Realistic Hamiltonian Research Articles

Combining symmetry breaking and restoration with configuration interaction: A highly accurate many-body scheme applied to the pairing Hamiltonian

Background: Ab initio many-body methods have been developed over the past ten years to address mid-mass nuclei... As progress in the design of inter-nucleon interactions is made, further efforts must be made to tailor many-body methods. Methods: We formulate a truncated configuration interaction method that consists of diagonalizing the Hamiltonian in a highly truncated subspace of the total N-body Hilbert space. The reduced Hilbert space is generated via the particle-number projected BCS state along with projected seniority-zero two and four quasi-particle excitations. Furthermore, the extent by which the underlying BCS state breaks U(1) symmetry is optimized in presence of the projected two and four quasi-particle excitations... The quality of the newly designed method is tested against exact solutions of the so-called attractive pairing Hamiltonian problem. Results: By construction, the method reproduce exact results for N=2 and N=4. For N=(8,16,20) the error on the ground-state correlation energy is less than (0.006, 0.1, 0.15) % across the entire range of inter-nucleon coupling defining the pairing Hamiltonian and driving the normal-to-superfluid quantum phase transition. The presently proposed method offers the advantage to automatically access the low-lying spectroscopy, which it does with high accuracy. Conclusions: The numerical cost of the newly designed variational method is polynomial (N$^6$) in system size. It achieves an unprecedented accuracy on the ground-state correlation energy, effective pairing gap and one-body entropy as well as on the excitation energy of low-lying states of the attractive pairing Hamiltonian. This constitutes a strong enough motivation to envision its application to realistic nuclear Hamiltonians in view of providing a complementary, accurate and versatile ab initio description of mid-mass open-shell nuclei in the future.

Core polarization and modern realistic shell-model Hamiltonians

The understanding of the convergence properties of the shell-model effective Hamiltonian, within the framework of the many-body perturbation theory, is a long-standing problem. The infinite summation of a certain class of diagrams, the so-called “bubble diagrams,” may be provided calculating the Kirson–Babu–Brown induced interaction, and provides a valid instrument to study whether or not the finite summation of the perturbative series is well-grounded. Here, we perform an application of the calculation of the Kirson–Babu–Brown induced interaction to derive the shell-model effective Hamiltonian for [Formula: see text]-shell nuclei starting from a modern nucleon–nucleon potential, obtained by way of the chiral perturbation theory. The outcome of our calculation is compared with a standard calculation of the shell-model Hamiltonian, where the core-polarization effects are calculated only up to third-order in perturbation theory. The results of the two calculations are very close to each other, evidencing that the perturbative approach to the derivation of the shell-model Hamiltonian is still a valid tool for nuclear structure studies.

How Static Disorder Mimics Decoherence in Anisotropy Pump-Probe Experiments on Purple-Bacteria Light Harvesting Complexes.

Anisotropy pump-probe experiments have provided insights into the character of excitons formed in photosynthetic complexes. Rapid decay in the observed anisotropy is cited as evidence of the strength of coupling of the excitonic degrees of freedom to their environment. Here we show that ensemble averaging over realistic model Hamiltonians leads to a rapid decay of anisotropy to a value close to the observed asymptote, and at a rate comparable to observed decay rates, even in the absence of coupling to the environment. While coupling to the environment will clearly play a role in the dynamics of such systems, our calculations suggest that caution is needed in deducing the strength of this coupling from anisotropy experiments. We also set out to clarify the nature of the quantum states and processes involved in the dynamics of such systems and the associated terminology.

Finding and proving the exact ground state of a generalized Ising model by convex optimization and MAX-SAT

Lattice models, also known as generalized Ising models or cluster expansions, are widely used in many areas of science and are routinely applied to alloy thermodynamics, solid-solid phase transitions, magnetic and thermal properties of solids, and fluid mechanics, among others. However, the problem of finding the true global ground state of a lattice model, which is essential for all of the aforementioned applications, has remained unresolved, with only a limited number of results for highly simplified systems known. In this article, we present the first general algorithm to find the exact ground states of complex lattice models and to prove their global optimality, resolving this fundamental problem in condensed matter and materials theory. We transform the infinite-discrete-optimization problem into a pair of combinatorial optimization (MAX-SAT) and non-smooth convex optimization (MAX-MIN) problems, which provide upper and lower bounds on the ground state energy respectively. By systematically converging these bounds to each other, we find and prove the exact ground state of realistic Hamiltonians whose solutions are completely intractable via traditional methods. Considering that currently such Hamiltonians are solved using simulated annealing and genetic algorithms that are often unable to find the true global energy minimum, and never able to prove the optimality of their result, our work opens the door to resolving long-standing uncertainties in lattice models of physical phenomena.

