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  • Monte Carlo Study of Quantum Phase Transitions at Zero Temperature  Open access

     Osychenko, Oleg
    Department of Applied Physics, Universitat Politècnica de Catalunya
    Theses

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    The Thesis is devoted to simulations of quantum phase transitions by means of Quantum Monte Carlo techniques. Quantum phase transition is a transition between phases at zero or low enough temperature, where quantum effects play an important role. The recent advances in the field of ultracold atom manipulation and optical lattices allowed to produce the systems with unique properties. This opened a perspective to observe quantum phase transitions in many-body systems with non-trivial interparticle interactions in a wide range of the system's characteristic physical parameters and geometries. First, we develop the explicit expressions for the Ewald sums in systems with an interaction potential of a generic 1/r^k type, and in 3D, 2D and 1D geometry. These generalizations can be useful in simulating systems with important interaction potentials as the dipole-dipole, van der Waals interaction, etc. In this Thesis we give the functional forms for the terms of the Ewald sums, ready for implementation in a code. The derivation and the functional form of the results differ in the cases of short-ranged, long-ranged and "marginal" forces, and for a jellium model. It is argued that in the case of some short-range potentials the Ewald method can be advantageous with respect to a direct summation due to a faster convergence rate. We also give a discussion of the convergence properties of a quasi-neutral Coulomb system. We have obtained the zero-temperature phase diagram of bosons interacting through Yukawa forces. We have used a diffusion Monte Carlo simulation starting from a good approximation to the optimal variational ground-state wave function obtained by solving the corresponding Euler-Lagrange hypernetted chain equations. The phase diagram shows that any fermionic mixture of pure elements will always be seen in gaseous form, as the mass ratios required for crystallization of weakly bound fermionic molecules are far beyond the ones that can be achieved in nature. We investigate an alternative mechanism based on the confinement of one of the species to a deep optical lattice which increases its effective mass. The resulting mass ratio of the mixture created in this way can then be tuned at will and could be used to check experimentally the predicted phase diagram both in the gas and crystal (superlattice) phases. We performed a QMC study of the system, comrised of Rydberg atoms. The applied QMC techniques allowed to parametrize a model with isotropic van der Waals interactions into a universal phase diagram. We have characterized the phase diagram of Rydberg atoms by considering a model of bosons with repulsive van der Waals 1/r^6 interaction, and determined solidification and Bose-Einstein condensation conditions. Relaxation mechanisms other than thermal motion should be considered if one considers Rydberg systems on timescales of several tenths of microseconds. We have also studied the excitation spectrum within the approximation of a classical harmonic crystal. We also discuss that interactions between Rydberg excitations open a possibility of new supersolid scenarios. In the last Chapter of the Thesis I present a study of the system of para-hydrogen atoms at low temperatures below the point of crystallization by means of QMC methods. The zero-temperature simulation was performed in order to investigate the properties of a metastable liquid phase and to find the fraction of the Bose-Einstein condensate in the relevant range of densities. The methods of choice for the zero-temperature simulations of the para-H2 system were VMC and DMC techniques. The results of the zero-temperature simulations suggest that the metastable liquid para-hydrogen is a strongly correlated liquid, which again serves as an evidence of high instability of this hypothetical system. The calculation of the Bose-Einstein condensate shows that the condensate fraction is substantially lower than in the liquid helium He4.

