Gergely Barcza

Quantum-information analysis of electronic states of different molecular structures

We have studied transition metal clusters from a quantum information theory perspective using the density-matrix renormalization group (DMRG) method. We demonstrate the competition between entanglement and interaction localization and discuss the application of the configuration interaction-based dynamically extended active space procedure, which significantly reduces the effective system size and accelerates the speed of convergence for complicated molecular electronic structures. Our results indicate the importance of taking entanglement among molecular orbitals into account in order to devise an optimal DMRG orbital ordering and carry out efficient calculations on transition metal clusters. Apart from these algorithmic observations, which lead to a recipe for black-box DMRG calculations, our work provides physical understanding of electron correlation in molecular and cluster structures in terms of entropy measures of relevance also to recent work on tensor-network representations of electronic states. We also identify those molecular orbitals which are highly entangled and discuss the consequences for chemical bonding and for the structural transition from an dioxygen binding copper cluster to an bis-oxygen-bridged system with broken O-O bond.

Tensor product methods and entanglement optimization for ab initio quantum chemistry

The treatment of high-dimensional problems such as the Schrodinger equation can be approached by concepts of tensor product approximation. We present general techniques that can be used for the treatment of high-dimensional optimization tasks and time-dependent equations, and connect them to concepts already used in many-body quantum physics. Based on achievements from the past decade, entanglement-based methods—developed from different perspectives for different purposes in distinct communities already matured to provide a variety of tools—can be combined to attack highly challenging problems in quantum chemistry. The aim of the present paper is to give a pedagogical introduction to the theoretical background of this novel field and demonstrate the underlying benefits through numerical applications on a text book example. Among the various optimization tasks, we will discuss only those which are connected to a controlled manipulation of the entanglement which is in fact the key ingredient of the methods considered in the paper. The selected topics will be covered according to a series of lectures given on the topic “New wavefunction methods and entanglement optimizations in quantum chemistry” at the Workshop on Theoretical Chemistry, February 18–21, 2014, Mariapfarr, Austria.

Orbital Entanglement in Bond-Formation Processes.

The accurate calculation of the (differential) correlation energy is central to the quantum chemical description of bond-formation and bond-dissociation processes. In order to estimate the quality of single- and multireference approaches for this purpose, various diagnostic tools have been developed. In this work, we elaborate on our previous observation [J. Phys. Chem. Lett.2012, 3, 3129] that one- and two-orbital-based entanglement measures provide quantitative means for the assessment and classification of electron correlation effects among molecular orbitals. The dissociation behavior of some prototypical diatomic molecules features all types of correlation effects relevant for chemical bonding. We demonstrate that our entanglement analysis is convenient to dissect these electron correlation effects and to provide a conceptual understanding of bond-forming and bond-breaking processes from the point of view of quantum information theory.

Entanglement patterns and generalized correlation functions in quantum many body systems

We define a generalized, entanglement-based correlation function related to the mutual information of two localized, typically single-site, subsystems of a larger many-body system. The two-site mutual information is defined in terms of the von Neumann entropy of the single-site and two-site density matrices, which, in turn, can be written in terms of expectation values of transition operators between localized states. It can be used to map out entanglement patterns between the subsystems, i.e., sites, of the system. Defining generalized correlation functions as two-point correlation functions of transition operators, we find that the long-distance decay of the mutual information follows the square of that of the most slowly decaying generalized correlation function. We show how the generalized correlation functions are related to conventional correlation functions for spin and fermion lattice models. We explore the behavior of the mutual information, the generalized correlation functions, and their relation for the general spin-1/2 Heisenberg model and for SU(n) Hubbard models with n = 2,3,4, and 5, demonstrating the principles on known phases of the spin and SU(2) Hubbard models and obtaining results characterizing the dimerized, trimerized, and quadrimerized phases in the SU(3), SU(4), and SU(5) Hubbard models, respectively. In addition, we extend the picture of the two-site mutual information and the corresponding generalized correlation functions to the n-site case.

