Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm.

By Michael Zwolak, Guifré Vidal. 2004

511 citations recorded by the source corpus.

We present an algorithm to study mixed-state dynamics in one-dimensional quantum lattice systems. The algorithm can be used, e.g., to construct thermal states or to simulate real time evolution given by a generic master equation. Its two main ingredients are (i) a superoperator renormalization scheme to efficiently describe the state of the system and (ii) the time evolving block decimation technique to efficiently update the state during a time evolution. The computational cost of a simulation increases significantly with the amount of correlations between subsystems, but it otherwise depends only linearly on the system size. We present simulations involving quantum spins and fermions in one spatial dimension.

Subfields: Atomic and Molecular Physics, and Optics

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

A literature survey of low‐rank tensor approximation techniques (2013, neutral): “For example, in the study of strongly correlated quantum systems, matrix product operators (MPO) were introduced in [262, 270], which corresponds to representing A in the TT decomposition.”
Time-evolution methods for matrix-product states (2019, methodology): “2004 both for MPS[4, 7, 8] and the original classical DMRG[5, 6].”
Entanglement scaling of operators: a conformal field theory approach, with a glimpse of simulability of long-time dynamics in 1 + 1d (2016, background): “In the past two decades, the way we think about quantum many-body systems, as well as the techniques we use to simulate them, have been revolutionized by Tensor Networks; for reviews, see for instance Refs.”
Cluster mean-field approach to the steady-state phase diagram of dissipative spin systems (2016, methodology): “(1) can be faithfully addressed using a MPO Ansatz for the density matrix [65,66].”
Signatures of Many-Body Localization in a Controlled Open Quantum System (2016, methodology): “We then simulate the time evolution of the quantum Lindblad equation (J2) for system size S = 20 and 30 disorder realizations using the time-evolving block decimation (TEBD) scheme for matrix product operators [51].”
Matrix product simulations of non-equilibrium steady states of quantum spin chains (2008, methodology): “We note that [8] originally proposed the idea of using the MPO for timedependent solutions of the Lindblad master equation; however it was implemented in a physically essentially different context of systems with bulk dissipation where each spin has been monitored by a Lindbladian bath (see also [51”
Quantum simulation with interacting photons (2016, methodology): “In turn for calculating dynamics, Matrix Product State representations of DMRG [193] in form of the TimeEvolving Block Decimation (TEBD) [250, 251, 263] have frequently been applied [110, 107, 95, 128, 198, 225, 202, 25].”