Recent Progress in Many-Body Theories

CONTENTS.

PREFACE.

SERIES EDITORIAL BOARD AND OTHER COMMITTEES.

FOREWORD BY THE EDITORS.

No abstract received.

Attempting to describe the "collapse of the wave function" of the orthodox quantum theory as a physical process, a natural assumption is that the measurement apparatus is subject to the same physical laws as the measured object, leading to a theory without rules for measurement. This - together with the loss of classical-quantum correspondence for chaotic systems - enforces the inclusion of the environment. I very shortly describe the present state of the art in this field - a challenge for the quantum many body community.

A consistent approach to Hamiltonian SU(N) lattice gauge field theory is developed using the maximal-tree gauge and an appropriately chosen set of angular variables. The various constraints are carefully discussed, as is a practical means for their implementation. A complete set of variables for the colourless sector is thereby determined. We show that the one-plaquette problem in SU(N) gauge theory can be mapped onto a problem of N fermions on a torus, which is solved numerically for the low-lying energy spectra for N ≤ 5. We end with a brief discussion of how to extend the approach to include the spatial (inter-plaquette) correlations of the full theory, by using a coupled-cluster method parametrisation of the full wave functional.

No abstract received.

Advances in statistical learning theory present the opportunity to develop statistical models of quantum many-body systems exhibiting remarkable predictive power. The potential of such "theory-thin" approaches is illustrated with the application of Support Vector Machines (SVMs) to global prediction of nuclear properties as functions of proton and neutron numbers Z and N across the nuclidic chart. Based on the principle of structural-risk minimization, SVMs learn from examples in the existing database of a given property Y, automatically and optimally identify a set of "support vectors" corresponding to representative nuclei in the training set, and approximate the mapping (Z, N) → Y in terms of these nuclei. Results are reported for nuclear masses, beta-decay lifetimes, and spins/parities of nuclear ground states. These results indicate that SVM models can match or even surpass the predictive performance of the best conventional "theory-thick" global models based on nuclear phenomenology.

No abstract received.

Macroscopic systems of hydrogen molecules exhibit a rich thermodynamic phase behavior. Due to the simplicity of the molecular constituents a detailed exploration of the thermal properties of these boson systems at low temperatures is of fundamental interest. Here, we report theoretical and experimental results on various spatial correlation functions and corresponding distributions in momentum space of liquid para-hydrogen close to the triple point. They characterize the structure of the correlated liquid and provide information on quantum effects present in this Bose fluid. Numerical calculations employ Correlated Density-Matrix (CDM) theory and Path-Integral Monte-Carlo(PIMC)simulations. A comparison of these theoretical results demonstrates the accuracy of CDM theory. This algorithm therefore permits a fast and efficient quantitative analysis of the normal phase of liquid para-hydrogen. We compare and discuss the theoretical results with available experimental data.

In this work, we study transport currents in excited states. This requires the calculation of particle currents to second order in the excitation amplitudes. For that purpose, we take a well-tested microscopic theory of inhomogeneous quantum liquids and extend it to find the mass currents created when atoms scatter off a surface or when excitations evaporate atoms. This is the first theoretical study of transport phenomena in a quantum liquid based on a quantitative microscopic theory.

We present theoretical results for the radial distribution function g(r) and the static liquid structure function S(k) of liquid para-hydrogen at low temperatures. The results have been obtained via quantum Monte Carlo Path Integral simulations, classical Monte Carlo calculations, and correlated density matrix theory.

Static and dynamic properties of a weakly interacting Bose gas of Hard Spheres in three dimensions are studied in the framework of the Correlated Basis Functions (CBF) approximation. Results are compared with explicit expressions for the same quantities derived within the Bogoliubov model. Despite the good agreement in the energy of the groundstate and the excited states, other quantities such as the dynamic structure function present important differences that become more significant when the density is raised.

Diffusion Monte Carlo calculations have been systematically performed to analyze the stability of small mixed ³He-⁴He clusters, as well as their excitation spectra. The picture that emerges is that of systems with strong shell effects whose binding and excitation energies are essentially determined by the monopole properties of an effective Hamiltonian.

We address the question if the ground state of solid ⁴He has the number of lattice sites equal to the number of atoms (commensurate state) or if it is different (incommensurate state). We point out that energy computation from simulation as performed by now cannot be used to decide this question and that the presently best variational wave function, a shadow wave function, gives an incommensurate state. We have extended the calculation of the one–body density matrix ρ₁ to the exact Shadow Path Integral Ground State method. Calculation of ρ₁ at ρ = 0.031 Å^-3 shows that Vacancy–Interstitial pair processes are present also in the exact computation but the simulated system size is is too small to infer the presence of off–diagonal long range order. Variational simulations of ⁴He confined in a narrow cylindrical pore are also discussed.

