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STOCHASTIC MODELING OF QUANTUM MANY-BODY SYSTEMS (QMC)
 Gaetano Senatore Stefano Baroni Silvio A. Beccara Federico Becca Stefano Fantoni Saverio Moroni Francesco Pederiva Sandro Sorella Flavio Toigo Sejij Yunoki O. Benhar J. Carlson A. Fabroncini D. Neilson A. Sarsa K.E. SchmidtMain research lines:
Personnel to be hired (man years): tenure-track position (electrons in low dimension and highly correlated systems), starting from year 3.Line 2: 2 yrs PostDoc + 3yrs PhD; Line 3: 4+0. The aim of this activity is the understanding of selected physical systems and/or models and the development and tuning of methodological tools and techniques, in the area of quantum many-body systems. This goal will be achieved by combining the effort of researchers possessing complementary backgrounds and expertises and a strong competence in quantum Monte Carlo (QMC) methods. The motivation of this research brings together the will to understand and predict properties of systems of technological interest, the will to gain insight into systems of fundamental interest, and the need to provide benchmark calculations to test approximate theories. Whenever correlation plays a major role in determining the observed properties of a physical system conventional approximate theories, such as density functional (DFT) based schemes or perturbation expansions , may become inapplicable. In such a situation even the qualitative nature of predictions may crucially depend on the the accuracy of the chosen theoretical technique. The method of choice is therefore QMC[1], as it provides to date the most accurate information on correlated quantum many-body systems and exact results for Bosons. QMC methods naturally complement the DFT techniques employed in the other research activities present in this CRS and in fact will be also used in combined efforts in selected cases. The confinement of electrons in low dimension, either accidental as in high temperature (HTc) superconductors or engineered as in semiconductor heterostructures, enhances correlation effects and yields a wealth of new and fascinating physics, whose comprehension is far from complete. Thus, in spite of the huge combined effort of experiment and theory over almost fifteen years, the nature of HTc superconductors remains an important unsolved problem in condensed matter physics[2]. While strong electronic correlations are widely believed to be crucial for the understanding of these materials, there is no general consensus yet on what is the correct theory for HTc: resonating valence bond theory of superconductivity, antiferromagnetism and spin bugs, SO(5) symmetry, stripes and/or phase separation, and so on and so forth. In an another context, electrons confined to two dimensions (2DEG) in solid state devices have also attracted a great deal of attention in the last decade, in connection with the apparent metal-insulator transition observed in the presence of disorder[3]. The hot issue there is the very nature of the transition, as well as the concomitant role played by spin polarization in the (de)stabilization of the apparent metallic phase. In fact, spin appears to play a central role also in more exotic systems[4] such as wires, ring and dots, especially in relation to the realization of devices that might render quantum computation feasible. The accurate description of correlation effects is crucial not only when studying electrons but also in the investigation of other quantum systems, ranging from the familiar helium liquid to stellar interiors. Thus, the understanding of the deep nature of superfluidity is still an open and challenging problem. Systems consisting in molecules embedded in He-4 droplets seem to be unique environments to investigate the superfluidity of the solvent, with the molecules behaving as local probes [5]. Such systems are also particularly suited to study nano-sized quantum systems. The clusters isolate the impurity molecules avoiding the possibility of aggregation, so that solvation with only one impurity can be studied. The above studies cannot be carried on at any realistic level without using QMC techniques. Many of the important processes occurring in the extreme conditions prevalent in stellar and primordial environments of our universe are essentially not reproducible in terrestrial laboratories with present technology. Ab initio calculations in nucleon matter at very large densities pose a great challenge to computational science. It is only recently that QMC theory has been able to deal with the spin problem arising from the strong spin-dependence of the NN force. This opens up a new scenario for theoretical studies of fundamental phenomena, such as the explosion of supernovae [6]. 1 QMC ON THE CONTINUUM: FROM SUPERFLUID HELIUM TO STARS We will perform quantum simulations of molecular complexes embedded in helium droplets, to study on one side the structural and dynamical properties of the impurity molecules, and on the other the superfluidity of the solvent [7]. Quantitative studies are planned on (i) effective moment of inertia of one molecular complex, like for instance OCS; (ii) rotational constants and vibrational and tunneling frequencies of two molecules, like hydrogen bonded dimers; (iii) ground state properties of para-hydrogen or mixed He4-pH_2 droplets. Green's Function and Path Integral Monte Carlo (PIMC) methods will be used in the first two studies, whereas we will relay on Variational Monte Carlo techniques based upon Shadow wave functions [8] for the last one. A second line of research will address important issues in nuclear astrophysics, which strongly ask for quantitative studies based on Quantum simulations, very much like as in condensed matter physics. We plan to study (i) the equation of state and (ii) the response