Zero-site density matrix renormalization group and the optimal low-rank correction

NÚÑEZ-FERNÁNDEZ, YURIEL; TORROBA, GONZALO

Physical Review B

American Physical Society

Año: 2020 vol. 101

2469-9950

A zero-site density matrix renormalization algorithm (DMRG0) is proposed tominimize the energy of matrix product states (MPS). Instead of the site tensorsthemselves, we propose to optimize sequentially the "message" tensors betweenneighbor sites, which contain the singular values of the bipartition. Thisleads to a local minimization step that is independent of the physicaldimension of the site. Conceptually, it separates the optimization anddecimation steps in DMRG. Furthermore, we introduce two new globalperturbations based on the optimal low-rank correction to the current state,which are used to avoid local minima. They are determined variationally as theMPS closest to the one-step correction of the Lanczos or Jacobi-Davidsoneigensolver, respectively. These perturbations mainly decrease the energy andare free of hand-tuned parameters. Compared to existing single-site enrichmentproposals, our approach gives similar convergence ratios per sweep while thecomputations are cheaper by construction. Our methods may be useful in systemswith many physical degrees of freedom per lattice site. We test our approach onthe periodic Heisenberg spin chain for various spins, and on free electrons onthe lattice.