The recent observation of non-classical rotational inertia in solid ⁴He for temperatures T < 200 mK, and the continued non-observation of unusual flow associated with "zero-point defectons", favors the Leggett picture of Non-Classical Rotational Inertia over the Andreev-Lifshitz zero-point defecton picture of possible superflow in this system. We discuss the nature of the wavefunction, the Leggett one-body phase function upper bound for the superfluid fraction, and more complex forms for the phase-function and how this affects the net momentum density of this many-body system. The general properties of quantum vortices in such a system are briefly discussed.

A recent interatomic potential, that includes two- and three-body interactions, is used to study the liquid and solid equations of state of ⁴He and other properties of this system. The high-order contributions are explicitly computed by multi-weight diffusion Monte Carlo. It turns out that this is an excellent interatomic potential for the description of condensed phases of helium atoms systems.

Adsorbed films of liquid ⁴He are analized, in the framework of Density Functional Theories (DF). In these systems, when the substrate becomes increasingly attractive, the thin films of ⁴He approaches the quasi-bidimensional limit. We study this strongly attractive substrate regime with two DF, the Orsay-Trento (OT) and a recent Hybrid proposal (Hyb), focusing in the energy behavior. It is showed that OT does not reproduce the correct limiting energy curve, and it implies that this functional could not provide reliable results for very strongly attractive substrates like Graphite (Gr). In other hand, with the Hyb DF, the correct energy behavior is found for the adsorption energy of ⁴He on Gr. These results show that OT should not be applied to quasi 2D (confinement) situations, and that Hyb DF provides a much more realistic description.

Boson lattices are theoretically well described by the Hubbard model. The basic model and its variants can be effectively simulated using Monte Carlo techniques. We describe two newly developed approaches, the Stochastic Series Expansion (SSE) with directed loop updates and continuous–time Diffusion Monte Carlo (CTDMC). SSE is a formulation of the finite temperature partition function as a stochastic sampling over product terms. Directed loops is a general framework to implement this stochastic sampling in a non–local fashion while maintaining detailed balance. CTDMC is well suited to finding exact ground–state properties, applicable to any lattice model not suffering from the sign problem; for a lattice model the evolution of the wave function can be performed in continuous time without any time discretization error. Both the directed loop algorithm and the CTDMC are important recent advances in development of computational methods. Here we present results for a Hubbard model for anti–ferromagnetic spin–1 bosons in one dimensions, and show evidence for a dimerized ground state in the lowest Mott lobe.

We examine the entanglement of thermal states of n spins interacting through an XYZ type Heisenberg coupling in the presence of a uniform magnetic field, by evaluating the negativities of bipartite partitions of the whole system and subsystems. The corresponding limit temperatures for entanglement are also examined. Results indicate that limit temperatures for global entanglement depend on the type of partition and are higher than those limiting pairwise entanglement, and that their behavior with anisotropy and applied magnetic field may differ significantly from that of the corresponding mean field critical temperature.

We consider quantum computational models defined via a Lie-algebraic theory. In these models, specified initial states are acted on by Lie-algebraic quantum gates and the expectation values of Lie algebra elements are measured at the end. We show that these models can be efficiently simulated on a classical computer in time polynomial in the dimension of the algebra, regardless of the dimension of the Hilbert space where the algebra acts. Similar results hold for the computation of the expectation value of operators implemented by a gate-sequence. We introduce a Lie-algebraic notion of generalized mean-field Hamiltonians and show that they are efficiently (exactly) solvable by means of a Jacobi-like diagonalization method. Our results generalize earlier ones on fermionic linear optics computation and provide insight into the source of the power of the conventional model of quantum computation.

We present quantum Monte Carlo calculations of the effective rotational constant B of several cromophore molecules embedded in He clusters, as a function of the cluster size. The predictive power of the computed B values is demonstrated not only by their agreement with available measurements, but also by their use in the assignment of several lines in both infrared and microwave spectra. The simulation results complement and extend the experimental information, offering insight into the relationship between structural and dynamical properties and the onset of superfluidity. The range of cluster sizes studied in our simulations includes systems of several tens particles, intermediate between the small-cluster and the nanodroplet regimes. In this size range we find unexpected trends for the evolution of B towards its asymptotic nano-droplet value.

