Single-particle Density Research Articles

Lattice density-functional theory of the attractive Hubbard model

The attractive Hubbard model is investigated in the framework of lattice density-functional theory (LDFT). The ground-state energy $E=T+W$ is regarded as a functional of the single-particle density matrix ${\ensuremath{\gamma}}_{ij}$ with respect to the lattice sites, where $T[\ensuremath{\gamma}]$ represents the kinetic and crystal-field energies and $W[\ensuremath{\gamma}]$ the interaction energy. Aside from the exactly known functional $T[\ensuremath{\gamma}]$, we propose a simple scaling approximation to $W[\ensuremath{\gamma}]$, which is based on exact analytic results for the attractive Hubbard dimer and on a scaling hypothesis within the domain of representability of $\ensuremath{\gamma}$. As applications, we consider one-, two-, and three-dimensional finite and extended bipartite lattices having homogeneous or alternating onsite energy levels. In addition, the Bethe lattice is investigated as a function of coordination number. Results are given for the kinetic, Coulomb, and total energies, as well as for the density distribution ${\ensuremath{\gamma}}_{ii}$, nearest-neighbor bond order ${\ensuremath{\gamma}}_{ij}$, and pairing energy $\ensuremath{\Delta}{E}_{p}$, as a function of the interaction strength $|U|/t$, onsite potential $\ensuremath{\varepsilon}/t$, and band filling $n={N}_{e}/{N}_{a}$. Remarkable even-odd and super-even oscillations of $\ensuremath{\Delta}{E}_{p}$ are observed in finite rings as a function of band filling. Comparison with exact Lanczos diagonalizations and density-matrix renormalization-group calculations shows that LDFT yields a very good quantitative description of the properties of the model in the complete parameter range, thus providing a significant improvement over the mean-field approaches. Goals and limitations of the method are discussed.

Superheavy magic nuclei in Relativistic Hartree-Fock-Bogoliubov theory

The occurrence of the spherical shell closures in superheavy nuclear systems is explored within the relativistic Hartree-Fock-Bogoliubov (RHFB) theory with density- dependent meson-nucleon couplings. We use the two-nucleon gaps δ2n(p) and pairing gaps Δv(π) to characterize the shell effects. The results depend slightly on the forces used, but the general set of magic numbers beyond 208Pb are Z = 120, 138 and N = 172, 184, 228 and 258. Our calculations are in favor of the nuclide 304120 as the next spherical doubly magic nucleus. Combined with the bulk properties of symmetric matter, we find that the shell effects are sensitive to the values of both scalar mass and effective mass. These two masses essentially determine the spin-orbit splittings and single-particle level density, respectively. Furthermore, the breaking of relativistic pseudo-spin symmetry influences the level structure and the occurrence of closed shells.

Microscopic analysis of 11 Li elastic scattering on protons and breakup processes within 9Li+2n cluster model

Theoretical analysis of the elastic scattering and breakup in interactions of the 11Li nucleus with protons are presented. The hybrid model of the microscopic optical potential (OP) is applied. The OP includes the single-folding real part, while its imaginary part is derived within the high-energy approximation (HEA) theory. The spin-orbit contribution to the OP is also included. The differential cross sections of 11Li+p elastic scattering and the total reaction cross sections are calculated at energies of 62, 68.4, and 75 MeV/nucleon and are compared with the available experimental data. The breakup cross sections at 62 MeV/nucleon and the momentum distributions of the fragments using a two cluster model of the 11 Li nucleus are obtained. An analysis of the single-particle density of 11Li is performed.

Competition between pairing correlations and deformation from the odd-even mass staggering of francium and radium isotopes

The masses of $^{222,224,226\text{--}233}\mathrm{Fr}$ and $^{233,234}\mathrm{Ra}$ have been determined with the Penning-trap mass spectrometer ISOLTRAP at the ISOLDE facility at CERN, including the previously unknown mass and half-life of $^{233}\mathrm{Fr}$. We study the evolution of the odd-even staggering of binding energies along the francium and radium isotopic chains and of its lowest-order estimator, ${\ensuremath{\Delta}}^{3}(N)$. An enhancement of the staggering of ${\ensuremath{\Delta}}^{3}(N)$ is observed towards neutron number $N=146$, which points to contributions beyond pairing correlations. These contributions are investigated in the Hartree-Fock and Hartree-Fock-Bogoliubov approaches, emphasizing the connections to the single-particle level density and nuclear deformation.

