Efficient non-Markovian quantum dynamics using time-evolving matrix product operators

Abstract

In order to model realistic quantum devices it is necessary to simulate quantum systems strongly coupled to their environment. To date, most understanding of open quantum systems is restricted either to weak system–bath couplings or to special cases where specific numerical techniques become effective. Here we present a general and yet exact numerical approach that efficiently describes the time evolution of a quantum system coupled to a non-Markovian harmonic environment. Our method relies on expressing the system state and its propagator as a matrix product state and operator, respectively, and using a singular value decomposition to compress the description of the state as time evolves. We demonstrate the power and flexibility of our approach by numerically identifying the localisation transition of the Ohmic spin-boson model, and considering a model with widely separated environmental timescales arising for a pair of spins embedded in a common environment.

Dressed quantum trajectories: novel approach to the non-Markovian dynamics of open quantum systems on a wide time scale

“…To handle this case efficiently, a more efficient discretization of the delay-time equations is needed. There is a number of options available, including the use of SVD compression for the tensor operations [50].…”

“…the memory function) decays only by the inverse power law [47]. This tail turns out to be important: whenever it is cut off (whether directly after a certain time cut t or indirectly by truncating N t ( )), a revival occurs after a finite time [48][49][50] so that the large-time asymptotical behavior of the observables is corrupted.…”

“…Different algorithms achieve varying degree of success for the specific models and parameter ranges. In particular, the case of the Ohmic bath was treated in [50] by a novel variant of the matrixproduct-states algorithm. This algorithm truncates the bath memory after t cut .…”

Driven quantum dot coupled to a fractional quantum Hall edge

“…[23]. This correspondence proves to be useful for our purposes, since many analytical and numerical techniques have been developed for the spin-boson model including the generalized master equation 31 , stochastic Schrödinger equation description 3 , Bethe-ansatz 32 solution, numerical renormalization group 7,33 , exact mapping between the spin-boson and the Kondo model 10 , and most recently tensor network methods 34,35 .…”

Exact quantum dynamics in structured environments

“…6). Previous studies have shown that spatial correlations in the bath can have a significant effect on population transfer between localized systems [14][15][16]32]. However, these studies focused on the case where the original spectral density J 0 (ω) is much broader than that given in Eq.…”