Matrix product state applications for the ALPS project

Dolfi, Michele; Bauer, Bela; Keller, Sebastian; Kosenkov, Alexandr; Ewart, Timothée; Kantian, Adrian; Giamarchi, Thierry; Troyer, Matthias

doi:10.1016/j.cpc.2014.08.019

Cited by 89 publications

(100 citation statements)

References 47 publications

Supporting

Mentioning

100

Contrasting

Order By: Relevance

“…To get an intuition about the effect of the new terms, we use the ALPS DMRG and MPS tools [74,75] to calculate the ground state of H (0) eff at half-filling. The many-body gap in the thermodynamic limit ∆ is extracted from simulations of even-length chains with open boundary conditions by extrapolation in the system size: ∆(L) = const/L + ∆.…”

mentioning

confidence: 99%

Schrieffer-Wolff Transformation for Periodically Driven Systems: Strongly Correlated Systems with Artificial Gauge Fields

2016

View full text Add to dashboard Cite

We generalize the Schrieffer-Wolff transformation to periodically driven systems using Floquet theory. The method is applied to the periodically driven, strongly interacting Fermi-Hubbard model, for which we identify two regimes resulting in different effective low-energy Hamiltonians. In the nonresonant regime, we realize an interacting spin model coupled to a static gauge field with a nonzero flux per plaquette. In the resonant regime, where the Hubbard interaction is a multiple of the driving frequency, we derive an effective Hamiltonian featuring doublon association and dissociation processes. The ground state of this Hamiltonian undergoes a phase transition between an ordered phase and a gapless Luttinger liquid phase. One can tune the system between different phases by changing the amplitude of the periodic drive.

show abstract

mentioning

confidence: 99%

Schrieffer-Wolff Transformation for Periodically Driven Systems: Strongly Correlated Systems with Artificial Gauge Fields

2016

View full text Add to dashboard Cite

show abstract

“…All DMRG calculations for the QM parts were carried out with QCMaquis [58][59][60][61][62] in a Hartree-Fock (HF) or HF-srDFT molecular orbital basis. The corresponding PE-DMRG and PE-DMRG-srDFT calculations employed PE-HF and PE-HF-srDFT molecular orbital bases, respectively.…”

Section: Computational Methodologymentioning

confidence: 99%

“…Our DMRG implementation employs an MPO form for all operators [58][59][60]. Accordingly, an operatorŴ will be of the form…”

Section: Dmrg With Matrix Product Operatorsmentioning

confidence: 99%

“…One of the most capable methods to recover static correlation is the density matrix renormalization group (DMRG) algorithm [46][47][48][49][50][51][52][53][54][55][56][57]. Our group recently reported the implementation of an efficient second-generation DMRG program [58][59][60][61][62] which relies entirely on matrix product operators. In this paper, we describe the coupling of this DMRG program with a PE scheme.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Polarizable Embedding Density Matrix Renormalization Group

Hedegård

Reiher

2016

J. Chem. Theory Comput.

View full text Add to dashboard Cite

The polarizable embedding (PE) approach is a flexible embedding model where a pre-selected region out of a larger system is described quantum mechanically while the interaction with the surrounding environment is modeled through an effective operator. This effective operator represents the environment by atom-centered multipoles and polarizabilities derived from quantum mechanical calculations on (fragments of) the environment. Thereby, the polarization of the environment is explicitly accounted for. Here, we present the coupling of the PE approach with the density matrix renormalization group (DMRG).This PE-DMRG method is particularly suitable for embedded subsystems that feature a dense manifold of frontier orbitals which requires large active spaces.Recovering such static electron-correlation effects in multiconfigurational electronic structure problems, while accounting for both electrostatics and polarization of a surrounding environment, allows us to describe strongly correlated electronic structures in complex molecular environments. We investigate various embedding potentials for the well-studied first excited state of water with active spaces that correspond to a full configuration-interaction treatment.

show abstract

“…The implementation of anticommutation relations for fermionic operators can also occur at the level of MPO representations of single-site operators [16]. Proper anticommutation within the local state space of a single site,…”

Section: A Fermionic Operatorsmentioning

confidence: 99%

Generic construction of efficient matrix product operators

2017

View full text Add to dashboard Cite

Matrix product operators (MPOs) are at the heart of the second-generation density matrix renormalization group (DMRG) algorithm formulated in matrix product state language. We first summarize the widely known facts on MPO arithmetic and representations of single-site operators. Second, we introduce three compression methods (rescaled SVD, deparallelization, and delinearization) for MPOs and show that it is possible to construct efficient representations of arbitrary operators using MPO arithmetic and compression. As examples, we construct powers of a short-ranged spin-chain Hamiltonian, a complicated Hamiltonian of a two-dimensional system and, as proof of principle, the long-range four-body Hamiltonian from quantum chemistry.

show abstract

Matrix product state applications for the ALPS project

Cited by 89 publications

References 47 publications

Schrieffer-Wolff Transformation for Periodically Driven Systems: Strongly Correlated Systems with Artificial Gauge Fields

Schrieffer-Wolff Transformation for Periodically Driven Systems: Strongly Correlated Systems with Artificial Gauge Fields

Polarizable Embedding Density Matrix Renormalization Group

Generic construction of efficient matrix product operators

Contact Info

Product

Resources

About