Calculations For Finite Systems Research Articles

Effective Floquet model for minimally twisted bilayer graphene

We construct an effective Floquet lattice model for the triangular network that emerges in interlayer-biased minimally twisted bilayer graphene and which supports two chiral channels per link for a given valley and spin. We introduce the Floquet scheme with the one-channel triangular network and subsequently extend it to the two-channel case. From the bulk topological index (winding number) and finite system calculations, we find that both cases host anomalous Floquet insulators (AFIs) with a different gap-opening mechanism. In the one-channel network, either time-reversal or in-plane inversion symmetry has to be broken to open a gap. In contrast, in the two-channel network, interchannel coupling can open a gap without breaking these symmetries yielding a valley AFI with counterpropagating edge states. This phase is topologically trivial with respect to the total winding number but robust in the absence of intervalley scattering. Finally, we demonstrate the applicability of the Floquet model with magnetotransport calculations.

Ab initio derivation of model energy density functionals

I propose a simple and manageable method that allows for deriving coupling constants of model energy density functionals (EDFs) directly from ab initio calculations performed for finite fermion systems. A proof-of-principle application allows for linking properties of finite nuclei, determined by using the nuclear nonlocal Gogny functional, to the coupling constants of the quasilocal Skyrme functional. The method does not rely on properties of infinite fermion systems but on the ab initio calculations in finite systems. It also allows for quantifying merits of different model EDFs in describing the ab initio results.

Majorana Fermions and Z2 Vortices on a Square Lattice

We present a simple model of Majorana fermions on a square lattice, and study zero-energy states due to Z$_2$ vortices. We show the relationship between the Chern number of the ground state and the number of the zero-energy states by numerical calculations for finite systems. We also discuss the relationship for the bulk system by observing the change of the spectral asymmetry. We finally present an effective continuum model with O(2) gauge potential which shows a topological change of the index at a half-flux.

Exact results for finite quantum Hall systems of electrons at filling factor one: Disk geometry

We obtain exact analytical expressions for the total energy per particle and related quantities corresponding to a finite quantum Hall system of electrons in a disk geometry when filling factor of the Landau level is one. Such exact results apply to finite systems of electrons with an arbitrary number of particles. The reported calculations for finite systems of electrons in a disk geometry complement earlier calculations for finite systems of electrons in a simpler spherical geometry. The results we provide can serve as benchmarks to gauge the accuracy of various theoretical approximations and numerical methods used to study the properties of strongly correlated many-body systems.

Hartree-Fock Ground State of the Three-Dimensional Electron Gas

In 1962, Overhauser showed that within Hartree-Fock (HF) the electron gas is unstable to a spin-density wave state. Determining the true HF ground state has remained a challenge. Using numerical calculations for finite systems and analytic techniques, we study the unrestricted HF ground state of the three-dimensional electron gas. At high density, we find broken spin symmetry states with a nearly constant charge density. Unlike previously discussed spin wave states, the observed wave vector of the spin-density wave is smaller than 2k(F). The broken-symmetry state originates from pairing instabilities at the Fermi surface, a model for which is proposed.

On the accuracy of correlation-energy expansions in terms of local increments

The incremental scheme for obtaining the energetic properties of extended systems from wave-function-based ab initio calculations of small (embedded) building blocks, which has been applied to a variety of van der Waals-bound, ionic, and covalent solids in the past few years, is critically reviewed. Its accuracy is assessed by means of model calculations for finite systems, and the prospects for applying it to delocalized systems are given.

Upper critical field for anisotropic superconductivity: A tight-binding approach

We study the problem of the upper critical field ($H_{c2}$) for tight-binding electrons in a two-dimensional lattice. The external magnetic field is introduced into the model Hamiltonian both via the Peierls substitution and the Zeeman term. Carrying out calculations for finite systems we analyze the influence of the external field in the commensurable and incommensurable case on an equal footing. The upper critical field has been discussed for intrasite as well as anisotropic intersite pairing that, in the absence of magnetic field, has a $d_{x^2-y^2}$ symmetry. A comparison of $H_{c2}$ determined for different symmetries shows that the on-site pairing is more affected by the external field i.e., the critical temperature for the on-site pairing decreases with the increase of the magnetic field faster than in the anisotropic case. Moreover, we have shown that the tight-binding form of the Bloch energy can lead to the upward curvature of $H_{c2}$, provided that the Fermi level is close enough to the van Hove singularity.