We present a new characterization of quantum states, what we call Projected Entangled-Pair States (PEPS). This characterization is based on constructing pairs of maximally entangled states in a Hilbert space of dimension D², and then projecting those states in subspaces of dimension d. In one dimension, one recovers the familiar matrix product states, whereas in higher dimensions this procedure gives rise to other interesting states. We have used this new parametrization to construct numerical algorithms to simulate the ground state properties and dynamics of certain quantum-many body systems in two dimensions.

We present a diffusion Monte Carlo simulation of metastable superfluid ⁴He at zero temperature and pressures beyond freezing (~ 25 bar) up to 275 bar. The equation of state of liquid ⁴He is extended to the overpressurized regime, where the pressure dependence of the static structure factor and the condensate fraction is obtained. Along this large pressure range, excited-state energy corresponding to the roton has been determined using the release-node technique. Our results show that both the roton energies and the condensate fraction decrease with increasing pressure but do not become zero. We compare our calculations to recent experimental data in overpressurized regime.

We have performed a fully non-perturbative calculation of the thermal properties of a system of spin 1/2 fermions in 3D in the unitary regime. We have determined the critical temperature for the superfluid-normal phase transition. The thermodynamic behavior of this system presents a number of unexpected features, and we conclude that spin 1/2 fermions in the BCS-BEC crossover should be classified as a new type of superfluid.

Despite the fact that by now one dimensional and three dimensional systems of interacting particles are reasonably well understood, very little is known on how to go from the one dimensional physics to the three dimensional one. This is in particular true in a quasi-one dimensional geometry where the hopping of particles between one dimensional chains or tubes can lead to a dimensional crossover between a Luttinger liquid and more conventional high dimensional states. Such a situation is relevant to many physical systems. Recently cold atoms in optical traps have provided a unique and controllable system in which to investigate this physics. We thus analyze a system made of coupled one dimensional tubes of interacting fermions. We explore the observable consequences, such as the phase diagram for isolated tubes, and the possibility to realize unusual superfluid phases in coupled tubes systems.

The exact Richardson solution of the reduced BCS Hamiltonian is used to study the BCS-to-BEC crossover, as well as the nature of Cooper pairs, in superconducting and Fermi superfluid media. Based on the exact eigenstate we will discuss the Cooper-pair concept proposing a scenario for the BCS-to-BEC crossover in which a mixture of quasifree fermions and pair resonances (BCS) evolves to a system of weakly bound molecules (BEC). In this single unified scenario the Cooper-pair wavefunction has a unique functional form. We propose a new definition of the condensate fraction which, within the limits of the BCS model, gives a qualitative description of recent experiments in ultracold atomic Fermi gases. Finally, we will introduce a new integrable model for asymmetric superfluid systems able to describe different homogeneous and inhomogeneous competing phases such as, breached superconductivity, deformed Fermi superfluidity, and the elusive Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) state.

The ground-state properties of a two-component Fermi gas with attractive short-range interactions are calculated using the fixed-node diffusion Monte Carlo method. The interaction strength is varied over a wide range by tuning the value a of the s-wave scattering length of the two-body potential. We calculate the energy per particle, the one- and two-body density matrix as a function of the interaction strength. Results for the momentum distribution of the atoms, as obtained from the Fourier transform of the one-body density matrix, are reported as a function of the interaction strength. Off-diagonal long-range order in the system is investigated through the asymptotic behavior of the two-body density matrix. The condensate fraction of pairs is calculated in the unitary limit and on both sides of the BCS-BEC crossover.

We study a confined mixture of Rb and K atoms in a one dimensional optical lattice, at low temperature, in the quantal degeneracy regime. This mixture exhibits an attractive boson-fermion interaction, and thus above certain values of the number of particles the mixture collapses. We investigate, in the mean-field approximation, the curve for which this phenomenon occurs, in the space of number of particles of both species. This is done for different types of optical lattices.

We discuss the superfluid phase transition in a gas of Fermi atoms with a Feshbach resonance. A tunable pairing interaction associated with the Feshbach resonance is shown to naturally lead to the BCS-BEC crossover, where the character of superfluidity continuously changes from the weak-coupling Bardeen-Cooper-Schrieffer (BCS) type to the Bose-Einstein condensation (BEC) of tightly bound molecules, as one decreases the threshold energy 2ν of the Feshbach resonance. We also discuss effects of a trap, as well as the p-wave BCS-BEC crossover adjusted by a p-wave Feshbach resonance.

We present in this paper an analytical model for a cold bosonic gas on an optical lattice (with densities of the order of 1 particle per site) targeting the critical regime of the Bose-Einstein Condensate superfluid - Mott insulator transition.

