Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2005-10-12
AIP Conf. Proc. 789, 93-163 (2005)
Physics
Condensed Matter
Strongly Correlated Electrons
51 pages; lecture notes on numerically exact methods. Pedagogical review appearing in the proceedings of the "IX. Training Cou
Scientific paper
10.1063/1.2080349
In these lecture notes, we present a pedagogical review of a number of related {\it numerically exact} approaches to quantum many-body problems. In particular, we focus on methods based on the exact diagonalization of the Hamiltonian matrix and on methods extending exact diagonalization using renormalization group ideas, i.e., Wilson's Numerical Renormalization Group (NRG) and White's Density Matrix Renormalization Group (DMRG). These methods are standard tools for the investigation of a variety of interacting quantum systems, especially low-dimensional quantum lattice models. We also survey extensions to the methods to calculate properties such as dynamical quantities and behavior at finite temperature, and discuss generalizations of the DMRG method to a wider variety of systems, such as classical models and quantum chemical problems. Finally, we briefly review some recent developments for obtaining a more general formulation of the DMRG in the context of matrix product states as well as recent progress in calculating the time evolution of quantum systems using the DMRG and the relationship of the foundations of the method with quantum information theory.
Manmana Salvatore R.
Noack Reinhard M.
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