Time evolution of an infinite projected entangled pair state: a gradient tensor update in the tangent space

• URL: http://arxiv.org/abs/2205.11067v3
• Date: Mon, 11 Jul 2022 15:03:07 GMT
• Title: Time evolution of an infinite projected entangled pair state: a gradient tensor update in the tangent space
• Authors: Jacek Dziarmaga
• Abstract summary: Suzuki-Trotter decomposition applied to infinite projected entangled pair state (iPEPS) This paper goes beyond simplified error measures -- like the one used in the full update (FU) It directly maximizes an overlap between the exact iPEPS with the increased bond dimension and the new iPEPS with the truncated one.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Time evolution of an infinite 2D many body quantum lattice system can be described by the Suzuki-Trotter decomposition applied to the infinite projected entangled pair state (iPEPS). Each Trotter gate increases the bond dimension of the tensor network, $D$, that has to be truncated back in a way that minimizes a suitable error measure. This paper goes beyond simplified error measures -- like the one used in the full update (FU), the simple update (SU), and their intermediate neighborhood tensor update (NTU) -- and directly maximizes an overlap between the exact iPEPS with the increased bond dimension and the new iPEPS with the truncated one. The optimization is performed in a tangent space of the iPEPS variational manifold. This gradient tensor update (GTU) is benchmarked by a simulation of a sudden quench of a transverse field in the 2D quantum Ising model and the quantum Kibble-Zurek mechanism in the same 2D system.

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