functions of dense nucleon matter at low temperature with the most realistic NN interactions and by using the recently developed Auxiliary Field Diffusion Monte Carlo (AFDMC) method[9]. Such kind of Quantum simulation studies are expected to have large impact for a better understanding of the neutron stars structure, and the important mechanisms governing the supernovae explosion. Finally, we plan to continue our researches on the Quantum Monte Carlo methods in the continuum. The existing ones, although very powerful, are not yet optimal. Significant fundamental algorithmic challenges remain, especially related to the sign problem and the spin problem . We will carry out studies and numerical analysis on (i) correlated walkers algorithm[10], and its application to the case of He-3 droplets; (ii) the implementation of the AFDMC ideas to other QMC methods, like the Reptation QMC [11] and the PIMC methods; (iii)the application of the Reptation QMC to the on-the-fly computation of low-order derivatives of the energy with respect to external parameters; (iv) the extension of Constrained Dynamics QMC [12] methods to simulate large planar organic molecules. 2 MODELING ELECTRONS IN LOW DIMENSION We shall investigate models of the low dimensional electron gas, relevant to carriers confined in semiconductor heterostructures, mostly using the diffusion Monte Carlo (DMC) method [1] in the fixed-node approximation. We shall study in particular the 2DEG with and without disorder, quantum wires, dots and rings. As a long term project, we shall calculate the phase diagram of the 2DEG in the presence of a disorder appropriate to Si MOSFETs [3], and investigate how the liquid-solid transition depends on details of the disorder, i.e., of the impurities distribution. From the strong disorder case of Si MOSFETs, we shall then move toward the weak disorder case [3] of GaAs based heterostructures. At present it is not clear yet to which extent systematic DMC simulations are feasible when the disorder is decreased too much. However, it will be certainly possible to investigate the weak disorder case building on our knowledge of (i) the 2DEG with no disorder and (ii) the linear response formalism, by treating the presence of impurities as a weak perturbation. We shall also study the magnetic properties [4] of a two component 2DEG, to mimic the situation encountered in a Si MOSFET 2DEG. Recently we have been studying confinement effects in model quantum wires, trying to address the range of validity of the one-subband approximation, which yields an effective strictly one dimensional (1D) system. Simulations for such a 1D system reveal severe ergodicity problems even at medium coupling. From the methodological point of view we plan to investigate methods of overcoming such problems in DMC simulations. In parallel we shall continue the investigation of realistic wires, described as three- or two-dimensional electron systems in the presence of a strong confining potential. To this end DFT calculations will be necessary to provide trial functions for the quantum simulations. 3 LATTICE MODELS FOR CORRELATED ELECTRONIC SYSTEMS The recent progress of QMC techniques [13,14] has allowed to deal with many model Hamiltonians on a lattice, providing in most cases a complete and accurate description of the crucial role played by the strong electron correlation for the ground state electron properties. We plan to extend our study in this field by considering one band models such as Hubbard and t-J with hopping and/or superexchange integrals not restricted to nearest neighbors. These effective one band parameters can be determined also by ab-initio LDA or LDA+U calculations (interaction with Hi-PT activity is expected to be important). In this way we can compare more closely with material properties of compounds where correlation play a crucial role: e.g. La2 Cu O4, the prototype High temperature superconductor or Fe O and Fe2 Si O4, materials with Mott insulator behavior not explained within LDA. Another very important subject of our research is to extend to realistic systems the recently developed approach [14], suited for Hamiltonians defined on a lattice, as it appears more and more evident that electron correlation is very important especially for biological systems. In particular iron-based proteins play a fundamental role for a large wealth of biological processes, from electron-transfer to enzymatic catalysis. For all these functions, they use the Fe(II)/Fe(III) pair. Unfortunately,conventional LDA techniques at times encounter difficulties to reproduce the ground state properties of these ions (such as the spin of the Fe(II) and Fe(III) ). A strong and fruitful collaboration with the BioMod activity is expected if the present project will be approved. BIBLIOGRAPHY [1] Quantum Monte Carlo Methods in Physics and Chemistry, ed. P. Nightingale and C. Umrigar, (Kluwer, Dordrecht, 1999). [2] E. Dagotto, Rev. Mod. Phys. 66, 763 (1994). [3] E. Abrahamas et al, Rev. Mod. Phys. 73, 251 (2001). [4]Spin effects in mesoscopic systems, Sol. St. 119 (2001). [5] S. Grebenev et al, Science 289, 1532 (2000). [6] G.G. Raffelt, Stars as Laboratories for fundamental physics (University of Chicago Press, Chicago, 1996). [7] Y.Kwon, et al., J.Chem.Phys. 113, 6469 (2000). [8] F.Pederiva, A.Ferrante, S.Fantoni, L.Reatto, Phys.Rev.Lett. 72 (1994) 2589. [9] K.E. Schmidt and S. Fantoni, Phys. Lett., B446, 99 (1999). [10] M.H. Kalos, F. Pederiva, Phys. Rev. Lett. 85,3547 (2000). [11] S. Baroni and S. Moroni, Phys. Rev. Lett, 82, 4745 (1999). [12] A. Sarsa, K. E. Schmidt and W. R. Magro, J. Chem. Phys. 113, 1366 (2000). [13] D. F. B. ten Haaf et al, Phys. Rev. B 51, 13039 (1995). [14]S. Sorella, Phys. Rev. Lett. 80, 4558 (1998); Phys. Rev. B64, 024512 (2001). |
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