We study the zero-temperature critical behavior of dissipative quantum Ising spin chains of finite and infinite length. The spins interact with either constant or random nearest-neighbor ferro-magnetic couplings. They are also subject to a transverse field and coupled to an Ohmic bath of quantum harmonic oscillators. We analyze the coupled system performing Monte Carlo simulations on a classical two-dimensional counterpart model. We find that the coupling to the bath enhances the extent of the ordered phase, as it is known for mean-field spin-glass models. In the case of finite chains we show that a generalization of the Caldeira-Leggett localization transition exists.

We briefly review the theory of Bose-Einstein condensation in the two-dimensional trapped Bose gas and, in particular the relationship to the theory of the homogeneous two-dimensional gas and the Berezinskii-Kosterlitz-Thouless phase. We obtain a phase diagram for the trapped two-dimensional gas, finding a critical temperature above which the free energy of a state with a pair of vortices of opposite circulation is lower than that for a vortex-free Bose-Einstein condensed ground state. We identify three distinct phases which are, in order of increasing temperature, a phase coherent Bose-Einstein condensate, a vortex pair plasma with fluctuating condensate phase and a thermal Bose gas. The thermal activation of vortex-antivortex pair formation is confirmed using finite-temperature classical field simulations.

We show the insulating region of the metal-insulator transition phenomena in disordered two-dimensional electron systems contains new information about the quantum critical dynamics at low T because the insulating region and the quantum critical region are two aspects of the localized phase.

We discuss symmetries intermediate between global and local and formalize the notion of dimensional reduction adduced from such symmetries. We apply this generalization to several systems including liquid crystalline phases of Quantum Hall systems, transition metal orbital systems, frustrated spin systems, (p+ip) superconducting arrays, and sliding Luttinger liquids. By considering space-time reflection symmetries, we illustrate that several of these systems are dual to each other. In some systems exhibiting these symmetries, low temperature local orders emerge by an "order out of disorder" effect while in other systems, the dimensional reduction precludes standard orders yet allows for multiparticle orders (including those of a topological nature).

We present, from an information theoretic viewpoint, an analysis of phase transitions and critical phenomena in quantum systems. Our study is based on geometrical considerations within the Riemannian space of thermodynamic parameters that characterize the system. A metric for the space can be derived from an appropriate definition of distance between quantum states. For this purpose, we consider generalized α-divergences that include the standard Kullback–Leibler relative entropy. The use of other measures of information distance is taken into account, and the thermodynamic stability of the system is discussed from this geometric perspective.

Given a dynamics in configuration or phase-space, it is often important to map the barriers, the separatrices emanating from them, and the current distributions of the reaction paths. We describe a strategy to do this efficiently.

We describe calculations of the properties of quantum fluids inside nanotubes of various sizes. Very small radius (R) pores confine the gases to a line, so that a one-dimensional (1D) approximation is applicable; the low temperature behavior of 1D ⁴He is discussed. Somewhat larger pores permit the particles to move off axis, resulting eventually in a transition to a cylindrical shell phase—a thin film near the tube wall; we explored this behavior for H₂. At even larger R ~ 1 nm, both the shell phase and an axial phase are present. Results showing strong binding of cylindrical liquids ⁴He and ³He are discussed.

Nature uses phase transitions as powerful regulators of processes ranging from climate to the alteration of phase behavior of cell membranes, building on the fact that thermodynamic properties of a solid, liquid, or gas are sensitive fingerprints of intermolecular interactions. The only known exceptions from this sensitivity are critical points, where two phases become indistinguishable and thermodynamic properties exhibit universal behavior: systems with widely different intermolecular interactions behave identically. Here we report a new, stronger form of universality, in which different members of a family of two-dimensional systems—the discrete p-state clock model—behave identically both near and away from critical points, if the temperature exceeds a value T_eu ('extended universality). We show that all thermal averages are identical to those of the continuous planar rotor model (p = ∞) above T_eu, that phase transitions above T_eu are identical to the Berezinskii-Kosterlitz-Thouless (BKT) transition, and that transitions below T_eu are distinctly non-BKT. The results generate a comprehensive map of the three phases of the model and, by virtue of the discrete rotors behaving like continuous rotors, an emergent symmetry, not present in the Hamiltonian. This symmetry, or many-to-one map of intermolecular interactions onto thermodynamic states, demonstrates previously unknown limits for macroscopic distinguishability of different microscopic interactions.

