Full Many-body Research Articles

Entropy and correlation functions of a driven quantum spin chain

We present an exact solution for a quantum spin chain driven through its critical points. Our approach is based on a many-body generalization of the Landau-Zener transition theory, applied to a fermionized spin Hamiltonian. The resulting nonequilibrium state of the system, while being a pure quantum state, has local properties of a mixed state characterized by finite entropy density associated with Kibble-Zurek defects. The entropy and the finite spin correlation length are functions of the rate of sweep through the critical point. We analyze the anisotropic $XY$ spin-$1∕2$ model evolved with a full many-body evolution operator. With the help of Toeplitz determinant calculus, we obtain an exact form of correlation functions. The properties of the evolved system undergo an abrupt change at a certain critical sweep rate, signaling the formation of ordered domains. We link this phenomenon to the behavior of complex singularities of the Toeplitz generating function.

A Quantum Many-Body Density Matrix Model for Sub-Femtosecond Transport in Mesoscopic Structures

Theoretical model for transient transport in mesoscopic structures was presented, and the approach with numerical simulation of a resonant-tunneling diode (RTD) was illustrated. A second-order master equation for the evolution of the many-body reduced density matrix of the active region was being introduced. This contains full quantum-mechanical information about the processes in the current-limiting active region. The master equation is derived directly form the Liouville equation for the active region+contacts, by using the partial-trace-free approach, and it incorporates the memory terms that describe the information exchange between the contacts and the active region. In this way, the state of the contacts is accounted for, but does not explicitly enter the calculation, allowing us to compute the full many-body reduced density matrix for the active region. The model accounts for the presence of the bias by assuming a special form of the forcing term in the master equation. The numerical simulation shows that incorporation of the memory terms is crucial for description of charging/discharging in the well, and obtaining the proper transient behavior. Electron-electron interaction between the active region and the contacts, as well as phonon scattering (within the relaxation-time approximation), have been taken into account.

The Asakura–Oosawa model in the protein limit: the role of many-body interactions

We study the Asakura–Oosawa model in the ‘protein limit’, where the penetrable sphere radiusRAO is much greater thanthe hard sphere radius Rc. The phase behaviour and structure calculated with a full many-body treatment showimportant qualitative differences when compared to a description based on pairpotentials alone. The overall effect of the many-body interactions is repulsive.

Evidence for intervalence band coherences in semiconductor quantum wells via coherently coupled optical Stark shifts.

We report the experimental observation of coherently coupled heavy-hole-light-hole Stark shifts, i.e., light-hole exciton shifts under heavy-hole exciton pumping conditions, in InGaAs quantum wells. The theoretical analysis of the data is based on a full many-body approach (dynamics-controlled truncation formalism) in the third-order nonlinear optical regime. It is shown that the Stark shift data can be interpreted as strong evidence of suitably defined nonradiative intervalence band coherences in a semiconductor quantum well. Hence, the observations establish a semiconductor analog of Raman coherences in three-level atoms.

Auger neutralization and de-excitation of helium at an aluminium surface: a unified treatment

The neutralization rate of He + and the de-excitation rates of excited He atoms in front of an Al surface are computed. This is achieved by evaluating the transition of electronic eigenstates of the He +–Al system to the He + core hole while producing surface excitations. These surface excitations are computed in a self-consistent way. The present work accounts for the full many-body excitation of the metal surface as well as the hybridization of the He–Al orbitals. This hybridization leads to a new qualitative picture of the Auger processes in which the neutralization and de-excitation processes are mixed.

Many-body calculation of the magnetic, optical, and charge-transfer spectra of solid oxygen in the alpha and beta phases.

The electronic spectra of \ensuremath{\alpha} and \ensuremath{\beta} solid ${\mathrm{O}}_{2}$ were calculated in a full many-body approach for a cluster consisting of four ${\mathrm{O}}_{2}$ molecules with periodic-boundary conditions. By including only the partially occupied \ensuremath{\pi} orbitals (16 spin orbitals, 8 electrons) the basis set consists of 12 870 many-electron states. The resulting spectra contains three basic types of excitations at very different energy ranges: (a) 81 states corresponding to the ground state and magnetic excitations (magnons) within 100 meV; (b) 1215 states of neutral molecular excitations (excitons) with energies from about 1 to 8 eV; and (c) 11 574 charge-transfer states with excitation energies up to 60 eV. Analysis of the properties of the ground states in both \ensuremath{\alpha} and \ensuremath{\beta} solid ${\mathrm{O}}_{2}$ has been carried out. The lowest many-body states, those that correspond to neutral, unexcited molecules, describe accurately the magnetic excitations of both solids. The two phases have very different spectra resulting, even at very low temperatures, in a sizeable difference in the (magnetic) entropy. The calculated entropy difference at the observed \ensuremath{\alpha}-\ensuremath{\beta} phase transition temperature agrees surprisingly well with the experimentally measured heat of transformation.

Magnetism and the αβ phase transition in solid oxygen

The electronic condition of α and β solid O 2 were calculated in a full many-body approach for a cluster consisting of four O 2 molecules with periodic boundary conditions. Only the partially occupied π orbitals (sixteen spin-orbitals, eight electrons) were included. The lowest 81 many-body states, which correspond to neutral, unexcited molecules, describe accurately the magnetic excitations of the solids. The two phases have very different spectra resulting, even at very low temperatures, in a large difference in the (magnetic) entropy. The calculated entropy difference at 23.9 K (the αβ phase transition temperature) agrees surprisingly well with the experimentally measured heat of transfomation.

