Real-time evolution using the density matrix renormalization group.

By S. White, Adrian E. Feiguin. Physical Review Letters, 2004

936 citations recorded by the source corpus.

We describe an extension to the density matrix renormalization group method incorporating real-time evolution. Its application to transport problems in systems out of equilibrium and frequency dependent correlation functions is discussed and illustrated in several examples. We simulate a scattering process in a spin chain which generates a spatially nonlocal entangled wave function.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/a3a48b846b55954cfa2261742adf7f87c6ec3fe3

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

Citations in the corpus

The Hubbard Model (2021, methodology): “DMRG methods have recently been extended and are beginning to be applied to study dynamical properties of ladders and cylinders (85, 86).”
Hand-waving and interpretive dance: an introductory course on tensor networks (2016, methodology): “Although the algorithms we discuss here are designed for finding MPS ground states, they can be adaped to simulate time evolution [49, 50], find Gibbs states [51], or optimise other operators acting on a statespace of interest [52].”
Ultrafast optical spectroscopy of strongly correlated materials and high-temperature superconductors: a non-equilibrium approach (2016, methodology): “On the other hand, we will not discuss in any details many other approaches and ideas that have been proposed to study strongly correlated systems out of equilibrium, including for example exact diagonalization and density-matrix renormalization group (DMRG)[520, 521], quantum versions of classical ”
The density-matrix renormalization group (2004, background): “…now reached complete formal equivalence between the description of a pure state and a mixed state, such that the time-evolving block decimation algorithm sVidal, 2003, 2004d or its DMRG incarnation sDaley et al., 2004; White and Feiguin, 2004d can be applied to the time evolution of this state.”
Quantum quenches in 1 + 1 dimensional conformal field theories (2016, background): “The linear growth of the entanglement entropy in time is also a very important physical phenomenon to understand why algorithms based on matrix product states [91] (such as the density matrix renormalisation group [92] in its time dependent version [93] or iTEBD [94]) fail to describe the quench dyn”
Quantum trajectories and open many-body quantum systems (2014, methodology): “Early development of time-dependent methods has included the time-evolving block decimation (TEBD) algorithm [228, 229], and its integration with DMRG to produce an adaptive time-dependent DMRG (t-DMRG) algorithm [230, 231].”
Tangent-space methods for uniform matrix product states (2018, methodology): “One of the many new applications has been the simulation of time evolution, where the MPS formalism has been of crucial value for coming up with algorithms such as the time-evolving block decimation [21–23].”
Solving the quantum many-body problem with artificial neural networks (2016, result): “Our results for the time evolution (and with α = 4 ) are compared with the numerically-exact MPS dynamics [36–38] for a system with open boundaries (see Fig.”
Matrix product simulations of non-equilibrium steady states of quantum spin chains (2008, background): “ 3]. Even though most versions of these methods can be re-interpreted in terms of the density matrix renormalization group [4] (for an excellent review see [5]) and its time-dependent generalizations [6, 7] they bring up a conceptual simplicity: namely, they represent the quantum many body states in”