Exciton Dynamics in Phthalocyanine Molecular Crystals

The exciton transport properties of an octa(butyl)-substituted metal-free phthalocyanine (H2-OBPc) molecular crystal have been explored by means of a combined computational (molecular dynamics and electronic structure calculations) and theoretical (model Hamiltonian) approximation. The excitonic couplings in phthalocyanines, where multiple quasi-degenerate excited states are present in the isolated chromophore, are computed with a multistate diabatization scheme which is able to capture both short- and long-range excitonic coupling effects. Thermal motions in phthalocyanine molecular crystals at room temperature cause substantial fluctuation of the excitonic couplings between neighboring molecules (dynamic disorder). The average values of the excitonic couplings are found to be not much smaller than the reorganization energy for the excitation energy transfer, and the commonly assumed incoherent regime for this class of materials cannot be invoked. A simple but realistic model Hamiltonian is proposed to s...

Vortex line in the unitary Fermi gas

We report diffusion Monte Carlo results for the ground state of unpolarized spin-1/2 fermions in a cylindrical container and properties of the system with a vortex-line excitation. The density profile of the system with a vortex line presents a non-zero density at the core. We calculate the ground-state energy per particle, the superfluid pairing gap, and the excitation energy per particle. These simulations can be extended to calculate the properties of vortex excitations in other strongly interacting systems, such as superfluid neutron matter using realistic nuclear Hamiltonians.

Polynomial similarity transformation theory: A smooth interpolation between coupled cluster doubles and projected BCS applied to the reduced BCS Hamiltonian

We present a similarity transformation theory based on a polynomial form of a particle-hole pair excitation operator. In the weakly correlated limit, this polynomial becomes an exponential, leading to coupled cluster doubles. In the opposite strongly correlated limit, the polynomial becomes an extended Bessel expansion and yields the projected BCS wavefunction. In between, we interpolate using a single parameter. The effective Hamiltonian is non-hermitian and this Polynomial Similarity Transformation Theory follows the philosophy of traditional coupled cluster, left projecting the transformed Hamiltonian onto subspaces of the Hilbert space in which the wave function variance is forced to be zero. Similarly, the interpolation parameter is obtained through minimizing the next residual in the projective hierarchy. We rationalize and demonstrate how and why coupled cluster doubles is ill suited to the strongly correlated limit whereas the Bessel expansion remains well behaved. The model provides accurate wave functions with energy errors that in its best variant are smaller than 1\% across all interaction stengths. The numerical cost is polynomial in system size and the theory can be straightforwardly applied to any realistic Hamiltonian.

Self-consistent second-order Green's function perturbation theory for periodic systems.

Despite recent advances, systematic quantitative treatment of the electron correlation problem in extended systems remains a formidable task. Systematically improvable Green's function methods capable of quantitatively describing weak and at least qualitatively strong correlations appear as promising candidates for computational treatment of periodic systems. We present a periodic implementation of temperature-dependent self-consistent 2nd-order Green's function (GF2) method, where the self-energy is evaluated in the basis of atomic orbitals. Evaluating the real-space self-energy in atomic orbitals and solving the Dyson equation in k-space are the key components of a computationally feasible algorithm. We apply this technique to the one-dimensional hydrogen lattice--a prototypical crystalline system with a realistic Hamiltonian. By analyzing the behavior of the spectral functions, natural occupations, and self-energies, we claim that GF2 is able to recover metallic, band insulating, and at least qualitatively Mott regimes. We observe that the iterative nature of GF2 is essential to the emergence of the metallic and Mott phases.

Quantum effects in ultrafast electron transfers within cryptochromes.

