Time-dependent density-matrix renormalization-group using adaptive effective Hilbert
spaces

Daley, Andrew J.; Kollath, Corinna; Schollwöck, Ulrich; Vidal, Guifré

doi:10.1088/1742-5468/2004/04/p04005

Cited by 1,135 publications

(1,308 citation statements)

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“…The Lindblad equation (1) allows efficient numerical simulation of the steady state of locally interacting systems, in terms of the time-dependent-density-matrixrenormalization-group method (tDMRG) [46,149,130] in the Liouville space of linear operators acting on wave functions [115]. In cases where the tDMRG method cannot be applied, like when the interaction is long-range (e.g., Coulomb), the QME can be solved using the method of quantum trajectories, (see, for example, [103]).…”

Section: Fourier Law In Quantum Mechanicsmentioning

confidence: 99%

From Thermal Rectifiers to Thermoelectric Devices

Benenti

Casati

Mejía‐Monasterio

et al. 2016

Thermal Transport in Low Dimensions

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We discuss thermal rectification and thermoelectric energy conversion from the perspective of nonequilibrium statistical mechanics and dynamical systems theory. After preliminary considerations on the dynamical foundations of the phenomenological Fourier law in classical and quantum mechanics, we illustrate ways to control the phononic heat flow and design thermal diodes. Finally, we consider the coupled transport of heat and charge and discuss several general mechanisms for optimizing the figure of merit of thermoelectric efficiency.

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Section: Fourier Law In Quantum Mechanicsmentioning

confidence: 99%

From Thermal Rectifiers to Thermoelectric Devices

Benenti

Casati

Mejía‐Monasterio

et al. 2016

Thermal Transport in Low Dimensions

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“…Fortunately, the adaptive time-dependent density-matrix renormalization group (TDDMRG) method [41,42,43] can be used instead. In the context of 1D correlated electronic and bosonic systems, the adaptive TDDMRG has been found to be a highly reliable real-time simulation method at economic computational cost, for example in the context of magnetization dynamics [44], of spin-charge separation [45,46], or far-from equilibrium dynamics of ultracold bosonic atoms [47].…”

Section: Introductionmentioning

confidence: 99%

Dynamical Simulations of Polaron Transport in Conjugated Polymers with the Inclusion of Electron−Electron Interactions

Schollwöck

2009

J. Phys. Chem. A

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Dynamical simulations of polaron transport in conjugated polymers in the presence of an external time-dependent electric field have been performed within a combined extended Hubbard model (EHM) and Su-Schrieffer-Heeger (SSH) model. Nearly all relevant electron-phonon and electronelectron interactions are fully taken into account by solving the time-dependent Schrödinger equation for the π-electrons and the Newton's equation of motion for the backbone monomer displacements by virtue of the combination of the adaptive time-dependent density matrix renormalization group (TDDMRG) and classical molecular dynamics (MD). We find that after a smooth turn-on of the external electric field the polaron is accelerated at first and then moves with a nearly constant velocity as one entity consisting of both the charge and the lattice deformation. An ohmic region (3 mV/Å ≤ E 0 ≤ 9 mV/Å) where the stationary velocity increases linearly with the electric field strength is observed for the case of U =2.0 eV and V =1.0 eV. The maximal velocity is well above the speed of sound. Below 3 mV/Å the polaron velocity increases nonlinearly and in high electric fields with strength E 0 ≥ 10.0 mV/Å the polaron will become unstable and dissociate. The relationship between electron-electron interaction strengths and polaron transport is also studied in detail. We find that the the on-site Coulomb interactions U will suppress the polaron transport and small nearest-neighbor interactions V values are also not beneficial to the polaronic motion while large V values favor the polaron transport.

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“…The key real-time methods thus far developed [3,4,5] rely on the Suzuki-Trotter (S-T) break-up of the evolution operator. This approach has a number of important advantages: it is surprisingly simple and easy to implement in an existing ground state DMRG program; the time evolution is very stable and the only source of non-unitarity is the truncation error; and the number of density matrix eigenstates needed for a given truncation error is minimal.…”

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confidence: 99%

Time-step targeting methods for real-time dynamics using the density matrix renormalization group

2005

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We present a time-step targetting scheme to simulate real-time dynamics efficiently using the density matrix renormalization group (DMRG). The algorithm works on ladders and systems with interactions beyond nearest neighbors, in contrast to existing Suzuki-Trotter based approaches.PACS numbers: 71.27.+a, 71.10.Pm, 72.15.Qm, 73.63.Kv Over the last ten years the density matrix renormalization group (DMRG) [1] has proven to be remarkably effective at calculating static, ground state properties of one-dimensional strongly correlated systems. During this period there has also been substantial progress made in calculating frequency dependent spectral functions [2]. However, the most significant progress in extending DMRG since its invention has occurred in the last year or two. Through a convergence of quantum information and DMRG ideas and techniques, a number of new approaches are being developed. The first of these are highly efficient and accurate methods for real-time evolution, allowing both the calculation of spectral functions via Fourier transforming, and also novel time development studies of systems out of equilibrium.The key real-time methods thus far developed [3, 4, 5] rely on the Suzuki-Trotter (S-T) break-up of the evolution operator. This approach has a number of important advantages: it is surprisingly simple and easy to implement in an existing ground state DMRG program; the time evolution is very stable and the only source of non-unitarity is the truncation error; and the number of density matrix eigenstates needed for a given truncation error is minimal. It also has two notable weaknesses: it has an error proportional to the time step τ squared, and, more importantly, it is limited to systems with nearest neighbor interactions on a single chain. As we show here, the accuracy can be improved using higher order expansions. The nearest-neighbor/single chain limitation is more problematic. In the case of narrow ladders with nearest-neighbor interactions, one can avoid the problem by lumping all sites in a rung into a single supersite. Unfortunately, this approach becomes very inefficient for wider ladders, and is not applicable to general long-range interaction terms.In this paper we propose a new time evolution scheme which produces a basis which targets the states needed to represent one time step. Once this basis is complete enough, the time step is taken and the algorithm proceeds to the next time step. This targetting is intermediate to previous approaches: the Trotter methods target precisely one instant in time at any DMRG step, while Luo, Xiang, and Wang's approach [7] targetted the entire range of time to be studied. Targetting a wider range of time requires more density matrix eigenstates be kept, slowing the calculation. By targetting only a small interval of time, our approach is nearly as efficient as the Trotter methods. In exchange for the small loss of efficiency, we gain the ability to treat longer range interactions, ladder systems, and narrow two-dimensional strips. In addition, ...

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Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces

Cited by 1,135 publications

References 41 publications

From Thermal Rectifiers to Thermoelectric Devices

From Thermal Rectifiers to Thermoelectric Devices

Dynamical Simulations of Polaron Transport in Conjugated Polymers with the Inclusion of Electron−Electron Interactions

Time-step targeting methods for real-time dynamics using the density matrix renormalization group

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