Flow‐equations for Hamiltonians

1994/01/01 by Franz Wegner · 17 citations
Physics and Astronomy · Chemistry · #Physics of Superconductivity and Magnetism #Advanced NMR Techniques and Applications #Theoretical and Computational Physics

paper · doi:10.1002/andp.19945060203

Abstract

Abstract Flow‐equations are introduced in order to bring Hamiltonians closer to diagonalization. It is characteristic for these equations that matrix‐elements between degenerate or almost degenerate states do not decay or decay very slowly. In order to understand different types of physical systems in this framework it is probably necessary to classify various types of these degeneracies and to investigate the corresponding physical behavior. In general these equations generate many‐particle interactions. However, for an n ‐orbital model the equations for the two‐particle interaction are closed in the limit of large n. Solutions of these equations for a one‐dimensional model are considered. There appear convergency problems, which are removed, if instead of diagonalization only a block‐diagonalization into blocks with the same number of quasiparticles is performed.

Cited by

• In-Medium Similarity Renormalization Group For Nuclei
• Theodore Dru Alison Cockerell
• Ab initio no core shell model
• Quantum lattice fluctuations in a frustrated Heisenberg spin-Peierls chain
• The In-Medium Similarity Renormalization Group: A novel ab initio method for nuclei
• Spin-phonon chains with bond coupling
• Krylov Complexity Under Hamiltonian Deformations and Toda Flows
• Improving the efficiency of the multireference driven similarity renormalization group via sequential transformation, density fitting, and the non-interacting virtual orbital approximation
• The structure of operators in effective particle-conserving models
• A practical introduction to tensor networks: Matrix product states and projected entangled pair states
• Systematic mapping of the Hubbard model to the generalizedt−Jmodel
• A Similarity Renormalization Group Approach to Green's Function Methods. [europepmc]
• NuHamil : A numerical code to generate nuclear two- and three-body matrix elements from chiral effective field theory. [europepmc]
• Monte Carlo Based Techniques for Quantum Magnets with Long-Range Interactions. [europepmc]
• Toward Accurate Spin-Orbit Splittings from Relativistic Multireference Electronic Structure Theory. [europepmc]
• Renormalized Internally Contracted Multireference Coupled Cluster with Perturbative Triples. [europepmc]
• Complete Active Space Iterative Coupled Cluster Theory. [europepmc]

Related

• Flow Equations for Hamiltonians from Continuous Unitary Transformations
• Continuous Unitary Transformations
• Solving QCD Hamiltonian for Bound States
• Quantum Processes and Energy-Momentum Flow
• Barrier penetration in a discrete-basis formalism