Density-matrix algorithms for quantum renormalization groups
Abstract
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 key 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.
- Publication:
-
Physical Review B
- Pub Date:
- October 1993
- DOI:
- Bibcode:
- 1993PhRvB..4810345W
- Keywords:
-
- 05.30.-d;
- 75.10.Jm;
- 02.70.-c;
- Quantum statistical mechanics;
- Quantized spin models;
- Computational techniques;
- simulations