Studying Two Dimensional Systems With the Density Matrix Renormalization Group

By E. Stoudenmire, S. White. 2011

418 citations recorded by the source corpus.

The density matrix renormalization group (DMRG) is one of the most powerful numerical methods for studying two-dimensional quantum lattice systems, despite a perception that it is only suitable for one dimension. Reviewing past applications of DMRG in 2D demonstrates its success in treating a wide variety of problems, although it remains underutilized in this context. We present techniques for performing cutting-edge 2D DMRG studies including methods for ensuring convergence, extrapolating finite-size data, and extracting gaps and excited states. Finally, we consider a selection of recently developed 2D tensor network methods and compare the performance of one of these to 2D DMRG.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/6e81e99ac1e3c6eca612fdbf55ab8548d138000e

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Identifying topological order by entanglement entropy (2012, methodology): “Our method consists simply of using the Density Matrix Renormalization Group (7, 8) (DMRG) to calculate the usual entanglement entropy for the division of a cylinder into two equal halves by a flat cut, and extracting the TEE from its asymptotic, large circumference limit (see below).”
The density matrix renormalization group for ab initio quantum chemistry (2014, background): “For higher-dimensional or critical systems, DMRG can still be useful [56].”
Towards the solution of the many-electron problem in real materials: equation of state of the hydrogen chain with state-of-the-art many-body methods (2017, methodology): “For k 1⁄4 1, this gives the subtraction trick based on a division of surface and bulk terms, namely, A0 1⁄4 1⁄2N1EðN1Þ − N2EðN2Þ =1⁄2N1 − N2 (omitting R), which has been used, for example, in DMRG calculations before [58].”
Absence of Superconductivity in the Pure Two-Dimensional Hubbard Model (2019, background): “Although DMRG is naturally formulated and most powerful for one-dimensional systems, it is now widely applied to 2D systems[84], and remains one of the most-accurate numerical methods in 2D.”
The ITensor Software Library for Tensor Network Calculations (2020, methodology): “In the implementation of this particular DMRG routine, projectors onto the previous states psi0 and psi1 are effectively added to the Hamiltonian times an “energy penalty", pushing up the energy of these states in the eigenvalue spectrum so they are no longer part of the low-energy subspace [25].”
Unsupervised Generative Modeling Using Matrix Product States (2017, methodology): “quantum lattice problems [31], modeling images with”
Prediction of Toric Code Topological Order from Rydberg Blockade (2020, background): “, giving all sites a one-dimensional labeling) [104].”