# Basic Principle of Infinite DMRG Algorithm

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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 $$m$$.

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