Ummethum, Jörg: Calculation of static and dynamical properties of giant magnetic molecules using DMRG. 2012
Inhalt
- Introduction
- Theoretical background: Magnetic molecules and spin Hamiltonians
- Introduction
- Spin Hamiltonian of magnetic molecules
- Classical spin systems, bipartiteness, and geometrical frustration
- Basis and good quantum numbers
- Spectra of antiferromagnetic spin Hamiltonians
- Typical observables and experimental techniques
- The density matrix renormalization group (DMRG)
- Introduction
- Basis truncation
- Algorithms
- Implementation and technical details
- Operators, states, and quantum numbers
- Detailed description of the basic DMRG steps
- Superblock diagonalization: Lanczos procedure and matrix-vector product
- Calculation of expectation values
- Target state transformation
- Connection to matrix product states
- General spin lattices
- Dynamical DMRG
- Basic properties of the algorithm and tests
- The antiferromagnetic Heisenberg icosidodecahedron
- Introduction
- Properties of systems with corner-sharing triangles
- Classical limit and the rotational band approximation
- DMRG results
- Antiferromagnetic spin rings
- Introduction
- DMRG calculations for uniform antiferromagnetic Heisenberg rings
- Accuracy of the rotational band approximation for spin rings
- Calculation of the low-energy spectrum using standard and dynamical DMRG
- Additional excitations
- Dynamical correlation function for an excited reference state (S=2 excitations)
- Fe18
- Summary and conclusion
- Appendix
- Bibliography
- Danksagung