Recent progress in the field of electron correlation

Electron correlation plays an important role in determining the properties of physical systems, from atoms and molecules to condensed phases. Recent theoretical progress in the field has proven possible using both analytical methods and numerical many-body treatments, for realistic systems as well as for simplified models. Within the models, one may mention the jellium and the Hubbard. The jellium model, while providing a simple, rough approximation to conduction electrons in metals, also constitutes a key ingredient in the treatment of electrons in condensed phases within density-functional formalism. The Hubbard- and the related Heisenberg-model Hamiltonians, on the other hand, are designed to treat situations in which very strong correlations tend to bring about site localization of electrons. The character of the interactions in these lattice models allows for a local treatment of correlations. This is achieved by the use of projection techniques that were first proposed by Gutzwiller for the multicenter problem, being the natural extension of the Coulson-Fischer treatment of the ${\mathrm{H}}_{2}$ molecule. Much work in this area is analytic or semianalytic and requires approximations. However, a full many-body treatment of both realistic and simplified models is possible by resorting to numerical simulations, i.e., to the so-called quantum Monte Carlo method. This method, which can be implemented in a number of ways, has been applied to atoms, molecules, and solids. In spite of continuing progress, technical problems still remain. Thus one may mention the fermion sign problem and the increase in computational time with the nuclear charge in atomic and related situations. Still, this method provides, to date, one of the most accurate ways to calculate correlation energies, both in atomic and in multicenter problems.

Independent-Cluster Parametrizations of Wave Functions in Model Field Theories: III. The Coupled-Cluster Phase Spaces and Their Geometrical Structure

In this third paper of a series we study the structure of the phase spaces of the independent-cluster methods. These phase spaces are classical symplectic manifolds which provide faithful descriptions of the quantum mechanical pure states of an arbitrary system. They are "superspaces" in the sense that the full physical many-body or field-theoretic system is described by a point of the space, in contrast to "ordinary" spaces for which the state of the physical system is described rather by the whole space itself. We focus attention on the normal and extended coupled-cluster methods (NCCM and ECCM). Both methods provide parametrizations of the Hilbert space which take into account in increasing degrees of completeness the connectivity properties of the associated perturbative diagram structure. This corresponds to an increasing incorporation of locality into the description of the quantum system. As a result the degree of nonlinearity increases in the dynamical equations that govern the temporal evolution and determine the equilibrium state. Because of the nonlinearity, the structure of the manifold becomes geometrically complicated. We analyse the neighbourhood of the ground state of the one-mode anharmonic bosonic field theory and derive the nonlinear expansion beyond the linear response regime. The expansion is given in terms of normal-mode amplitudes, which provide the best local coordinate system close to the ground state. We generalize the treatment to other nonequilibrium states by considering the similarly defined normal coordinates around the corresponding phase space point. It is pointed out that the coupled-cluster method (CCM) maps display such features as (an)holonomy, or geometric phase. For example, a physical state may be represented by a number of different points on the CCM manifold. For this reason the whole phase spaces in the NCCM or ECCM cannot be covered by a single chart. To account for this non-Euclidean nature we introduce a suitable pseudo-Riemannian metric structure which is compatible with an important subset of all canonical transformations. It is then shown that the phase space of the configuration-interaction method is flat, namely the complex Euclidean space; that the NCCM manifold has zero curvature even though its Reimann tensor does not vanish; and that the ECCM manifold is intrinsically curved. It is pointed out that with the present metrization many of the dimensions of the ECCM phase space are effectively compactified and that the overall topological structure of the space is related to the distribution of the zeros of the Bargmann wave function.

Extracting infinite system properties from finite size clusters: “phase randomization/boundary condition averaging”

When electron-electron correlations are important, it is often necessary touse “exact” numerical methods, such as Lanczös diagonalization, to study the full many-body Hamiltonian. Unfortunately, such exact diagonalization methods are restricted to small system sizes. We show that if the Hubbard U term is replaced by a “periodic Hubbard” term, the full many body Hamiltonian may be exactly solved, even for very large systems, though for low fillings. However, for half-filled systems and large U this approach is not only no longer exact, it no longer improves extrapolation to larger systems. We discuss how generalized “randomized variable averaging” (RVA) or “phase randomization” schemes can be reliably employed to improve extrapolation to large system sizes in this regime. This general approach can be combined with any many-body method and is thus of broad interest and applicability.

Surface magnetism in an exactly soluble many-body periodic-cluster model of bcc iron

An exact solution of a two-dimensionally periodic two-site cluster, a {l brace}001{r brace} two-layer thin film with body-centered-cubic (bcc) crystal structure, is presented for iron. The purpose is to study the surface magnetism of bcc iron in a full many-body approach. The model consists of five {ital d} orbitals per site per spin, with interatomic hopping terms, a one-electron occupation energy for each orbital, and an on-site Coulomb interaction of the fullest generality allowed by atomic symmetry. A realistic local-density-approximation single-particle electronic structure is used. Crystal-field effects in the iron-film structure are discussed. The many-body energy-level spectrum and thermodynamic averages of energy and spin of the system are calculated. The physical picture for the enhancement of magnetization at the true iron surface is discussed.

T=0 Green's function for the exciton

The excitons as electronic excitations of an insulator are obtained from the full manybody Hamiltonian by means of T=0Green's function techniques. Exciton amplitudes and energies are obtained via the vertex-part equation from an eigenvalue equation which in the Wannier limit is the effective-mass equation. A formula is obtained for the frequency dependent effective interaction whose static limit (ω=0) goes over into the Haken-Schottky dielectric-constant interaction for excitons of large electron-hole separations. A simple criterion will result to answer the question on when one is allowed to replace the frequency dependent interaction by its ω=0 limit.