Quantum transfer-matrix and momentum-space DMRG

Tao Xiang

A momentum-space approach of the density-matrix renormalization-group (DMRG) method is developed. Ground-state energies of the Hubbard model are evaluated using this method and compared with exact diagonalization as well as quantum Monte Carlo results. It is shown that the momentum-space DMRG is a very useful numerical tool for studying the Hubbard model and other fundamental models of interacting electrons in two dimensions. For the Hubbard model in two dimensions, the momentum-space DMRG method reproduces accurately the exact diagonalization results of ground-state energies on a 4\ifmmode\times\else\texttimes\fi{}4 lattice and yields new upper bounds of ground-state energies on an 8\ifmmode\times\else\texttimes\fi{}8 lattice.

Hiromi Otsuka, 博巳 大塚

Adrian E. Feiguin, Steven R. White

We apply a generalization of the time-dependent density matrix renormalization group (DMRG) to study finite-temperature properties of several quantum spin chains, including the frustrated ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model. We discuss several practical issues with the method, including use of quantum numbers and finite-size effects. We compare with transfer-matrix DMRG, finding that both methods produce excellent results.

Kenn Kubo

Johannes Motruk, Michael P. Zaletel, Roger S. K. Mong +1 more

We develop a variant of the density matrix renormalization group (DMRG) algorithm for two-dimensional cylinders that uses a real space representation in the direction along the axis of the cylinder and a momentum space representation in the direction around the circumference. The mixed representation allows us to use the momentum around the cylinder as a conserved quantity in the DMRG algorithm. Compared with the traditional purely real-space approach, we find a significant speedup in computation time and a considerable reduction in memory usage. Applying the method to the interacting fermionic Hofstadter model, we demonstrate a reduction in computation time by over 20-fold, in addition to a sixfold memory reduction.