Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0403310 · Physical Review Letters

Real-Time Evolution Using the Density Matrix Renormalization Group

Steven R. White, Adrian E. Feiguin

Published Aug 10, 2004• 1,393 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.93.076401

Related papers

The adaptive time-dependent density matrix renormalization group method : development and applications

Corinna Kollath, Ulrich Schollwöck

In this work we develop a new numerical method, the adaptive time-dependent density-matrix renormalization-group (adaptive t-DMRG), which turns out to be very well suited to investigate time-dependent phenomena in one-dimensional strongly correlated systems. The method is based on the original density-matrix renormalization group method by White and the time evolving block-decimation procedure by Vidal. We further show the applicability of the new method to different physical systems: bosonic, fermionic, and spin chains. We first discuss the consequences of the presence of an external trapping potential on the static properties of trapped cold bosonic atoms in an optical lattice using the Bose-Hubbard model. It is shown that a properly rescaled one-particle density matrix characterizes superfluid versus insulating states just as in the homogeneous system. We note that the superfluid to Mott-insulating transition is seen most directly in the half width of the interference peak. Then we turn to the evolution of density perturbations in these systems. In particular, we discuss the dependence of the velocity and the decay of the amplitude on density, interaction strength, and the extent and height of the perturbation in a numerically exact way, covering a wide range of interaction and perturbation strengths. By comparing our results for the sound velocity to theoretical predictions, we determine the limits of a Gross-Pitaevskii or Bogoliubov type description and the regime where repulsive one-dimensional Bose gases exhibit fermionic behaviour. As a second application of the adaptive t-DMRG, we investigate the phenomenon of spin-charge separation in the Hubbard model and propose an experimental setup for its observation in cold Fermi gases. We show the robustness of this separation beyond the low-energy regime by studying the time evolution of density wave packets of finite strength and at length scales down to a few lattice spacings. A striking signature of spin-charge separation is found in 1D cold Fermi gases in a harmonic trap using the different propagation properties of the liquid and Mott-insulating phases. The third application relates to the area of spintronics. A simplified model for the magnetization transport between two coupled reservoirs with opposite spin polarization is studied. We investigate whether a simple long time limit for the spin transport exists and if so, how it depends on the properties of the system such as integrability and criticality. Time-scales accessible to us are of the order of 100 units of time measured in 1/J while maintaining insignificant error in the observables.

•Jan 1, 2005•0 citations

Nonequilibrium electron transport using the density matrix renormalization group method

Peter Schmitteckert

We extended the density matrix renormalization group method to study the real time dynamics of interacting one-dimensional spinless Fermi systems by applying the full time evolution operator to an initial state. As an example we describe the propagation of a density excitation in an interacting clean system and the transport through an interacting nano structure.

arXiv:cond-mat/0403759•Physical Review B•Sep 8, 2004•233 citations

The time-dependent density matrix renormalisation group method

Haibo Ma, Zhen Luo, Yao Yao

Substantial progress of the time-dependent density matrix renormalisation group (t-DMRG) method in the recent 15 years is reviewed in this paper. By integrating the time evolution with the sweep procedures in density matrix renormalisation group (DMRG), t-DMRG provides an efficient tool for real-time simulations of the quantum dynamics for one-dimensional (1D) or quasi-1D strongly correlated systems with a large number of degrees of freedom. In the illustrative applications, the t-DMRG approach is applied to investigate the nonadiabatic processes in realistic chemical systems, including exciton dissociation and triplet fission in polymers and molecular aggregates as well as internal conversion in pyrazine molecule.

Molecular Physics•Nov 30, 2017•24 citations

Matrix product simulations of non-equilibrium steady states of quantum spin chains

Tomaž Prosen

Time-dependent density matrix renormalization group method with a matrix product ansatz is employed for explicit computation of non-equilibrium steady state density operators of several integrable and non-integrable quantum spin chains, which are driven far from equilibrium by means of Markovian couplings to external baths at the two ends. It is argued that even though the time-evolution can not be simulated efficiently due to fast entanglement growth, the steady states in and out of equilibrium can be typically accurately approximated, so that chains of length of the order n ~ 100 are accessible. Our results are demonstrated by performing explicit simulations of steady states and calculations of energy/spin densities/currents in several problems of heat and spin transport in quantum spin chains. Previously conjectured relation between quantum chaos and normal transport is re-confirmed with high acurracy on much larger systems.

