2018

mpnum
Magnetic field fluctuations analysis for the ion trap implementation of the quantum Rabi model in the deep strong coupling regime – R. Puebla, J. Casanova, and M. B. Plenio,
J. Mod. Opt. (Special Issue: Quantum optics, cooling and collisions of ions and atoms), 603-611 (2017) | ArXiv

Probabilistic low-rank factorization accelerates tensor network simulations of critical quantum many-body ground statesProbabilistic low-rank factorization accelerates tensor network simulations of critical quantum many-body ground states – L. Kohn, F. Tschirsich, M. Keck, M. B. Plenio, D. Tamascelli, and S. Montangero, Physical Review E, 97, 013301 (2018) | ArXiv
DOI:https://doi.org/10.1103/PhysRevE.97.013301
The gist of it

Tensor Networks(TN) methods are indispensable tools in simulating quantum and classical many-body problems by providing an efficient parametrization of the wave function in the many-body phase space. In order to find such efficient parametrization, truncated Singular Value Decomposition (SVD) is widely used to compress states into their respective TN manifold. The SVD lies therefore at the heart of many TN methods, but also represents the most time-consuming part of a wide class of TN algorithms.

In this work we demonstrate that a randomized version of SVD (RSVD), which was proven to reduce the complexity of the Time-Evolving-Block-Decimation TN algorithm [D. Tamascelli, R. Rosenbach, and M. B. Plenio, Physical Review E 91, 063306 (2015)], can be applied to a relevant class of many-body systems, namely systems undergoing a quantum phase transition. Such regime is much more challenging regime since long-range correlations are building up and risk to compromise the effectiveness of the RSVD compression. We provide evidence that RSVD delivers the same accuracy as standard SVD routines with speed-up that can go up to 24 times. We show that the accuracy of the results is not influenced by the speedups and discuss the impact of techniques typical for TN studies.