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Physical review. B, Condensed matter

Symmetrized density-matrix renormalization-group method for excited states of Hubbard models

S. Ramasesha, Swapan Kumar Pati, H. R. Krishnamurthy, Zhigang Shuai, Jean‐Luc Brédas

Published Sep 15, 1996• 85 citations
Publisher

Abstract

We extend the density-matrix renormalization-group (DMRG) method to exploit parity, ${\mathit{C}}_{2}$ (rotation by \ensuremath{\pi}), and electron-hole symmetries of model Hamiltonians. We demonstrate the power of this method by obtaining the lowest-energy states in all eight symmetry subspaces of Hubbard chains with up to 50 sites. The ground-state energy, optical gap, and spin gap of regular U=4t and U=6t Hubbard chains agree very well with exact results. This development extends the scope of the DMRG method and allows future applications to study of optical properties of low-dimensional conjugated polymeric systems. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physrevb.54.7598

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We extend the density-matrix renormalization-group (DMRG) method to exploit parity, C2{\mathit{C}}_{2}C2​ (rotation by \ensuremath{\pi}), and electron-hole symmetries of model Hamiltonians. We demonstrate the power of this method by obtaining the lowest-energy states in all eight symmetry subspaces of Hubbard chains with up to 50 sites. The ground-state energy, optical gap, and spin gap of regular U=4t and U=6t Hubbard chains agree very well with exact results. This development extends the scope of the DMRG method and allows future applications to study of optical properties of low-dimensional conjugated polymeric systems. \textcopyright{} 1996 The American Physical Society.
We extend the density matrix renormalization group method to exploit Parity, C2C_2C2​ (rotation by πππ) and electron-hole symmtries of model Hamiltonians. We demonstrate the power of this method by obtaining the lowest energy states in all the eight symmetry subspaces of Hubbard chains with upto 50 sites. The ground-state energy, optical gap and spin gap of regular U=4tU=4tU=4t and U=6tU=6tU=6t Hubbard chains agree very well with exact results. This development extends the scope of the DMRG method and allows future applications to study of optical properties of low-dimensional conjugated polymeric systems.
The symmetry adapted density matrix renormalization group (SDMRG) technique has been an efficient method for studying low-lying eigenstates in one- and quasi-one-dimensional electronic systems. However, the SDMRG method had bottlenecks involving the construction of linearly independent symmetry adapted basis states as the symmetry matrices in the DMRG basis were not sparse. We have developed a modified algorithm to overcome this bottleneck. The new method incorporates end-to-end interchange symmetry (C2)({C}_{2})(C2​), electron-hole symmetry (J)(J)(J), and parity or spin-flip symmetry (P)(P)(P) in these calculations. The one-to-one correspondence between direct-product basis states in the DMRG Hilbert space for these symmetry operations renders the symmetry matrices in the new basis with maximum sparseness, just one nonzero matrix element per row. Using methods similar to those employed in the exact diagonalization technique for Pariser-Parr-Pople (PPP) models, developed in the 1980s, it is possible to construct orthogonal SDMRG basis states while bypassing the slow step of the Gram-Schmidt orthonormalization procedure. The method together with the PPP model which incorporates long-range electronic correlations is employed to study the correlated excited-state spectra of 1,12-benzoperylene and a narrow mixed graphene nanoribbon with a chrysene molecule as the building unit, comprising both zigzag and cove-edge structures.
We extend the symmetrized density matrix renormalization group (SDMRG) method to compute the dynamic nonlinear optic coefficients for long chains. By computing correction vectors in the appropriate symmetry subspace we obtain the dynamic polarizabilities, αij(ω)α_{ij}(ω)αij​(ω), and third-order polarizabilities γijkl(ω,ω,ω)γ_{ijkl}(ω,ω,ω)γijkl​(ω,ω,ω) of the Hubbard and "U−VU-VU−V" chains in an all−transall-transall−trans polyacetylene geometry, with and without dimerization. We rationalize the behavior of αˉ\barααˉ and γˉ\barγγˉ​ on the basis of the low-lying excitation gaps in the system. This is the first study of the dynamics of a fermionic system within the DMRG framework.
The density matrix renormalization group (DMRG) method generates the low-energy states of linear systems of NNN sites with a few degrees of freedom at each site by starting with a small system and adding sites step by step while keeping constant the dimension of the truncated Hilbert space. DMRG algorithms are adapted to open chains with inversion symmetry at the central site, to cyclic chains and to weakly coupled chains. Physical properties rather than energy accuracy is the motivation. The algorithms are applied to the edge states of linear Heisenberg antiferromagnets with spin S≥1S \ge 1S≥1 and to the quantum phases of a frustrated spin-1/2 chain with exchange between first and second neighbors. The algorithms are found to be accurate for extended Hubbard and related 1D models with charge and spin degrees of freedom.
Discrepancies between the single-particle band structure and the exact many-particle behavior are particularly striking in one-dimensional systems. The one-dimensional alternating Hubbard model is especially interesting as a nontrivial model for conjugated polymer chains, such as polyacetelyne. We study this model for chains of 60 sites using the density-matrix renormalization-group method. We obtain the first electronic and magnetic excited-state energies at half filling as a function of an alternating hopping parameter and on-site electron-electron interaction. We also study the effect of the interaction on the dimerization and discuss its relation to the charge gap and spin triplet gap. In addition, we calculate the local spin and charge densities of some excited states, which manifest a clear crossover from bandlike to strongly correlated behavior.
Using both the density-matrix renormalization group method and the constrained-path quantum Monte Carlo method, we studied the ground-state energies and the spin and hole densities of a 12x3 Hubbard model with open boundary conditions and six holes doped away from half-filling. Results obtained with these two methods agree well in the small and intermediate U regimes. For U/t{>=}6 we find a ground-state with charge inhomogeneities consistent with stripes. (c) 2000 The American Physical Society.