    Los avances recientes en manipulación de átomos ultrafrios y retículos ópticos abrieron la posibilidad de observar las transiciones de fase en sistemas de muchos cuerpos con las interacciones interparticulares no triviales para un amplio rango de los parámetros físicos característicos y geometrías del sistema. En principio desarrollamos las expresiones explicitas para las sumas de Ewald en el caso del potencial de interacción genérico 1/r^k, y en las geometrías arbitrarias: 3D, 2D y 1D. Dichas generalizaciones pueden ser útiles para simular sistemas con los potenciales importantes como dipolo-dipolo, interacción de van der Waals, etc. En la Tesis presentamos las formas funcionales para los términos de las sumas de Ewald, listas para la implementación actual. La derivación y las formas funcionales cambian en función de la potencial de corto, largo o alcance "marginal", y en particular para el modelo de jellium. Argüimos que en el caso del potencial de corto alcance el método de Ewald puede ser ventajoso respecto a la sumatorio directo gracias a la convergencia más rápida. También presentamos la discusión sobre las propiedades de convergencia del sistema de Coulomb сuasi-neutro. Hemos obtenido el diagrama de fase a temperatura cero de los bosones interactuando mediante a las fuerzas de Yukawa. Hemos usado la simulación de Monte Carlo difusivo empezando de una buena aproximación a la función de onda óptima del estado de base obtenida a través de la solución de las ecuaciones de Euler-Lagrange del método HNC. El diagrama de fase demuestra que la mezcla fermiónica de los elementos puros siempre aparece en la forma gaseosa, como los parametros requeridos para la cristalización de estas moléculas fermiónicas están fuera de lo que puede ser visto en la naturaleza. Investigamos el mecanismo alternativo basado en el confinamiento de una de las especies en el retículo óptico, que aumenta su masa efectiva. El cociente de masas de la mezcla creada de esta manera puede ser ajustada arbitrariamente y usada para comprobar el diagrama de fase predicha en el estudio tanto en fase liquida como en la cristalina. Hemos hecho el estudio QMC del sistema de los átomos de Rydberg. Las técnicas de Monte Carlo cuánticas aplicadas nos permitieron parametrizar el modelo mediante la interacción de van der Waals isotrópica y así obtener el diagrama de fase universal. Caracterizamos el diagrama de fase de los átomos de Rydberg considerando el modelo de bosones con la interacción repulsiva 1/r^6, y determinamos las condiciones de solidificación y condensación de Bose-Einstein. Los mecanismos de relajación aparte del movimiento térmico deben de ser tenidos en cuenta a escala de tiempo de decenas de microsegundos. Estudiamos también el espectro de excitaciones dentro de la aproximación de cristal clásico harmónico. Finalmente, discutimos que las interacciones entre las excitaciones de Rydberg abren la posibilidad de los escenarios nuevos del supersólido.

  • Path Integral Monte Carlo and Bose-Einstein condensation in quantum fluids and solids  Open access

     Rota, Riccardo
    Department of Applied Physics, Universitat Politècnica de Catalunya
    Theses

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    Several microscopic theories point out that Bose-Einstein condensation (BEC), i.e., a macroscopic occupation of the lowest energy single particle state in many-boson systems, may appear also in quantum fluids and solids and that it is at the origin of the phenomenon of superfluidity. Nevertheless, the connection between BEC and superfluidity is still matter of debate, since the experimental evidences indicating a non zero condensate fraction in superfluid helium are only indirect. In the theoretical study of BEC in quantum fluids and solids, perturbative approaches are useless because of the strong correlations between the atoms, arising both from the interatomic potential and from the quantum nature of the system. Microscopic Quantum Monte Carlo simulations provide a reliable description of these systems. In particular, the Path Integral Monte Carlo (PIMC) method is very suitable for this purpose. This method is able to provide exact results for the properties of the quantum system, both at zero and finite temperature, only with the definition of the Hamiltonian and of the symmetry properties of the system, giving an easy picture for superfluidity and BEC in many-boson systems. In this thesis, we apply PIMC methods to the study of several quantum fluids and solids. We describe in detail all the features of PIMC, from the sampling methods to the estimators of the physical properties. We present also the most recent techniques, such as the high-order approximations for the thermal density matrix and the worm algorithm, used in PIMC to provide reliable simulations. We study the liquid phase of condensed 4He, providing unbiased estimations of the one-body density matrix g1(r). We analyze the model for g1(r) used to fit the experimental data, highlighting its merits and its faults. In particular we see that, even if it presents some difficulties in the description of the overall behavior of g1(r), it can provide an accurate estimation of the kinetic energy K and of the condensate fraction n0 of the system. Furthermore, we show that our results for n0 as a function of the pressure are in a good agreement with the most recent experimental results. The study of the solid phase of 4He is the most significant part of this thesis. The recent observation of non classical rotational inertia (NCRI) effects in solid helium has generated big interest in the study of an eventual supersolid phase, characterized at the same time by crystalline order and superfluidity. Nevertheless, until now it has been impossible to give a theoretical model able to describe all the experimental evidences. In this work, we perform PIMC simulations of 4He at high densities, according to different microscopic configurations of the atoms. In commensurate crystals we see that BEC does not appear, our model being able to reproduce the momentum distribution obtained form neutron scattering experiments. In a crystal with vacancies, we have been able to see a transition to a superfluid phase at temperatures in agreement with experimental results if the vacancy concentration is low enough. In amorphous solids, superfluid effects are enhanced but appear at temperatures higher than the experimental estimation for the transition temperature. Finally, we study also metastable disordered configurations in molecular para-hydrogen at low temperature. The aim of this study is to investigate if a Bose liquid other than helium can display superfluidity. Choosing accurately a ¿quantum liquid¿ initial configuration and the dimensions of the simulation box, we have been able to frustrate the formation of the crystal and to calculate the temperature dependence of the superfluid density, showing a transition to a superfluid phase at temperatures close to 1 K.

