ON-LINE TensorTalk: Daniel Stilck França

Speaker: Daniel Stilck França

Title: Going to the boundary of the tensor network manifold

Abstract: Tensor network states are the variational ansatz class in the background of state of the art approaches for the study of quantum many-body systems, both analytically and numerically. However, somewhat surprisingly, the manifold of tensor network states of a given bond dimension is not closed in general.

Recent work has shown that considering states on the boundary of the manifold can yield more efficient representations for states of physical interest, but it remained unclear how to systematically find and optimize over such representations. We address this issue and define a new ansatz class of states that includes those at the boundary of tensor network states of a given bond dimension.

We show how to efficiently optimize over this class in order to find ground states of local Hamiltonians by only slightly modifying standard algorithms and code.

This is based on joint work with Matthias Christandl, Fulvio Gesmundo and Albert H. Werner.

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