A generalized complexity measure based on Rényi entropy

The intrinsic statistical complexities of finite many-particle systems (i.e., those defined in terms of the single-particle density) quantify the degree of structure or patterns, far beyond the entropy measures. They are intuitively constructed to be minima at the opposite extremes of perfect order and maximal randomness. Starting from the pioneering LMC measure, which satisfies these requirements, some extensions of LMC-Renyi type have been published in the literature. The latter measures were shown to describe a variety of physical aspects of the internal disorder in atomic and molecular systems (e.g., quantum phase transitions, atomic shell filling) which are not grasped by their mother LMC quantity. However, they are not minimal for maximal randomness in general. In this communication, we propose a generalized LMC-Renyi complexity which overcomes this problem. Some applications which illustrate this fact are given.

Nonequilibrium Dynamics of One-Dimensional Hard-Core Anyons Following a Quench: Complete Relaxation of One-Body Observables

We demonstrate the role of interactions in driving the relaxation of an isolated integrable quantum system following a sudden quench. We consider a family of integrable hard-core lattice anyon models that continuously interpolates between noninteracting spinless fermions and strongly interacting hard-core bosons. A generalized Jordan-Wigner transformation maps the entire family to noninteracting fermions. We find that, aside from the singular free-fermion limit, the entire single-particle density matrix and, therefore, all one-body observables relax to the predictions of the generalized Gibbs ensemble (GGE). This demonstrates that, in the presence of interactions, correlations between particles in the many-body wave function provide the effective dissipation required to drive the relaxation of all one-body observables to the GGE. This relaxation does not depend on translational invariance or the tracing out of any spatial domain of the system.

Understanding disorder-induced zero-bias anomalies in systems with short-range interactions: An atomic-limit perspective

Motivated by the novel electronic behaviors seen in transition-metal oxides, we look for physical insight into disordered, strongly correlated systems by exploring the atomic limit. In recent work, the atomic limit has provided a useful reference point in systems with strong local interactions. For comparison with experiments, the exploration of nonlocal interactions is of interest. In the atomic limit, both the case of on-site interactions alone and the case of infinite-range $(1/r)$ interactions are well understood; however, not so the intervening possibilities. Here we study the atomic limit of the extended Anderson-Hubbard model using classical Monte Carlo to calculate the single-particle density of states. We show that the combination of nearest-neighbor interactions and site disorder produces a zero-bias anomaly caused by residual charge ordering, and the addition of on-site interactions has a nonmonotonic effect on the depth of this zero-bias anomaly. A key conclusion is that the form of the density of states in this classical system strongly resembles density of states results obtained for the full extended Anderson-Hubbard model when $U<4V$.

Multiplicity fluctuation analysis of target residues in nucleus-emulsion collisions at a few hundred MeV/nucleon

Multiplicity fluctuation of the target evaporated fragments emitted in 290 MeV/u 12C-AgBr, 400 MeV/u 12C-AgBr, 400 MeV/u 20Ne-AgBr and 500 MeV/u 56Fe-AgBr interactions is investigated using the scaled factorial moment method in two-dimensional normal phase space and cumulative variable space, respectively. It is found that in normal phase space the scaled factorial moment (ln〈Fq〉) increases linearly with the increase of the divided number of phase space (lnM)for lower q-value and increases linearly with the increase of lnM, and then becomes saturated or decreased for a higher q-value. In cumulative variable space ln〈Fq〉 decreases linearly with increase of lnM. This indicates that no evidence of non-statistical multiplicity fluctuation is observed in our data sets. So, any fluctuation indicated in the results of normal variable space analysis is totally caused by the non-uniformity of the single-particle density distribution.

