Matrix Product State applications for the ALPS project

Abstract

The density-matrix renormalization group method has become a standard computational approach to the low-energy physics as well as dynamics of low-dimensional quantum systems. In this paper, we present a new set of applications, available as part of the ALPS package, that provide an efficient and flexible implementation of these methods based on a matrix-product state (MPS) representation. Our applications implement, within the same framework, algorithms to variationally find the ground state and low-lying excited states as well as simulate the time evolution of arbitrary one-dimensional and two-dimensional models. Implementing the conservation of quantum numbers for generic Abelian symmetries, we achieve performance competitive with the best codes in the community. Example results are provided for (i) a model of itinerant fermions in one dimension and (ii) a model of quantum magnetism.

11+5 pages, 8 figures, 2 examples

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Cited by in corpus (19)

• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains
• The Density Matrix Renormalization Group in Chemistry and Molecular Physics: Recent Developments and New Challenges
• Generic Construction of Efficient Matrix Product Operators
• Effective theory and emergent $SU(2)$ symmetry in the flat bands of attractive Hubbard models
• Multi-reference perturbation theory with Cholesky decomposition for the density matrix renormalization group
• Spin-orbit physics of j=1/2 Mott insulators on the triangular lattice
• Prethermal time crystals in a one-dimensional periodically driven Floquet system
• Self-Consistent Embedding of Density-Matrix Renormalization Group Wavefunctions in a Density Functional Environment
• Transcorrelated Density Matrix Renormalization Group
• Efficient Continuous-time Quantum Monte Carlo Method for the Ground State of Correlated Fermions
• Induced pairing of fermionic impurities in a one-dimensional strongly correlated Bose gas
• Unraveling the Excitation Spectrum of Many-Body Systems from Quantum Quenches
• Study of the phase diagram of the Kitaev-Hubbard chain
• Twofold correlation spreading in a strongly correlated lattice Bose gas
• Minimizing nonadiabaticities in optical-lattice loading
• Magnetic phase diagram of the infinite-U Hubbard model with nearest- and next nearest-neighbor hoppings
• Low dimensional correlations under thermal fluctuations
• Density redistribution effects in fermionic optical lattices
• Emergent Phases in an Extended Bose-Hubbard Model with Three-body On-site Interaction