  • Monte Carlo study of quantum phase diagram of Rydberg atoms with repulsive 1/r6 interaction

     Astrakharchik, Grigori; Boronat Medico, Jordi; Lutsyshyn, Yaroslav; Osychenco, Oleg; Lozovik, Yu. E.
    Bose-Einstein Condensation
    Presentation's date: 2011-09-15
    Presentation of work at congresses

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  • Two-component Fermi gas of unequal masses at unitarity.

     Astrakharchik, Grigori; Boronat Medico, Jordi; Giorgini, Stefano
    Workshop on Frontiers in Ultracold Fermi Gases
    Presentation's date: 2011-06-06
    Presentation of work at congresses

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  • Organización Conferencia/'Correlations in Quantum Gases/'

     Boronat Medico, Jordi
    Competitive project

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  • GRUP DE SIMULACIO PER ORDINADOR EN MATERIA CONDENSADA

     Pastor Satorras, Romualdo; Sese Castel, Gemma; Rey Oriol, Rosendo; Casulleras Ambros, Joaquin; Trullàs Simó, Joaquim; Bitrian Varea, Vicente; Baronchelli, Andrea; Osychenco, Oleg; Canales Gabriel, Manel; Boronat Medico, Jordi; Marti Rabassa, Jordi; Macia Rey, Adrian; Calvo Minguillon, Ausias March; Ortiz de Urbina Viade, Jordi; Mazzanti Castrillejo, Fernando Pablo; Astrakharchik, Grigori; Rota, Riccardo; Sala2 Viñas, Jonàs; Alcaraz Sendra, Olga; Guardia Manuel, Elvira
    Competitive project

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  • SUPERFLUIDEZ Y CONDESACION DE BOSE-EINSTEIN EN MATERIA ULTRAFRIA

     Rota, Riccardo; Casulleras Ambros, Joaquin; Astrakharchik, Grigori; Mazzanti Castrillejo, Fernando Pablo; Osychenco, Oleg; Macia Rey, Adrian; Boronat Medico, Jordi
    Competitive project

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  • A new wavew function for describing supersolid 4He at zero temperature

     Boronat Medico, Jordi
    25th International Conference on Low Temperature Physics
    Presentation's date: 2008-08-08
    Presentation of work at congresses

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  • Crystallization of para-H2 clusters at zero temperature

     Boronat Medico, Jordi
    25th International Conference on Low Temperature Physics
    Presentation's date: 2008-08-08
    Presentation of work at congresses

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  • Higher-order actions for PIMC simulations

     Boronat Medico, Jordi
    Quantum Monte Carlo in the Apuan Alps IV
    Presentation's date: 2008-07-28
    Presentation of work at congresses

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  • Bose-Einstein quantum statistics and the ground state of solid 4He

     Boronat Medico, Jordi
    Workshop on Supersolids
    Presentation's date: 2008-07-18
    Presentation of work at congresses

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  • Quantum fluids adsorbed in carbon nanotubes

     Boronat Medico, Jordi
    Conference on Molecular Simulations in Biosystems and Material Science
    Presentation's date: 2008-04-03
    Presentation of work at congresses

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  • Study of small spin-polarized pure and mixed tritium clusters

     Boronat Medico, Jordi
    14th International Conference on Recent Progress in Many-Body Physics
    Presentation's date: 2007-07-16
    Presentation of work at congresses

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  • Study of small spin-polarized pure and mixed triium clusters

     Beslic, Ivana; Vranje¿ Markic, Leandra; Boronat Medico, Jordi
    14th International Conference on Recent Progress in Many-Body Physics
    p. 79
    Presentation of work at congresses

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  • 4He adsorbed inside (10,10) single walled carbon nanotubes

     Gordillo Bargueño, Maria Carmen; Boronat Medico, Jordi; Casulleras Ambros, Joaquin
    14th International Conference on Recent Progress in Many-Body Physics
    p. 92
    Presentation of work at congresses

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  • Quantum Monte Carlo study of quantized vortices in 4He drops

     Sola, E; Boronat Medico, Jordi; Casulleras Ambros, Joaquin
    14th International Conference on Recent Progress in Many-Body Physics
    p. 112
    Presentation of work at congresses