Singular behavior at the edge of Laughlin states

A distinguishing feature of fractional quantum Hall (FQH) states is a singular behavior of equilibrium densities at boundaries. In contrast to states at integer filling fraction, such quantum liquids posses an additional dipole moment localized near edges. It enters observable quantities such as universal dispersion of edge states and Lorentz shear stress. For a Laughlin state, this behavior is seen as a peak, or overshoot, in the single-particle density near the edge, reflecting a general tendency of electrons in FQH states to cluster near edges. We compute the singular edge behavior of the one-particle density by a perturbative expansion carried out around a completely filled Landau level. This correction is shown to fully capture the dipole moment and the major features of the overshoot observed numerically. Furthermore, it exhibits the Stokes phenomenon with the Stokes line at the boundary of the droplet, decaying like a Gaussian inside and outside the liquid with different decay lengths. In the limit of vanishing magnetic length, the shape of the overshoot is a singular double layer with a capacity that is a universal function of the filling fraction. Finally, we derive the edge dipole moment of Pfaffian FQH states. The result suggests an explicit connection between the magnitude of the dipole moment and the bulk odd viscosity.

Vibrational Properties of Hydrogen-Bonded Systems Using the Multireference Generalization to the "On-the-Fly" Electronic Structure within Quantum Wavepacket ab Initio Molecular Dynamics (QWAIMD).

We discuss a multiconfigurational treatment of the "on-the-fly" electronic structure within the quantum wavepacket ab initio molecular dynamics (QWAIMD) method for coupled treatment of quantum nuclear effects with electronic structural effects. Here, multiple single-particle electronic density matrices are simultaneously propagated with a quantum nuclear wavepacket and other classical nuclear degrees of freedom. The multiple density matrices are coupled through a nonorthogonal configuration interaction (NOCI) procedure to construct the instantaneous potential surface. An adaptive-mesh-guided set of basis functions composed of Gaussian primitives are used to simplify the electronic structure calculations. Specifically, with the replacement of the atom-centered basis functions positioned on the centers of the quantum-mechanically treated nuclei by a mesh-guided band of basis functions, the two-electron integrals used to compute the electronic structure potential surface become independent of the quantum nuclear variable and hence reusable along the entire Cartesian grid representing the quantum nuclear coordinates. This reduces the computational complexity involved in obtaining a potential surface and facilitates the interpretation of the individual density matrices as representative diabatic states. The parametric nuclear position dependence of the diabatic states is evaluated at the initial time-step using a Shannon-entropy-based sampling function that depends on an approximation to the quantum nuclear wavepacket and the potential surface. This development is meant as a precursor to an on-the-fly fully multireference electronic structure procedure embedded, on-the-fly, within a quantum nuclear dynamics formalism. We benchmark the current development by computing structural, dynamic, and spectroscopic features for a series of bihalide hydrogen-bonded systems: FHF(-), ClHCl(-), BrHBr(-), and BrHCl(-). We find that the donor-acceptor structural features are in good agreement with experiments. Spectroscopic features are computed using a unified velocity/flux autocorrelation function and include vibrational fundamentals and combination bands. These agree well with experiments and other theories.

Strictly finite-range potential for light and heavy nuclei

Strictly finite-range (SFR) potentials are exactly zero beyond their finite range. Single-particle energies and densities as well as S-matrix pole trajectories are studied in a few SFR potentials suited for the description of neutrons interacting with light and heavy nuclei. The SFR potentials considered are the standard cut-off Woods--Saxon (CWS) potentials and two potentials approaching zero smoothly: the SV potential introduced by Salamon and Vertse and the SS potential of Sahu and Sahu. The parameters of these latter were set so that the potentials may be similar to the CWS shape. The range of the SV and SS potentials scales with the cube root of the mass number of the core like the nuclear radius itself. For light nuclei a single term of the SV potential (with a single parameter) is enough for a good description of the neutron-nucleus interaction. The trajectories are compared with a bench-mark for which the starting points (belonging to potential depth zero) can be determined independently. Even the CWS potential is found to conform to this bench-mark if the range is identified with the cutoff radius. For the CWS potentials some trajectories show irregular shapes, while for the SV and SS potentials all trajectories behave regularly.

