title: Positive Tensor Network Approach for Simulating Open Quantum Many-Body Systems.
abstract: Open quantum many-body systems play an important role in quantum optics and condensed matter physics, and capture phenomena like transport, the interplay between Hamiltonian and incoherent dynamics, and topological order generated by dissipation. We introduce a versatile and practical method to numerically simulate one-dimensional open quantum many-body dynamics using tensor networks. It is based on representing mixed quantum states in a locally purified form, which guarantees that positivity is preserved at all times. Moreover, the approximation error is controlled with respect to the trace norm. Hence, this scheme overcomes various obstacles of the known numerical open-system evolution schemes. To exemplify the functioning of the approach, we study both stationary states and transient dissipative behavior, for various open quantum systems ranging from few to many bodies.
authors.affiliation: Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany.
authors.forename: A H
authors.initials: AH
authors.lastname: Werner
authors.affiliation: Institute for Complex Quantum Systems & Center for Integrated Quantum Science and Technologies (IQST), Universität Ulm, 89069 Ulm, Germany.|Department of Physics, Colorado School of Mines, Golden, Colorado 80401, USA.
authors.forename: D
authors.initials: D
authors.lastname: Jaschke
authors.affiliation: Institute for Complex Quantum Systems & Center for Integrated Quantum Science and Technologies (IQST), Universität Ulm, 89069 Ulm, Germany.
authors.forename: P
authors.initials: P
authors.lastname: Silvi
authors.affiliation: Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany.
authors.forename: M
authors.initials: M
authors.lastname: Kliesch
authors.affiliation: Institute for Complex Quantum Systems & Center for Integrated Quantum Science and Technologies (IQST), Universität Ulm, 89069 Ulm, Germany.
authors.forename: T
authors.initials: T
authors.lastname: Calarco
authors.affiliation: Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany.
authors.forename: J
authors.initials: J
authors.lastname: Eisert
authors.affiliation: Institute for Complex Quantum Systems & Center for Integrated Quantum Science and Technologies (IQST), Universität Ulm, 89069 Ulm, Germany.
authors.forename: S
authors.initials: S
authors.lastname: Montangero