A simple tensor network algorithm for two-dimensional steady states

authored by: Augustine Kshetrimayum, Hendrik Weimer, Román Orús
Abstract: Understanding dissipation in 2D quantum many-body systems is an open challenge which has proven remarkably difficult. Here we show how numerical simulations for this problem are possible by means of a tensor network algorithm that approximates steady states of 2D quantum lattice dissipative systems in the thermodynamic limit. Our method is based on the intuition that strong dissipation kills quantum entanglement before it gets too large to handle. We test its validity by simulating a dissipative quantum Ising model, relevant for dissipative systems of interacting Rydberg atoms, and benchmark our simulations with a variational algorithm based on product and correlated states. Our results support the existence of a first order transition in this model, with no bistable region. We also simulate a dissipative spin 1/2 XYZ model, showing that there is no re-entrance of the ferromagnetic phase. Our method enables the computation of steady states in 2D quantum lattice systems.
Organisation(s): Institute of Theoretical Physics
CRC 1227 Designed Quantum States of Matter (DQ-mat)
External Organisation(s): Johannes Gutenberg University Mainz
Type: Article
Journal: Nature Communications
Volume: 8
ISSN: 2041-1723
Publication date: 03.11.2017
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: General Chemistry, General Biochemistry,Genetics and Molecular Biology, General Physics and Astronomy
Electronic version(s): https://doi.org/10.1038/s41467-017-01511-6 (Access: Open)

BibTeX

@article{18c1f86eb68445959ae78f6016bb3238,
title = "A simple tensor network algorithm for two-dimensional steady states",
abstract = "Understanding dissipation in 2D quantum many-body systems is an open challenge which has proven remarkably difficult. Here we show how numerical simulations for this problem are possible by means of a tensor network algorithm that approximates steady states of 2D quantum lattice dissipative systems in the thermodynamic limit. Our method is based on the intuition that strong dissipation kills quantum entanglement before it gets too large to handle. We test its validity by simulating a dissipative quantum Ising model, relevant for dissipative systems of interacting Rydberg atoms, and benchmark our simulations with a variational algorithm based on product and correlated states. Our results support the existence of a first order transition in this model, with no bistable region. We also simulate a dissipative spin 1/2 XYZ model, showing that there is no re-entrance of the ferromagnetic phase. Our method enables the computation of steady states in 2D quantum lattice systems.",
author = "Augustine Kshetrimayum and Hendrik Weimer and Rom{\'a}n Or{\'u}s",
note = "Funding information: A.K. and R.O. acknowledge JGU, DFG GZ OR 381/1-1, DFG GZ OR 381/3-1, and discussions with I. McCulloch, A. Gangat, Y.-Jer Kao, M. Rizzi, D. Porras, J. Eisert, J. J. Garc{\'i}a-Ripoll, and C. Ciuti. H.W. acknowledges the Volkswagen Foundation, DFG SFB 1227 (DQ-mat) and SPP 1929 (GiRyd).",
year = "2017",
month = nov,
day = "3",
doi = "10.1038/s41467-017-01511-6",
language = "English",
volume = "8",
journal = "Nature Communications",
issn = "2041-1723",
publisher = "Nature Publishing Group",
}