•Jan 1, 2008•216 citations

Density-Matrix Renormalization Group Methods for Momentum- and Frequency-Resolved Dynamical Correlation Functions

Eric Jeckelmann

Several density-matrix renormalization group methods have been proposed to compute the momentum- and frequency-resolved dynamical correlation functions of low-dimensional strongly correlated systems. The most relevant approaches are discussed in this contribution. Their applications in various studies of quasi-one-dimensional strongly correlated systems (spin chains, itinerant electron systems, electron-phonon systems) are reviewed.

arXiv:0808.2620•Progress of Theoretical Physics Supplement•Jan 1, 2008•24 citations

Time-Dependent Density-Matrix Renormalization Group: A Systematic Method for the Study of Quantum Many-Body Out-of-Equilibrium Systems

Miguel A. Cazalilla, John Bradley Marston

The density-matrix renormalization-group algorithm is extended to treat time-dependent problems. The method provides a systematic and robust tool to explore out-of-equilibrium phenomena in quantum many-body systems. We illustrate the method by showing that attractive interactions enhance the tunneling current between two Luttinger liquids, whereas repulsive interactions suppress it, in qualitative agreement with analytical predictions. Enhancement of the transport current through a quantum dot in the Kondo regime is also exhibited.

arXiv:cond-mat/0109158•Physical Review Letters•Jun 6, 2002•194 citations
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.
In this work we develop a new numerical method, the adaptive time-dependent density-matrix renormalization-group (adaptive t-DMRG), which turns out to be very well suited to investigate time-dependent phenomena in one-dimensional strongly correlated systems. The method is based on the original density-matrix renormalization group method by White and the time evolving block-decimation procedure by Vidal. We further show the applicability of the new method to different physical systems: bosonic, fermionic, and spin chains. We first discuss the consequences of the presence of an external trapping potential on the static properties of trapped cold bosonic atoms in an optical lattice using the Bose-Hubbard model. It is shown that a properly rescaled one-particle density matrix characterizes superfluid versus insulating states just as in the homogeneous system. We note that the superfluid to Mott-insulating transition is seen most directly in the half width of the interference peak. Then we turn to the evolution of density perturbations in these systems. In particular, we discuss the dependence of the velocity and the decay of the amplitude on density, interaction strength, and the extent and height of the perturbation in a numerically exact way, covering a wide range of interaction and perturbation strengths. By comparing our results for the sound velocity to theoretical predictions, we determine the limits of a Gross-Pitaevskii or Bogoliubov type description and the regime where repulsive one-dimensional Bose gases exhibit fermionic behaviour. As a second application of the adaptive t-DMRG, we investigate the phenomenon of spin-charge separation in the Hubbard model and propose an experimental setup for its observation in cold Fermi gases. We show the robustness of this separation beyond the low-energy regime by studying the time evolution of density wave packets of finite strength and at length scales down to a few lattice spacings. A striking signature of spin-charge separation is found in 1D cold Fermi gases in a harmonic trap using the different propagation properties of the liquid and Mott-insulating phases. The third application relates to the area of spintronics. A simplified model for the magnetization transport between two coupled reservoirs with opposite spin polarization is studied. We investigate whether a simple long time limit for the spin transport exists and if so, how it depends on the properties of the system such as integrability and criticality. Time-scales accessible to us are of the order of 100 units of time measured in 1/J while maintaining insignificant error in the observables.
Substantial progress of the time-dependent density matrix renormalisation group (t-DMRG) method in the recent 15 years is reviewed in this paper. By integrating the time evolution with the sweep procedures in density matrix renormalisation group (DMRG), t-DMRG provides an efficient tool for real-time simulations of the quantum dynamics for one-dimensional (1D) or quasi-1D strongly correlated systems with a large number of degrees of freedom. In the illustrative applications, the t-DMRG approach is applied to investigate the nonadiabatic processes in realistic chemical systems, including exciton dissociation and triplet fission in polymers and molecular aggregates as well as internal conversion in pyrazine molecule.
Time-dependent density matrix renormalization group method with a matrix product ansatz is employed for explicit computation of non-equilibrium steady state density operators of several integrable and non-integrable quantum spin chains, which are driven far from equilibrium by means of Markovian couplings to external baths at the two ends. It is argued that even though the time-evolution can not be simulated efficiently due to fast entanglement growth, the steady states in and out of equilibrium can be typically accurately approximated, so that chains of length of the order n ~ 100 are accessible. Our results are demonstrated by performing explicit simulations of steady states and calculations of energy/spin densities/currents in several problems of heat and spin transport in quantum spin chains. Previously conjectured relation between quantum chaos and normal transport is re-confirmed with high acurracy on much larger systems.
The density-matrix renormalization-group algorithm is extended to treat time-dependent problems. The method provides a systematic and robust tool to explore out-of-equilibrium phenomena in quantum many-body systems. We illustrate the method by showing that attractive interactions enhance the tunneling current between two Luttinger liquids, whereas repulsive interactions suppress it, in qualitative agreement with analytical predictions. Enhancement of the transport current through a quantum dot in the Kondo regime is also exhibited.