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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• Multi-reference perturbation theory with Cholesky decomposition for the density matrix renormalization group
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• The Delicate Balance of Static and Dynamic Electron Correlation
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• Automated Identification of Relevant Frontier Orbitals for Chemical Compounds and Processes
• Calculation of Ligand Dissociation Energies in Large Transition-Metal Complexes
• Pair Correlations in Doped Hubbard Ladders
• Measuring Multi-Configurational Character by Orbital Entanglement
• Vibrational Density Matrix Renormalization Group
• Open source Matrix Product States: Opening ways to simulate entangled many-body quantum systems in one dimension
• 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
• Synthetic dimensions in the strong-coupling limit: supersolids and pair-superfluids
• Markovian Treatment of non-Markovian Dynamics of Open Fermionic Systems
• Transcorrelated Density Matrix Renormalization Group
• Efficient Continuous-time Quantum Monte Carlo Method for the Ground State of Correlated Fermions
• Anomalies and entanglement renormalization
• The Polarizable Embedding Density Matrix Renormalization Group Method
• Induced pairing of fermionic impurities in a one-dimensional strongly correlated Bose gas
• Nuclear-Electronic All-Particle Density Matrix Renormalization Group
• Auxiliary master equation for nonequilibrium dual-fermion approach
• Study of the phase diagram of the Kitaev-Hubbard chain
• Unraveling the Excitation Spectrum of Many-Body Systems from Quantum Quenches
• Twofold correlation spreading in a strongly correlated lattice Bose gas
• Quantum Proton Effects from Density Matrix Renormalization Group Calculations
• Understanding repulsively mediated superconductivity of correlated electrons via massively parallel DMRG
• Minimizing nonadiabaticities in optical-lattice loading
• Phase Diagram and Entanglement of two interacting topological Kitaev chains
• Flux-Stabilized Majorana Zero Modes in Coupled One-Dimensional Fermi Wires
• Emergent interacting spin islands in a depleted strong-leg Heisenberg ladder
• Exact results for a $Z_3$ clock-type model and some close relatives
• Symmetry-protected non-Fermi liquids, Kagome spin liquids, and the chiral Kondo lattice model
• Bipartite charge fluctuations in one-dimensional ${\mathbb{Z}}_2$ superconductors and insulators
• Origin of magnetic frustration in Bi${}_3$Mn${}_4$O${}_{12}$(NO${}_3$)
• Helical gaps in interacting Rashba wires at low electron densities
• Enhanced visibility of the Fulde-Ferrell-Larkin-Ovchinnikov state in one dimensional Bose-Fermi mixtures near the immiscibility point
• Tangential finite-size scaling of the Gaussian topological transition in the quantum spin-1 anisotropic chain
• Phase diagram of the ${\mathbb{Z}}_3$-Fock parafermion chain with pair hopping
• Majorana edge state in a number-conserving Fermi gas with tunable p-wave interaction
• Distributed-Memory DMRG via Sparse and Dense Parallel Tensor Contractions
• Superconducting pairing from repulsive interactions of fermions in a flat-band system
• Fulde-Ferrell-Larkin-Ovchinnikov pairing states of a polarized dipolar Fermi gas trapped in a one-dimensional optical lattice
• Magnetic phase diagram of the infinite-U Hubbard model with nearest- and next nearest-neighbor hoppings
• Two Coupled Chains are Simpler than One: Field-induced Chirality in a Frustrated Quantum Spin Ladder
• The Transformation of the Superconducting Gap to an Insulating Pseudogap at a Critical Hole Density in the Cuprates
• Non-equilibrium boundary driven quantum systems: models, methods and properties
• Orbital Entanglement and The Double $d$-Shell Effect in Binary Transition Metal Molecules
• Low dimensional correlations under thermal fluctuations
• True exciton condensate of one-dimensional electrons through interwire tunneling
• Signatures of gapless fermionic spinons on a strip of the kagome Heisenberg antiferromagnet
• The eigenstate distribution fluctuation from thermal to localized transitions
• Itinerant ferromagnetism in the repulsive Hubbard chain with anisotropic odd-wave attraction
• Efficient simulation of many-body localized systems
• Implementing Entangled States on a Quantum Computer
• The Software Landscape for the Density Matrix Renormalization Group
• Three-component fractional quantum Hall effect in topological flat bands
• Non-adiabatic dynamics of the entanglement entropy in a symmetry-breaking Haldane insulator
• Density redistribution effects in fermionic optical lattices
• Bosonic realization of SU(3) chiral Haldane phases
• Emergent Phases in an Extended Bose-Hubbard Model with Three-body On-site Interaction