Blind deconvolution of density-matrix renormalization-group spectra

We present a numerical method for calculating piecewise smooth spectral functions of correlated quantum systems in the thermodynamic limit from the spectra of finite systems computed using the dynamical or correction-vector density-matrix renormalization group method. The key idea is to consider this problem as a blind deconvolution with an unknown kernel which causes both a broadening and finite-size corrections of the spectrum. In practice, the method reduces to a least-square optimization under non-linear constraints which enforce the positivity and piecewise smoothness of spectral functions. The method is demonstrated on the single-particle density of states of one-dimensional paramagnetic Mott insulators represented by the half-filled Hubbard model on an open chain. Our results confirm that the density of states has a step-like shape but no square-root singularity at the spectrum onset.

Microscopic-macroscopic method for studying single-particle level density of superheavy nuclei

The intrinsic level densities of superheavy nuclei in the a-decay chains of 296,298,300120 nuclei are calculated using the single-particle spectra obtained with the modified two-center shell model. The level density parameters are extracted and compared with their phenomenological values used in the calculations of the survival of excited heavy nuclei. The dependences of the level density parameters on the mass and charge numbers as well as on the ground-state shell corrections are studied.

Properties of single-particle states in a fully self-consistent particle-vibration coupling approach

The properties of single-particle states in the magic nuclei $^{40}\mathrm{Ca}$ and $^{208}\mathrm{Pb}$, in particular the energies, spectroscopic factors, and the effective mass, have been studied in a fully self-consistent particle-vibration coupling (PVC) approach within the framework of Skyrme energy density functional theory. All selected phonons are obtained by the random phase approximation, and the same Skyrme interaction is also used in the PVC vertex. We focus on the effect of the noncentral two-body spin-orbit and tensor interactions on the single-particle properties. It has been found that the contributions of those terms are important to improve the results for $^{208}\mathrm{Pb}$. The calculated single-particle energies and spectroscopic factors are compared to available experimental data. The single-particle level density around the Fermi surface is significantly increased due to the effect of PVC.

A multiscale variational approach to the kinetics of viscous classical liquids: The coarse-grained mean field approximation

A closed kinetic equation for the single-particle density of a viscous simple liquid is derived using a variational method for the Liouville equation and a coarse-grained mean-field (CGMF) ansatz. The CGMF ansatz is based on the notion that during the characteristic time of deformation a given particle interacts with many others so that it experiences an average interaction. A trial function for the N-particle probability density is constructed using a multiscale perturbation method and the CGMF ansatz is applied to it. The multiscale perturbation scheme is based on the ratio of the average nearest-neighbor atom distance to the total size of the assembly. A constraint on the initial condition is discovered which guarantees that the kinetic equation is mass-conserving and closed in the single-particle density. The kinetic equation has much of the character of the Vlasov equation except that true viscous, and not Landau, damping is accounted for. The theory captures condensation kinetics and takes much of the character of the Gross-Pitaevskii equation in the weak-gradient short-range force limit.

