Speaker
Description
Classical simulation of quantum dynamics from many-body systems with tensor networks is hindered by the exponential growth of entanglement contained at the bonds of a chosen wavefunction factorization (typically Matrix Product States). Modern algorithms try to overcome this entanglement barrier by folding and contracting transversely the network [1], or optimizing schemes to exploit only physical subset of nodes participating in the light cone of local observables [2].
All current proposals are still trying to handle the full entanglement content of the many-body wavefunction. Our target will be the study of thermalization in generic quantum spin chains; in this specific type of evolution, reduced density matrices lose purity and coherence as they converge to the thermal one. At the present stage of our work, we focus on showing that there exists a network predicting local observables for any time which includes insertions that we call decoherers/mixers (equivalent to the disentanglers in MERA). These mixers are structured as 2-spin rotations followed by a total decoherence and a back rotation, and are alternated in the time evolution à la Trotter, emulating a depolarizing channel. We will explain how to optimize them in order to faithfully reproduce the relaxation of local observables, and study the entanglement properties of this auxiliary network, which by construction can be envisioned as a classical stochastic system.
[1] Müller-Hermes, A., Cirac, J. I., & Banuls, M. C. (2012). Tensor network techniques for the computation of dynamical observables in one-dimensional quantum spin systems. New Journal of Physics, 14(7), 075003.
[2] Frías-Pérez, M., & Bañuls, M. C. (2022). Light cone tensor network and time evolution. arXiv preprint arXiv:2201.08402.
