Basic Principle of Infinite DMRG Algorithm

Basic Principle of Infinite DMRG
Image »Basic Principle of Infinite DMRG Algorithm« download Sharing and adapting of the illustration is allowed with the reference "Alexander Fufaev ("
The Infinite Density Matrix Renormalization Group (DMRG) is a numerical method used to study strongly correlated quantum systems, particularly in one dimension. For explanation, let us consider a spinless one-dimensional chain with fermions.

The infinite DMRG starts with a left block \( B_{\text L}(l, m) \) and an equally sized right block \( B_{\text R}(l, m) \), each describing half of the superblock \( B_{\text L'}(l, m^2) \), which has length \( L' = 2l \) and dimension \( m^2 \) and whose ground state can be calculated exactly.

The two blocks are each increased by one lattice site in the next step: \( B_{\text L}(l+1,2m) \) and \( B_{\text R}(l+1, 2m) \) (these new blocks are called enlarged blocks). As a result, the dimension of the Hilbert space of the blocks is doubled. Adding one more site quadruples the original dimension \(m\), so the dimension of the blocks grows exponentially with each additional site. After increasing the block size by one, infinite DMRG truncates the dimension back to the value \(m\).

+ Perfect for high school and undergraduate physics students
+ Contains over 500 illustrated formulas on just 140 pages
+ Contains tables with examples and measured constants
+ Easy for everyone because without vectors and integrals

Learn more