Time evolution of matrix product operators with energy conservation

Christian B. Mendl

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arXiv · 1812.11876

Time evolution of matrix product operators with energy conservation

Christian B. Mendl

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Abstract

We devise a numerical scheme for the time evolution of matrix product operators by adapting the time-dependent variational principle for matrix product states [J. Haegeman et al, Phys. Rev. B 94, 165116 (2016)]. A simple augmentation of the initial operator $\mathcal{O}$ by the Hamiltonian $H$ helps to conserve the average energy $\mathrm{tr}[H \mathcal{O}(t)]$ in the numerical scheme and increases the overall precision. As demonstration, we apply the improved method to a random operator on a small one-dimensional lattice, using the spin-1 Heisenberg XXZ model Hamiltonian; we observe that the augmentation reduces the trace-distance to the numerically exact time-evolved operator by a factor of 10, at the same computational cost.

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Christian B. Mendl. 2018-12-31. Time evolution of matrix product operators with energy conservation. https://arxiv.org/abs/1812.11876

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