Excited states in polydiacetylene chains: A density matrix renormalization group study

We study theoretically poly-diacetylene chains diluted in their monomer matrix. We employ the density-matrix renormalization group method (DMRG) on finite chains to calculate the ground state and low-lying excitations of the corresponding Peierls--Hubbard-Ohno Hamiltonian which is characterized by the electron transfer amplitude t0 between nearest neighbors, by the electron-phonon coupling constant \alpha, by the Hubbard interaction U, and by the long-range interaction V. We treat the lattice relaxation in the adiabatic limit, i.e., we calculate the polaronic lattice distortions for each excited state. Using chains with up to 102 lattice sites, we can safely perform the extrapolation to the thermodynamic limit for the ground-state energy and conformation, the single-particle gap, and the energies of the singlet exciton, the triplet ground state, and the optical excitation of the triplet ground state. The corresponding gaps are known with high precision from experiment. We determine a coherent parameter set (t0*=2.4 eV, \alpha*=3.4 eV/\AA, U*=6 eV, V*=3 eV) from a fit of the experimental gap energies to the theoretical values which we obtain for 81 parameter points in the four dimensional search space (t0, \alpha, U, V). We identify dark in-gap states in the singlet and triplet sectors as seen in experiment. Using a fairly stiff spring constant, the length of our unit cell is about one percent larger than its experimental value.

Density matrix renormalization group study of excitons in polydiacetylene chains

We study the elementary excitations of a model Hamiltonian for the

Dimerized phase in the cross-coupled antiferromagnetic spin ladder

\pi

The correlation theory of the chemical bond

-electrons in poly-diacetylene chains. In these materials, the bare band gap is only half the size of the observed single-particle gap and the binding energy of the exciton of 0.5 eV amounts to 20% of the single-particle gap. Therefore, exchange and correlations due to the long-range Coulomb interaction require a numerically exact treatment which we carry out using the density-matrix renormalization group (DMRG) method. Employing both the Hubbard--Ohno potential and the screened potential in one dimension, we reproduce the experimental results for the binding energy of the singlet exciton and its polarizability. Our results indicate that there are optically dark states below the singlet exciton, in agreement with experiment. In addition, we find a weakly bound second exciton with a binding energy of 0.1 eV. The energies in the triplet sector do not match the experimental data quantitatively, probably because we do not include polaronic relaxation effects.

Dissecting the bond‑formation process of d 10 ‑metal-ethene complexes with multireference approaches

We revisit the phase diagram of the frustrated s=1/2 spin ladder with antiferromagnetic rung and diagonal couplings. In particular, we reexamine the evidence for the columnar dimer phase, which has been predicted from analytic treatment of the model and has been claimed to be found in numerical calculations. By considering longer chains and by keeping more states than in previous work using the density-matrix renormalization group, we show that the numerical evidence presented previously for the existence of the dimerized phase is not unambiguous in view of the present more careful analysis. While we cannot completely rule out the possibility of a dimerized phase in the cross-coupled ladder, we do set limits on the maximum possible value of the dimer order parameter that are much smaller than those found previously.

The density matrix renormalization group algorithm on kilo-processor architectures: Implementation and trade-offs

The quantum mechanical description of the chemical bond is generally given in terms of delocalized bonding orbitals, or, alternatively, in terms of correlations of occupations of localised orbitals. However, in the latter case, multiorbital correlations were treated only in terms of two-orbital correlations, although the structure of multiorbital correlations is far richer; and, in the case of bonds established by more than two electrons, multiorbital correlations represent a more natural point of view. Here, for the first time, we introduce the true multiorbital correlation theory, consisting of a framework for handling the structure of multiorbital correlations, a toolbox of true multiorbital correlation measures, and the formulation of the multiorbital correlation clustering, together with an algorithm for obtaining that. These make it possible to characterise quantitatively, how well a bonding picture describes the chemical system. As proof of concept, we apply the theory for the investigation of the bond structures of several molecules. We show that the non-existence of well-defined multiorbital correlation clustering provides a reason for debated bonding picture.