Constructing a Matrix Product Operator for the time evolution operator

Ian McCulloch^1*, Laurens Vanderstraeten², Jutho Haegeman², Maarten Van Damme²

¹Department of Physics, NTHU, Hsinichu, Taiwan
²Department of Physics and Astronomy, University of Ghent, Ghent, Belgium

* Presenter:Ian McCulloch, email:ian@phys.nthu.edu.tw

Simulating the real or imaginary time evolution of a quantum state using tensor networks requires constructing a representation of the time evolution operator, which can only be done approximately (except in some trivial cases). As an alternative to the common Trotter-Suzuki decomposition, we look at constructing directly a Matrix Product Operator representation of the exponential function[1], which has some advantages over other methods. In recent work, this extends quite naturally to the case where the Hamiltonian is time-dependent. Some examples will be presented for calculating spectral functions, and non-equilibrium driven systems.

[1] https://arxiv.org/abs/2302.14181 (to appear in SciPost Physics)

Keywords: tensor network, time evolution, matrix product states