensional Hamiltonians. PHYSICAL REVIEW B, 101 (10.1103/PhysRevB.101.144305
DOI: doi:10.1103/PhysRevB.101.144305
ISSN: 2469-9950
EISSN: 2469-9969
Type of Material: Journal Article
Journal/Proceeding Title: PHYSICAL REVIEW B
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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