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Bulletin of the American Physical Society

Combining the density matrix renormalization group and truncated spectrum approach for two-dimensional strongly correlated systems

Yury Adamov, Robert Konik

Published Mar 6, 2007• 0 citations
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The density-matrix renormalization group (DMRG) is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a rather general decimation prescription. This algorithm has achieved unprecedented precision in the description of one-dimensional quantum systems. It has therefore quickly become the method of choice for numerical studies of such systems. Its applications to the calculation of static, dynamic, and thermodynamic quantities in these systems are reviewed here. The potential of DMRG applications in the fields of two-dimensional quantum systems, quantum chemistry, three-dimensional small grains, nuclear physics, equilibrium and nonequilibrium statistical physics, and time-dependent phenomena is also discussed. This review additionally considers the theoretical foundations of the method, examining its relationship to matrix-product states and the quantum information content of the density matrices generated by the DMRG.
The recently proposed combination of the valence-space in-medium similarity renormalization group (VS-IMSRG) with the density matrix renormalization group (DMRG) offers a scalable and flexible many-body approach for strongly correlated open-shell nuclei. We use the VS-DMRG to investigate the low-lying spectroscopy of N = 50 isotones, which are characteristic for their transition between single-particle and collective excitations . We also study electromagnetic transitions and show the advantage of the VS-DMRG to capture the underlying physics more efficiently, with significantly improved convergence compared to state-of-the-art shell-model truncations. Combined with an analysis of quantum information measures, this further establishes the VS-DMRG as a valuable method for ab initio calculations of nuclei.
We study the spectrum of two dimensional coupled arrays of continuum one-dimensional systems by wedding a density matrix renormalization group procedure to a renormalization group improved truncated spectrum approach. To illustrate the methodology, we study the spectrum of large arrays of coupled quantum Ising chains. We demonstrate explicitly that the method can treat the various regimes of chains, in particular, the three dimensional Ising ordering transition the chains undergo as a function of interchain coupling.