202 research outputs found
The density matrix renormalization group for ab initio quantum chemistry
During the past 15 years, the density matrix renormalization group (DMRG) has
become increasingly important for ab initio quantum chemistry. Its underlying
wavefunction ansatz, the matrix product state (MPS), is a low-rank
decomposition of the full configuration interaction tensor. The virtual
dimension of the MPS, the rank of the decomposition, controls the size of the
corner of the many-body Hilbert space that can be reached with the ansatz. This
parameter can be systematically increased until numerical convergence is
reached. The MPS ansatz naturally captures exponentially decaying correlation
functions. Therefore DMRG works extremely well for noncritical one-dimensional
systems. The active orbital spaces in quantum chemistry are however often far
from one-dimensional, and relatively large virtual dimensions are required to
use DMRG for ab initio quantum chemistry (QC-DMRG). The QC-DMRG algorithm, its
computational cost, and its properties are discussed. Two important aspects to
reduce the computational cost are given special attention: the orbital choice
and ordering, and the exploitation of the symmetry group of the Hamiltonian.
With these considerations, the QC-DMRG algorithm allows to find numerically
exact solutions in active spaces of up to 40 electrons in 40 orbitals.Comment: 24 pages; 10 figures; based on arXiv:1405.1225; invited review for
European Physical Journal
N-representability conditions on the three-particle density matrix constrained to wave functions of the DOCI class
DMRG-CASPT2 study of the longitudinal static second hyperpolarizability of all-trans polyenes
We have implemented internally contracted complete active space second order
perturbation theory (CASPT2) with the density matrix renormalization group
(DMRG) as active space solver [Y. Kurashige and T. Yanai, J. Chem. Phys. 135,
094104 (2011)]. Internally contracted CASPT2 requires to contract the
generalized Fock matrix with the 4-particle reduced density matrix (4-RDM) of
the reference wavefunction. The required 4-RDM elements can be obtained from
3-particle reduced density matrices (3-RDM) of different wavefunctions, formed
by symmetry-conserving single-particle excitations op top of the reference
wavefunction. In our spin-adapted DMRG code chemps2
[https://github.com/sebwouters/chemps2], we decompose these excited
wavefunctions as spin-adapted matrix product states, and calculate their 3-RDM
in order to obtain the required contraction of the generalized Fock matrix with
the 4-RDM of the reference wavefunction. In this work, we study the
longitudinal static second hyperpolarizability of all-trans polyenes
CH [n = 4 - 12] in the cc-pVDZ basis set. DMRG-SCF and
DMRG-CASPT2 yield substantially lower values and scaling with system size
compared to RHF and MP2, respectively.Comment: 9 pages, 4 figure
Faddeev Random Phase Approximation for Molecules
The Faddeev Random Phase Approximation is a Green's function technique that
makes use of Faddeev-equations to couple the motion of a single electron to the
two-particle--one-hole and two-hole--one-particle excitations. This method goes
beyond the frequently used third-order Algebraic Diagrammatic Construction
method: all diagrams involving the exchange of phonons in the particle-hole and
particle-particle channel are retained, but the phonons are described at the
level of the Random Phase Approximation. This paper presents the first results
for diatomic molecules at equilibrium geometry. The behavior of the method in
the dissociation limit is also investigated
Perturbations on the superconducting state of metallic nanoparticles: influence of geometry and impurities
The pair condensation energy of a finite-size superconducting particle is
studied as a function of two control parameters. The first control parameter is
the shape of the particle, and the second parameter is a position-dependent
impurity introduced in the particle. Whereas the former parameter is known to
induce strong fluctuations in the condensation energy, the latter control
parameter is found to be a more gentle probe of the pairing correlations.Comment: Submitted for the special issue of the International Symposium on
Small Particles and Inorganic Clusters XVI, at KULeuven (July 8-13, 2012).
PACS: 74.78.Na, 74.20.F
Exact solution of the pairing Hamiltonian by deforming the pairing algebra
The present paper makes a connection between collective bosonic states and
the exact solutions of the pairing Hamiltonian. This makes it
possible to investigate the effects of the Pauli principle on the energy
spectrum, by gradually reintroducing the Pauli principle. It also introduces an
efficient and stable numerical method to probe all the eigenstates of this
class of Hamiltonians.Comment: 18 pages, 10 figure
A new variational, information theory based atoms in molecules method
A new iterative Hirshfeld type AIM method, called Hirshfeld-I-Lambda, is presented. The weight function that defines the AIM is constructed by minimizing the information loss on formation of the molecule, with explicitly requiring that the promolecular densities integrate to the same number of electrons as the AIM densities constructed. The atoms defined by this AIM method are the ones that minimize the information lost upon formation of the molecule out of its isolated atoms. The resulting Hirshfeld-I-Lambda AIM scheme is examined and discussed
Read-Green resonances in a topological superconductor coupled to a bath
We study a topological superconductor capable of exchanging particles with an
environment. This additional interaction breaks particle-number symmetry and
can be modelled by means of an integrable Hamiltonian, building on the class of
Richardson-Gaudin pairing models. The isolated system supports zero-energy
modes at a topological phase transition, which disappear when allowing for
particle exchange with an environment. However, it is shown from the exact
solution that these still play an important role in system-environment particle
exchange, which can be observed through resonances in low-energy and -momentum
level occupations. These fluctuations signal topologically protected Read-Green
points and cannot be observed within traditional mean-field theory.Comment: 7 pages, 4 figure
Inner products in integrable Richardson-Gaudin models
We present the inner products of eigenstates in integrable Richardson-Gaudin
models from two different perspectives and derive two classes of Gaudin-like
determinant expressions for such inner products. The requirement that one of
the states is on-shell arises naturally by demanding that a state has a dual
representation. By implicitly combining these different representations, inner
products can be recast as domain wall boundary partition functions. The
structure of all involved matrices in terms of Cauchy matrices is made explicit
and used to show how one of the classes returns the Slavnov determinant
formula. This framework provides a further connection between two different
approaches for integrable models, one in which everything is expressed in terms
of rapidities satisfying Bethe equations, and one in which everything is
expressed in terms of the eigenvalues of conserved charges, satisfying
quadratic equations.Comment: 21+16 pages, minor revisions compared to the previous versio
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