Automatic differentiation applied to excitations with Projected Entangled Pair States

Abstract

The excitation ansatz for tensor networks is a powerful tool for simulating the low-lying quasiparticle excitations above ground states of strongly correlated quantum many-body systems. Recently, the two-dimensional tensor network class of infinite entangled pair states gained new ground state optimization methods based on automatic differentiation, which are at the same time highly accurate and simple to implement. Naturally, the question arises whether these new ideas can also be used to optimize the excitation ansatz, which has recently been implemented in two dimensions as well. In this paper, we describe a straightforward way to reimplement the framework for excitations using automatic differentiation, and demonstrate its performance for the Hubbard model at half filling.

26 pages, 5 figures

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• The Cytnx Library for Tensor Networks
• Interacting Dirac magnons in the van der Waals ferromagnet CrBr${}_3$
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• Single-layer framework of variational tensor network states
• Dispersion Relations in Two- and Three-Dimensional Quantum Systems
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• Dynamical Spectral Function of the Kagome Quantum Spin Liquid
• Itinerant magnetism in the triangular lattice Hubbard model at half-doping: Application to twisted transition-metal dichalcogenides