Year: 2000
Type: article
Abstract: Based on the original idea of the density matrix renormalization group (DMRG), i.e. to include the missing boundary conditions between adjacent blocks of the blocked quantum system, we present a rigorous and non-perturbative mathematical formulation for the real-space renormalization group idea conceived by Kadanoff and further developed by Wilson. This is achieved by using additional Hilbert spaces called auxiliary spaces in the construction of each single isolated block, which is then termed a superblock, in accordance with the original nomenclature. On this superblock we define two maps, called embedding and truncation, for successively integrating out the small-scale structure. Our method overcomes the known difficulties of the numerical DMRG, i.e. the limitation to zero temperature and one space dimension.
Author: Andreas Degenhard
Institution: Bielefeld University
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1964530187