Cryptochromes and photolyases are flavoproteins that may undergo ultrafast charge separation upon electronic excitation of their flavin cofactors. Charge separation involves chains of three or four tryptophan residues depending on the protein of interest. The molecular mechanisms of these processes are not completely clear. In the present work we investigate the relevance of quantum effects like the occurrence of nuclear tunneling and of coherences upon charge transfer in Arabidopsis thaliana cryptochromes. The possible breakdown of the Condon approximation is also investigated. We have devised a simulation protocol based on the realization of molecular dynamics simulations on diabatic potential energy surfaces defined at the hybrid constrained density functional theory/molecular mechanics level. The outcomes of the simulations are analyzed through various dedicated kinetics schemes related to the Marcus theory that account for the aforementioned quantum effects. MD simulations also provide a basic material to define realistic model Hamiltonians for subsequent quantum dissipative dynamics. To carry out quantum simulations, we have implemented an algorithm based on the Hierarchical Equations of Motion. With this new tool in hand we have been able to model the electron transfer chain considering either two- or three-state models. Kinetic models and quantum simulations converge to the conclusion that quantum effects have a significant impact on the rate of charge separation. Nuclear tunneling involving atoms of the tryptophan redox cofactors as well as of the environment (protein atoms and water molecules) is significant. On the other hand non-Condon effects are negligible in most simulations. Taken together, the results of the present work provide new insights into the molecular mechanisms controlling charge separation in this family of flavoproteins.

Description of the four-nucleon collisions by including breakup

Four-nucleon reactions above the breakup threshold are described by solving Faddeev-Yakubovsky equations for the realistic nuclear Hamiltonians. Complex-scaling method is applied in order to simplify the boundary conditions.

Erratum: More realistic Hamiltonians for the fractional quantum Hall regime in GaAs and graphene [Phys. Rev. B87, 245129 (2013)

Erratum: More realistic Hamiltonians for the fractional quantum Hall regime in GaAs and graphene [Phys. Rev. B<b>87</b>, 245129 (2013)

Finite temperature orbital and spin magnetism of small Fe linear chains

The finite temperature spin and orbital magnetism of FeN linear chains is theoretically studied in the framework of a spin fluctuation theory based on a realistic d-band model Hamiltonian, which includes the spin–orbit coupling interaction in a non-perturbative way. Spin and orbital magnetic moments are calculated as a function of the temperature by using an exchange Monte Carlo method that takes into account in a full way the short-range magnetic order. The finite temperature anisotropy effects on the spin and orbital cluster moment values are analysed by considering magnetization directions perpendicular to and along the chain axis. The temperature dependence of the orbital cluster moment follows a general trend similar to that of the spin one and shows clear anisotropy effects at low and intermediate temperatures, before total thermal disorder appears. Interesting anisotropy effects driven by thermal spin fluctuations are also observed for the spin results in most of the systems.

Phonon-assisted ultrafast charge separation in the PCBM band structure

Organic solar cells must separate strongly bound electron-hole pairs into free charges. This is achieved at interfaces between electron donor and acceptor organic semiconductors. The most popular electron acceptor is the fullerene derivative PCBM. Electron-hole separation has been observed on femtosecond timescales, which is incompatible with conventional Marcus theories of organic transport. In this work we show that ultrafast charge transport in PCBM arises from its broad range of electronic eigenstates, provided by the presence of three closely spaced delocalised bands near the LUMO level. Vibrational fluctuations enable rapid transitions between these bands, which drives an electron transport of $\sim$3 nm within 100 fs. All this is demonstrated within a realistic tight binding Hamiltonian containing transfer integrals no larger than 8 meV.

Solution of the Multiparticle Scattering Problems in Configuration Space by Using Trivial Boundary Conditions

A formalism based on the complex-scaling method is used to solve a four-nucleon scattering problem above the breakup threshold using the realistic nuclear Hamiltonians. This method allows to solve diverse scattering problems based on very trivial boundary conditions and is compatible with the techniques used to solve bound state problems.