Initiation of combustion waves in solids, and the effects of geometry

AbstractIn a recent paper Weber et al. [9] examined the propagation of combustion waves in a semi-infinite gaseous or solid medium. Whereas their main concern was the behaviour of waves once they had been initiated, we concentrate here on the initiation of such waves in a solid medium and have not examined in detail the steadiness or otherwise of the waves subsequent to their formation. The investigation includes calculations for finite systems. The results for a slab, cylinder and sphere are compared.Critical conditions for initiation of ignition by a power source are established. For a slab the energy input is spread uniformly over one boundary surface. In the case of cylindrical or spherical symmetry it originates from a cylindrical core or from a small, central sphere, respectively. The size of source and reactant body is important in the last two cases. With the exception of the initial temperature distribution, the equations investigated are similar in form to those of Weber et al. [5,9] and, as a prelude to the present study, with very simple adaptation, it has been possible to reproduce the results of the earlier work. We then go on to report the result of calculations for the initiation of ignition under different geometries with various initial and boundary conditions.

Properties of strange hadronic matter in bulk and in finite systems

The hyperon-hyperon potentials due to a recent SU(3) Nijmegen soft-core potential model are incorporated within a relativistic mean field calculation of strange hadronic matter. We find considerably higher binding energy in bulk matter compared to several recent calculations which constrain the composition of matter. For small strangeness fractions ${(f}_{S}\ensuremath{\lesssim}1),$ matter is dominated by $N\ensuremath{\Lambda}\ensuremath{\Xi}$ composition and the calculated binding energy closely follows that calculated by using the hyperon potentials of our previous calculations. For larger strangeness fractions ${(f}_{S}\ensuremath{\gtrsim}1),$ the calculated binding energy increases substantially beyond any previous calculation due to a phase transition into $N\ensuremath{\Sigma}\ensuremath{\Xi}$ dominated matter. We also compare bulk matter calculations with finite system calculations, again highlighting the consequences of reducing the Coulomb destabilizing effects in finite strange systems.

Supercell technique for total-energy calculations of finite charged and polar systems

We study the behavior of total-energy supercell calculations for dipolar molecules and charged clusters. Using a cutoff Coulomb interaction within the framework of a plane-wave basis set formalism, with all other aspects of the method (pseudopotentials, basis set, exchange-correlation functional) unchanged, we are able to assess directly the interaction effects present in the supercell technique. We find that the supercell method gives structures and energies in almost total agreement with the results of calculations for finite systems, even for molecules with large dipole moments. We also show that the performance of finite-grid calculations can be improved by allowing a degree of aliasing in the Hartree energy, and by using a reciprocal space definition of the cutoff Coulomb interaction.

Physical manifestations of valence-bond structures in correlated systems

Using the Hubbard model and the corresponding t-J model, we study the properties of correlated states with valence-bond structures. Mixed states with such structures and with antiferromagnetic spin ordering can be constructed by means of local unitary transformations of uncorrelated states. The latter turn out to have lower energy than mean-field antiferromagnetic solutions. Spin correlations for various degrees of doping δ=n−1 are in good agreement with the results of exact calculations for finite systems. In contrast to mean-field solutions, allowance for valence-bond correlations leads to a reasonable value of the critical δ, at which long-range antiferromagnetic order disappears. A calculation of the spectral functions that describe photoemission reveals typical behavior in two bands of effective hole (and electron) excitations, and energy transport in bands as the quasimomentum varies from (0,0) to (π,π), consistent with calculations in finite systems. We construct a homogeneous correlated state of fluctuating valence bonds (the band-model analog of states of fluctuating valence bonds), and demonstrate that its energy is lower than that of valence-bond alternant structures.

A VARIATIONAL BETHE-ANSATZ APPROACH TO THE HEISENBERG ANTIFERROMAGNET AT NON-ZERO FIELD

The antiferromagnetic Heisenberg chain with axial anisotropy and applied magnetic field parallel to the axis, is probed through a new variational approach based on the Bethe–Ansatz solution at zero field. The variational ket is built by rotating the spins in the Bethe solution, with the angles and the value of the local magnetic moment as variational parameters. This procedure allows for a description of the various magnetic phases in the presence of a parallel field, such as ferromagnetic (F), antiferromagnetic (AF), and spin-flop (SF) phases. The approximation reduces to the exact Bethe solution for vanishing field. We compare with exact numerical results (Lanczos calculations for finite systems), and exact solutions when available.

Collapse of the fractional quantum Hall effect in a parabolic quantum well.