Here, we use a first-principles approach, implemented directly in real space, which allows us to investigate the behavior of 3d nanostructures deposited onto metallic surfaces. To illustrate the flexibility of the approach, results of the exchange coupling J for 3d dimers on Cu(001) are presented. Calculations indicate that Cr and Mn dimers have antiferromagnetic alignment, while Fe, Co and Ni are stable in the ferromagnetic configuration. We also use the method to investigate the electronic structure of Fe, Co and Ni nanoclusters on Cu(001) surfaces. Our main purpose is to understand, from first principles, how electronic charge around the 3d sites is affected by the changes on the local environment associated with the lower coordination number of surfaces sites. Charge transfers, as well as charge character (s, p or d) around ferromagnetic Fe, Co and Ni clusters are investigated. If we consider a region defined by the volume per atom in the corresponding metal, we find that large charge transfers are present at cluster sites. These transfers are mainly due to a drastic decrease in the number of s and p electrons around the site, while the number of 3d electrons around the site remains practically unchanged.

Within finite temperature Density Functional Theory, we have calculated the energy of the transitions from the ground state to the first two excited states in the electron bubbles in liquid helium at pressures from zero to about the solidification pressure. For ⁴He at low temperatures, our results are in very good agreement with infrared absorption experiments. We have found that the 1s - 2p transition energies are sensitive not only to the size of the electron bubble, but also to its surface thickness. We also present results for the infrared transitions in the case of liquid ³He.

Treating competing fluctuations, e.g., density, spin, current, need a tractable, self-consistent approach. One method that treats particle-particle and particle-hole correlations self-consistently is the diagrammatic "crossing-symmetric equations" method. In a general calculation for pairing, non-local interaction plays an important role in enhancing certain quantum fluctuations and thereby determining the pairing symmetry.

Quantum dots may display fascinating features of strong correlation such as finite-size Wigner crystallization. We here review a few electron spectroscopies and predict that both inelastic light scattering and tunneling imaging experiments are able to capture clear signatures of crystallization.

We study the nucleation of vortices in a thin mesoscopic superconducting disk in an applied magnetic field perpendicular to the disc. We write down an expression for the free energy of the system with an arbitrary number of vortices and anti-vortices. For a given applied field, we minimize the free energy to find the optimal position of the vortices and anti-vortices. We also calculate the magnetization of the disk as a function of the applied field and hence the determine the different configurations possible in which a fixed number of fluxoids can penetrate the disk.

A new linked cluster expansion for the calculation of ground state observables of many-body nuclei with realistic interactions has been developed, in order to single out the major contributions to the relevant quantities when Nucleon-Nucleon correlations are taken into account in the wave function. Using the V8' potential the ground state energy, density and momentum distribution of complex nuclei have been calculated and found to be in good agreement with the results obtained within the Fermi Hyper Netted Chain, and Variational Monte Carlo approaches. Using the same cluster expansion, with wave function and correlations parameters fixed from the calculation of the ground-state observables, we have calculated various high energy scattering processes off complex nuclei. We made use of the Glauber multiple scattering theory, which can be readily included into the cluster expansion we have developed, to take into account final state interaction effects in the semi-inclusive reaction A(e, e'p)X, and calculated the distorted momentum distribution, which is a necessary ingredient to estimate the cross section.

Three– and four–nucleon systems are described using the hyperspherical harmonic (HH) method. Bound and scattering states are expanded in the HH basis and the corresponding binding energies and S-matrices are obtained using a variational principle. Modern nucleon-nucleon potentials plus three-nucleon interactions are considered. The calculated quantities as binding energies, cross section and polarization observables are accurate at the level of 1% or better.

RPA and its quasiparticle generalization (QRPA) have been widely used to study electromagnetic transitions and beta decays in medium and heavy nuclei, being the pn-QRPA charge exchange mode extensively employed in the description of single and double beta decays in vibrational nuclei. However develops a collapse, i.e. it presents imaginary eigenvalues for strengths beyond a critical value of the force. Extensions called renormalized QRPA (RQRPA) do not develop any collapse going beyond the simplest quasiboson approximation, however they present several drawbacks which will be analyzed.

This presentation focuses on some of the recent developments in low-energy nuclear structure theory, with emphasis on applications of coupled-cluster theory. We report on results for ground and excited states in ⁴He and ¹⁶O, and about extensions of coupled-cluster theory to treat three-body forces.

The single-particle spectral functions in asymmetric nuclear matter are computed using the ladder approximation within the theory of finite temperature Green's functions. The internal energy and the momentum distributions of protons and neutrons are studied as a function of the density and the asymmetry of the system. The proton states are more strongly depleted when the asymmetry increases, whereas the occupation of the neutron states is enhanced compared to the symmetric case. Preliminary results for the entropy and the free energy are also presented.

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