Nuclear clustering using a modern shell model approach

Nuclear clustering, alpha decays, and multiparticle correlations are important components of nuclear dynamics. In this work we put forward the cluster-nucleon configuration interaction model. We use the modern configuration interaction approach with advanced realistic shell-model Hamiltonians in order to study clustering phenomena; the study is facilitated by the algebraic properties of many-nucleon configurations in the harmonic oscillator basis. Using a translationally invariant formalism we built cluster channels that satisfy the Pauli exclusion principle as well as orthogonality and normalization conditions. We formally justify the formalism and demonstrate that, within the new method, clustering strengths satisfy sum rules that are consistent with the statistical properties of nuclear reactions with composite particles. Using properly renormalized cluster form factors our approach appears to resolve long-standing problems related to absolute normalization of the alpha clustering spectroscopic factors and their behavior in $sd$-shell nuclei. Our methods are demonstrated in studies of $\ensuremath{\alpha}$ spectroscopic factors in $sd$-shell nuclei and in $^{16}\mathrm{O}$ treated in $p\ensuremath{-}sd$ shells. Comparison with experimental data supports the validity of the approach.

Effective-interaction approach to the Fermi hard-sphere system

The formalism based on correlated basis functions and the cluster expansion technique has been recently employed to derive an effective interaction from a realistic nuclear hamiltonian. To gauge the reliability of this scheme, we perform a systematic comparison between the results of its application to the Fermi hard-sphere system and the predictions obtained from low-density expansions, as well as from other many-body techniques. The analysis of a variety of properties, including the ground state energy, the effective mass and the momentum distribution, shows that the effective interaction approach is remarkably accurate, thus suggesting that it may be employed to achieve a consistent description of the structure and dynamics of nuclear matter in the density region relevant to astrophysical applications.

Spin superradiance by magnetic nanomolecules and nanoclusters

Spin dynamics of assemblies of magnetic nanomolecules and nanoclusters can be made coherent by inserting the sample into a coil of a resonant electric circuit. Coherence is organized through the arising feedback magnetic field of the coil. The coupling of a magnetic sample with a resonant circuit induces fast spin relaxation and coherent spin radiation, that is, superradiance. We consider spin dynamics described by a realistic Hamiltonian, typical of magnetic nanomolecules and nanoclusters. The role of magnetic anisotropy is studied. A special attention is paid to geometric effects related to the mutual orientation of the magnetic sample and resonator coil.

The Nuclear Pairing Gap – How Low Can It Go?

The pairing gap for 53Ca obtained from new experimental data on the masses of 52-54Ca has the smallest value yet observed. This is explained in the framework of the nuclear shell model with schematic and realistic Hamiltonians as being due to shell gaps around the low-j orbital 1p1/2. Minima in the pairing gaps for all nuclei are shown and discussed.

Application of the complex scaling method for few-body scattering problems including the breakup

A formalism based on the complex-scaling method is used to solve a few-particle scattering problem in configuration space. This method allows to use trivial boundary conditions and is compatible with most of the bound state techniques. In this contribution calculations of neutron scattering on triton is presented using realistic nuclear Hamiltonians for neutron energies above four-nucleon breakup threshold.

Local Hamiltonians for quantitative Green's function embedding methods.

Embedding calculations that find approximate solutions to the Schrödinger equation for large molecules and realistic solids are performed commonly in a three step procedure involving (i) construction of a model system with effective interactions approximating the low energy physics of the initial realistic system, (ii) mapping the model system onto an impurity Hamiltonian, and (iii) solving the impurity problem. We have developed a novel procedure for parametrizing the impurity Hamiltonian that avoids the mathematically uncontrolled step of constructing the low energy model system. Instead, the impurity Hamiltonian is immediately parametrized to recover the self-energy of the realistic system in the limit of high frequencies or short time. The effective interactions parametrizing the fictitious impurity Hamiltonian are local to the embedded regions, and include all the non-local interactions present in the original realistic Hamiltonian in an implicit way. We show that this impurity Hamiltonian can lead to excellent total energies and self-energies that approximate the quantities of the initial realistic system very well. Moreover, we show that as long as the effective impurity Hamiltonian parametrization is designed to recover the self-energy of the initial realistic system for high frequencies, we can expect a good total energy and self-energy. Finally, we propose two practical ways of evaluating effective integrals for parametrizing impurity models.