We study using finite-system calculations, the behavior of the quasiparticle-quasihole energy gap and the collective excitation energy gap of a parabolically confined quasi-two-dimensional electron system subjected to a perpendicular magnetic field. We find the collapse of the energy gap as the areal density of the electron system is increased. Our results, which are in an excellent qualitative agreement with recent experiments, indicate that the collapse of the fractional quantum Hall effect in a parabolic quantum well is due to the electric-subband mixing. The effect of the finite layer thickness is also discussed

Fractional quantum Hall effect in a parabolic quantum well in tilted magnetic fields.

The quasiparticle-quasihole energy gap is studied for a parabolically confined quasi-two-dimensional electron system subjected to a tilted magnetic field. The energy gap is obtained using finite system calculations in a periodic rectangular geometry, and the single-particle mode coupling due to tilting of the magnetic field and the level mixing due to the interparticle Coulomb interaction are taken into account. Spin-polarized electron systems are considered and it is found that adding the magnetic field, parallel to the quasi-two-dimensional electron system, decreases the quasiparticle-quasihole energy gap and compresses the electron system to be thinner. Our results indicate that it is possible to observe a collapse of the fractional quantum Hall effect in a wide parabolic quantum well by tilting the magnetic field.

Methodology for relativistic Hartree calculations

An efficient method for performing relativistic Hartree calculations for finite systems is described. The method combines a derivative expansion of the high-energy contributions to the induced vacuum polarization density with a numerical evaluation of the low-energy contributions, allowing calculations to be performed with a minimum of numerical work. The method is applied to theories of fermions coupled to scalar mesons in 1 + 1 dimensions as an illustration.

Thermal properties of the ±J infinite-range Sherrington-Kirkpatrick model by analysis of the partition function zeros

An explicit and simple (approximated) solution of the ± J infinite-range Sherrington-Kirkpatrick (SK) model of spin glasses is presented: standard thermodynamic functions, valid for all temperatures, are derived by analysis of the partition function zeros in the complex temperature plane. Learning from computer calculations in finite systems, general thermodynamic considerations and a subsidiary heuristic assumption are used. The ground state energy is found to be −(6 log 2+5)/12 ≈ −0.76324, and the low-temperature specific heat as well the entropy are quadratic: 1.5 T 2 and 0.75 T 2 respectively.

Quasi-elastic Coulomb response function for finite systems and elimination of the Landau ghost in the relativistic σ-ω model

The quasi-elastic Coulomb response function of finite nuclei including vacuum polarization effects is investigated in the relativistic σ-ω model. For the consistent elimination of the Landau ghost in meson propagators, the description of the ground state and the response function of the system is formulated utilizing the effective action method, and the effects of the ghost elimination on the nuclear matter response function are discussed. Finite system calculations are performed for 12 C (|q|= 300, 400, 550 MeV) and 40 Ca (|q|= 410, 500, 550 MeV) , in which particle-hole continuum states are fully taken into account by the method of continuum RPA, while the vacuum polarization effects are included by the local density approximation. The effects of the particle-hole effective interaction and the medium modified single-nucleon form factor on the response function are also discussed.

Implication of nonintegral occupation number and Fermi-Dirac statistics in the local-spin-density approximation applied to finite systems.

In electronic-structure calculations for finite systems using the local-spin-density (LSD) approximation, it is assumed that the eigenvalues of the Kohn-Sham equation should obey Fermi-Dirac (FD) statistics. In order to comply with this assumption for some of the transition-metal atoms, a nonintegral occupation number is used which also minimizes the total energy. It is shown here that for finite systems it is not necessary that the eigenvalues of the Kohn-Sham equation obey FD statistics. It is also shown that the Kohn-Sham exchange potential used in all LSD models is correct only for integer occupation number. With a noninteger occupation number the LSD exchange potential will be smaller than that given by the Kohn-Sham potential. Ab initio self-consistent spin-polarized calculations have been performed numerically for the total energy of an iron atom. It is found that the ground state belongs to the 3d/sup 6/4s/sup 2/ configuration. The ionization potentials of all the Fe/sup n//sup +/ ions are reported and are in agreement with experiment.

Valence bond analysis of the Kondo chain Hamiltonian

Accurate extrapolations for the ground state energy per site of the one - dimensional Kondo chain system is obtained from exact finite system calculations carried out employing a valence bond scheme. An analysis of the ground state wave function indicates that the localized spin is quenched for all nonzero values of the Kondo exchange constant in one dimension.

Rotational ordering and symmetry breaking in the triangular antiferromagnetic Heisenberg lattice

Finite system calculations suggest a rotational ordering in the ground state of the triangular antiferromagnetic Heisenberg lattice. This rotational ordering may result in a rotational symmetry breaking for quantum-spin systems, which does not show a net sublattice magnetization.