DENSITY-MATRIX ALGORITHMS FOR QUANTUM RENORMALIZATION-GROUPS

A formulation of numerical real space renormalization groups for quantum many-body problems is presented and several algorithms utilizing this formulation are outlined. The methods are presented and demonstrated using S = 1/2 and S = 1 Heisenberg chains as test cases. The kev idea of the formulation is that rather than keep the lowest-lying eigenstates of the, Hamiltonian in forming a new effective Hamiltonian of a block of sites, one should keep the most significant eigenstates of the block density matrix, obtained from diagonalizing the Hamiltonian of a larger section of the lattice which includes the block. This approach is much more accurate than the standard approach; for example, energies for the S = 1 Heisenberg chain can be obtained to an accuracy of at least 10(-9). The method can be applied to almost any one-dimensional quantum lattice system, and can provide a wide variety of static properties.