Effects ofδmesons in relativistic mean field theory

The effect of $\ensuremath{\delta}$- and $\ensuremath{\omega}\text{\ensuremath{-}}\ensuremath{\rho}$-meson cross couplings on asymmetry nuclear systems are analyzed in the framework of an effective field theory motivated relativistic mean field formalism. The calculations are done on top of the G2 parameter set, where these contributions are absent. To show the effect of $\ensuremath{\delta}$ meson on the nuclear system, we split the isospin coupling into two parts: (i) ${g}_{\ensuremath{\rho}}$ due to $\ensuremath{\rho}$ meson and (ii) ${g}_{\ensuremath{\delta}}$ for $\ensuremath{\delta}$ meson. Thus, our investigation is based on varying the coupling strengths of the $\ensuremath{\delta}$ and $\ensuremath{\rho}$ mesons to reproduce the binding energies of the nuclei $^{48}\mathrm{Ca}$ and $^{208}\mathrm{Pb}$. We calculate the root mean square radius, binding energy, single particle energy, density, and spin-orbit interaction potential for some selected nuclei and evaluate the ${L}_{\mathrm{sym}}$ and ${E}_{\mathrm{sym}}$ coefficients for nuclear matter as function of $\ensuremath{\delta}$- and $\ensuremath{\omega}\text{\ensuremath{-}}\ensuremath{\rho}$-meson coupling strengths. As expected, the influence of these effects are negligible for the symmetric nuclear system, but substantial for the contribution with large isospin asymmetry.

Ferromagnetic response of a “high-temperature” quantum antiferromagnet

We study the finite temperature antiferromagnetic phase of the ionic Hubbard model in the strongly interacting limit using quantum Monte Carlo based dynamical mean field theory. We find that the ionic potential plays a dual role in determining the antiferromagnetic order. A small ionic potential (compared to Hubbard repulsion) increases the super-exchange coupling in the projected sector of the model, leading to an increase in the Neel temperature of the system. A large ionic potential leads to resonance between projected antiferromagnetically ordered configurations and density ordered configurations with double occupancies, thereby killing antiferromagnetism in the system. This novel way of degrading antiferromagnetism leads to spin polarization of the low energy single particle density of states. The dynamic response of the system thus mimics ferromagnetic behaviour, although the system is still an antiferromagnet in terms of the static spin order.

Satellite structures in the spectral functions of the two-dimensional electron gas in semiconductor quantum wells: AGWplus cumulant study

We present theoretical calculations for the spectral functions and single-particle densities of states of the two-dimensional electron gas in semiconductor quantum wells at different electron densities using the $GW$ plus cumulant method. We compare our results to $GW$ only calculations and find significant differences in the description of the satellites between the two theories: While $GW$ theory predicts the existence of a plasmaron excitation, no such excitation is found in $GW$ plus cumulant theory. We compare our results to experimental tunneling spectra from semiconductor quantum wells and find good agreement for the satellite properties.

Effect of isospin asymmetry in a nuclear system

The effect of δ- and ω–ρ-meson cross couplings on asymmetry nuclear systems is analyzed in the framework of an effective field theory motivated relativistic mean field formalism. The calculations are done on top of the G2 parameter set, where these contributions are absent. We calculate the root mean square radius, binding energy, single particle energy (for the first and last occupied orbits), density and spin–orbit interaction potential for some selected nuclei and evaluate the Lsym- and Esym-coefficients for nuclear matter as a function of δ- and ω–ρ-meson coupling strengths. As expected, the influence of these effects is negligible for the symmetry nuclear system and these effects are very important for systems with large isospin asymmetry.

Uniform spin susceptibility and spin-gap phenomenon in the BCS-BEC-crossover regime of an ultracold Fermi gas

We investigate the uniform spin susceptibility $\chi_{\rm s}$ in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas. Including pairing fluctuations within the framework of an extended $T$-matrix approximation, we show that $\chi_{\rm s}$ exhibits non-monotonic temperature dependence in the normal state. In particular, $\chi_{\rm s}$ is suppressed near the superfluid phase transition temperature $T_{\rm c}$ due to strong pairing fluctuations. To characterize this anomalous behavior, we introduce the spin-gap temperature $T_{\rm s}$ as the temperature at which $\chi_{\rm s}$ takes a maximum value. Determining $T_{\rm s}$ in the whole BCS-BEC crossover region, we identify the spin-gap regime in the phase diagram of a Fermi gas in terms of the temperature and the strength of a pairing interaction. We also clarify how the spin-gap phenomenon is related to the pseudogap phenomenon appearing in the single-particle density of states. Our results indicate that an ultracold Fermi gas in the BCS-BEC crossover region is a very useful system to examine the pseudogap phenomenon and the spin-gap phenomenon in a unified manner.