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  • STUDY OF HELIUM DROPLETS USING QUANTUM MONTE CARLO TECHNIQUES

     Sola Badia, Ester
    Department of Physics and Nuclear Engineering, Universitat Politècnica de Catalunya
    Theses

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  • Physical review letters

     Boronat Medico, Jordi
    Collaboration in journals

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  • Thermal effects on the microscopic properties of 4He drops

     Boronat Medico, Jordi
    International Symposium on Quantum Fluids and Solids
    Presentation's date: 2006-08-05
    Presentation of work at congresses

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  • Physics of plasmas

     Boronat Medico, Jordi
    Collaboration in journals

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  • Physical Review B, condensed matter and materials physics

     Boronat Medico, Jordi
    Collaboration in journals

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  • Journal of low temperature physics

     Boronat Medico, Jordi
    Collaboration in journals

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  • Journal of low temperature physics

     Boronat Medico, Jordi
    Collaboration in journals

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  • Ground-state properties of small 3He drops from Quantum Monte Carlo simulations

     Boronat Medico, Jordi
    30th International Workshop on Condensed Matter Theories
    Presentation's date: 2006-06-06
    Presentation of work at congresses

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  • Physical review B, condensed matter and materials physics

     Boronat Medico, Jordi
    Collaboration in journals

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  • Physical review letters

     Boronat Medico, Jordi
    Collaboration in journals

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  • QUANTUM MONTE CARLO STUDY OF BOSONIC QUANTUM SOLIDS AT ZERO TEMPERATURE

     Cazorla Silva, Claudio
    Department of Physics and Nuclear Engineering, Universitat Politècnica de Catalunya
    Theses

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  • Physical review letters

     Boronat Medico, Jordi
    Collaboration in journals

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  • Physical review A

     Boronat Medico, Jordi
    Collaboration in journals

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  • Higher-order actions for path integral Monte Carlo simulations

     Boronat Medico, Jordi
    Microscopic approaches to Many-Body Theory
    Presentation's date: 2005-09-02
    Presentation of work at congresses

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  • Physical review A

     Boronat Medico, Jordi
    Collaboration in journals

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  • Journal of low temperature physics

     Boronat Medico, Jordi
    Collaboration in journals

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  • Physical review letters

     Boronat Medico, Jordi
    Collaboration in journals

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  • EPL: europhysics letters

     Boronat Medico, Jordi
    Collaboration in journals

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  • Journal of low temperature physics

     Boronat Medico, Jordi
    Collaboration in journals

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  • Physical review letters

     Boronat Medico, Jordi
    Collaboration in journals

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  • Physical review B, condensed matter and materials physics

     Boronat Medico, Jordi
    Collaboration in journals

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  • Some applications of quantum Monte Carlo to the study of dilute bosonic and fermionic gases

     Boronat Medico, Jordi
    International Workshop on Condensed Matter Theories (CMT28)
    Presentation's date: 2004-09-27
    Presentation of work at congresses

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  • Physical review B, condensed matter and materials physics

     Boronat Medico, Jordi
    Collaboration in journals

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  • Physical review letters

     Boronat Medico, Jordi
    Collaboration in journals

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  • Solving N-body Quantum Mechanics with the Monte Carlo method

     Boronat Medico, Jordi
    CMA Workshop on Computational Finance and Physics
    Presentation's date: 2004-03-22
    Presentation of work at congresses

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  • Higher-order actions for path integral Monte Carlo simulations

     Sakkos, Constantinos; Casulleras Ambros, Joaquin; Boronat Medico, Jordi
    Europhysics Conference on Computational Physics 2004
    p. 200-201
    Presentation of work at congresses

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  • Physical Review B, condensed matter and materials physics

     Boronat Medico, Jordi
    Collaboration in journals

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  • Collective and single-particle excitations in two- and three-dimensional 3He

     Boronat Medico, Jordi
    Quantum Fluids and Solids 2003
    Presentation's date: 2003-08-07
    Presentation of work at congresses

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  • High momentum response of liquid 3He

     Boronat Medico, Jordi; Mazzanti Castrillejo, Fernando Pablo; Polls, A
    Date of publication: 2003-08-31
    Book chapter

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  • Diffusion Monte Carlo approach to liquid 3He: from bulkm to clusters

     Boronat Medico, Jordi
    Recent Advances in the Nuclear Shell Model
    Presentation's date: 2003-07-09
    Presentation of work at congresses

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  • Physical review letters

     Boronat Medico, Jordi
    Collaboration in journals

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  • Physical Review B, condensed matter and materials physics

     Boronat Medico, Jordi
    Collaboration in journals

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