Alexander Fufaev
My name is Alexander FufaeV and here I will explain the following topic:

Basic Principle of Infinite DMRG Algorithm

Basic Principle of Infinite DMRG
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 \(m\).