897 research outputs found
Hilbert space renormalization for the many-electron problem
Renormalization is a powerful concept in the many-body problem. Inspired by
the highly successful density matrix renormalization group (DMRG) algorithm,
and the quantum chemical graphical representation of configuration space, we
introduce a new theoretical tool: Hilbert space renormalization, to describe
many-electron correlations. While in DMRG, the many-body states in nested Fock
subspaces are successively renormalized, in Hilbert space renormalization,
many-body states in nested Hilbert subspaces undergo renormalization. This
provides a new way to classify and combine configurations. The underlying
wavefunction ansatz, namely the Hilbert space matrix product state (HS-MPS),
has a very rich and flexible mathematical structure. It provides low-rank
tensor approximations to any configuration interaction (CI) space through
restricting either the 'physical indices' or the coupling rules in the HS-MPS.
Alternatively, simply truncating the 'virtual dimension' of the HS-MPS leads to
a family of size-extensive wave function ansaetze that can be used efficiently
in variational calculations. We make formal and numerical comparisons between
the HS-MPS, the traditional Fock-space MPS used in DMRG, and traditional CI
approximations. The analysis and results shed light on fundamental aspects of
the efficient representation of many-electron wavefunctions through the
renormalization of many-body states.Comment: 23 pages, 14 figures, The following article has been submitted to The
Journal of Chemical Physic
Time-reversal symmetry adaptation in relativistic density matrix renormalization group algorithm
In the nonrelativistic Schr\"{o}dinger equation, the total spin and spin
projection are good quantum numbers. In contrast, spin symmetry is lost in
the presence of spin-dependent interactions such as spin-orbit couplings in
relativistic Hamiltonians. Previous implementations of relativistic density
matrix renormalization group algorithm (R-DMRG) only employing particle number
symmetry are much more expensive than nonrelativistic DMRG. Besides, artificial
breaking of Kramers degeneracy can happen in the treatment of systems with odd
number of electrons. To overcome these issues, we introduce time-reversal
symmetry adaptation for R-DMRG. Since the time-reversal operator is
antiunitary, this cannot be simply achieved in the usual way. We define a
time-reversal symmetry-adapted renormalized basis and present strategies to
maintain the structure of basis functions during the sweep optimization. With
time-reversal symmetry adaptation, only half of the renormalized operators are
needed and the computational costs of Hamiltonian-wavefunction multiplication
and renormalization are reduced by half. The present construction of
time-reversal symmetry-adapted basis also directly applies to other tensor
network states without loops.Comment: 13 page
A Perturbative Density Matrix Renormalization Group Algorithm for Large Active Spaces
We describe a low cost alternative to the standard variational DMRG (density
matrix renormalization group) algorithm that is analogous to the combination of
selected configuration interaction plus perturbation theory (SCI+PT). We denote
the resulting method p-DMRG (perturbative DMRG) to distinguish it from the
standard variational DMRG. p-DMRG is expected to be useful for systems with
very large active spaces, for which variational DMRG becomes too expensive.
Similar to SCI+PT, in p-DMRG a zeroth-order wavefunction is first obtained by a
standard DMRG calculation, but with a small bond dimension. Then, the residual
correlation is recovered by a second-order perturbative treatment. We discuss
the choice of partitioning for the perturbation theory, which is crucial for
its accuracy and robustness. To circumvent the problem of a large bond
dimension in the first-order wavefunction, we use a sum of matrix product
states (MPS) to expand the first-order wavefunction, yielding substantial
savings in computational cost and memory. We also propose extrapolation schemes
to reduce the errors in the zeroth- and first-order wavefunctions. Numerical
results for Cr 2 with a (28e,76o) active space and 1,3-butadiene with a
(22e,82o) active space reveal that p-DMRG provides ground state energies of a
similar quality to variational DMRG with very large bond dimensions, but at a
significantly lower computational cost. This suggests that p-DMRG will be an
efficient tool for benchmark studies in the future
Electronic landscape of the P-cluster of nitrogenase as revealed through many-electron quantum wavefunctions
The electronic structure of the nitrogenase metal cofactors is central to
nitrogen fixation. However, the P-cluster and iron molybdenum cofactor, each
containing eight irons, have resisted detailed characterization of their
electronic properties. Through exhaustive many-electron wavefunction
simulations enabled by new theoretical methods, we report on the low-energy
electronic states of the P-cluster in three oxidation states. The energy scales
of orbital and spin excitations overlap, yielding a dense spectrum with
features we trace to the underlying atomic states and recouplings. The clusters
exist in superpositions of spin configurations with non-classical spin
correlations, complicating interpretation of magnetic spectroscopies, while the
charges are mostly localized from reorganization of the cluster and its
surroundings. Upon oxidation, the opening of the P-cluster significantly
increases the density of states, which is intriguing given its proposed role in
electron transfer. These results demonstrate that many-electron simulations
stand to provide new insights into the electronic structure of the nitrogenase
cofactors.Comment: 23 pages, 5 figure
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