In this thesis we show results of Quantum Monte Carlo simulations for fluid 3He in the ground state. We studied 3He in a quasi two dimensional environment and we designed a new class of trial wave functions for strongly correlated fermions. 3He is a typical example of Fermi liquid, and is the focus of several theoretical and experimental studies; since two dimensional 3 He in the ground state is believed to be a homogeneous liquid up to freezing, two dimensional 3He is the ideal system to study the effects of correlation in a wide density range. In this thesis we have worked in two regimes: we studied the behaviour of low density 3He adsorbed on substrates and we designed a new class of trial wave function to be used in the strongly correlated, high density systems. While great focus has been devoted to study the strongly correlated regime at high density, some important questions about the low density behaviour of this system still have to be addressed. Recent heat capacity data were interpreted as the evidence of the presence of a self bound liquid phase for 3He adsorbed on graphite; moreover it was argued that the the appearance of a liquid phase does not depend on the substrate, but is an intrinsic property of two dimensional 3He. This is in stark contrast with theoretical studies, that exclude the presence of a self bound liquid. We performed Quantum Monte Carlo simulations, using the Variational Monte Carlo and the Fixed Node - Diffusion Monte Carlo methods, to investigate the presence of a low density liquid phase in two dimensional 3He and in 3He adsorbed on alkali, magnesium and graphite substrates. Our results exclude the formation of a self bound liquid in the strictly two dimensional environment, while in the presence of substrates the situation changes; on weakly attractive substrates the formation of a liquid phase is indeed possible, while on stronger substrates, that are closer approximations of the two dimensional system, we can’t observe any liquid. We find out however that the corrugation a the substrate helps the stabilization of a liquid phase, and can lead to phase coexistence of different fluid phases even on a substrate as strong as graphite. When performing Quantum Monte Carlo simulations it is crucial to have good trial wave functions. Designing good wave functions on the other hand in a hard task, especially when we study Fermi liquids at high density. In order to study strongly correlated systems more accurate and sophisticated wave functions were designed. Including backflow transformations has proven to significantly increase the quality of trial wave functions for Fermi liquids, especially at high density, but some results still show a poor quantitative agreement with experimental data for example for the spin polarization of 3He. We introduce a new class of trial wave functions for strongly correlate Fermi systems. These wave functions are based on iterated backflow transformations and on the introduction of correlations between backflow coordinates. While exact results are usually not available in Quantum Monte Carlo simulations of Fermi system our iterative backflow procedure allows to define a set of increasingly accurate wave functions that can be used to obtain both a strict upper bound and a strict lower bound to the exact ground state energy, and have an estimate of the exact energy. We used these wave functions to study two dimensional 3 He at freezing. We could obtain variational energy estimates that are significantly lower than the ones available in literature; moreover the upper and lower bound we could obtain for 3 He allowed us to give an estimate for the ground state energy that is in good agreement with exact data obtained with the Transient Estimate technique. Having seen the good results that can be obtained using these wave functions we used them to simulate another system, three dimensional 4He; we studied this system in different conditions, at negative pressure, at equilibrium and at freezing; in all cases we could obtain variational energies that are lower than the ones obtained using Shadow Wave Functions, and the upper and lower bounds for the energy are consistent with exact Diffusion Monte Carlo data. The good results we obtained in the study of a Bose system suggest that the iterative backflow transformations could find applications that can go well beyond the simulations of strongly correlated fermions.

Quantum Monte Carlo simulations of two dimensional 3He: low-density gas-liquid coexistence on substrates and iterative backflow wave functions for strongly correlated systems / Ruggeri, Michele. - (2015 Oct 30).

Quantum Monte Carlo simulations of two dimensional 3He: low-density gas-liquid coexistence on substrates and iterative backflow wave functions for strongly correlated systems

Ruggeri, Michele
2015-10-30

Abstract

In this thesis we show results of Quantum Monte Carlo simulations for fluid 3He in the ground state. We studied 3He in a quasi two dimensional environment and we designed a new class of trial wave functions for strongly correlated fermions. 3He is a typical example of Fermi liquid, and is the focus of several theoretical and experimental studies; since two dimensional 3 He in the ground state is believed to be a homogeneous liquid up to freezing, two dimensional 3He is the ideal system to study the effects of correlation in a wide density range. In this thesis we have worked in two regimes: we studied the behaviour of low density 3He adsorbed on substrates and we designed a new class of trial wave function to be used in the strongly correlated, high density systems. While great focus has been devoted to study the strongly correlated regime at high density, some important questions about the low density behaviour of this system still have to be addressed. Recent heat capacity data were interpreted as the evidence of the presence of a self bound liquid phase for 3He adsorbed on graphite; moreover it was argued that the the appearance of a liquid phase does not depend on the substrate, but is an intrinsic property of two dimensional 3He. This is in stark contrast with theoretical studies, that exclude the presence of a self bound liquid. We performed Quantum Monte Carlo simulations, using the Variational Monte Carlo and the Fixed Node - Diffusion Monte Carlo methods, to investigate the presence of a low density liquid phase in two dimensional 3He and in 3He adsorbed on alkali, magnesium and graphite substrates. Our results exclude the formation of a self bound liquid in the strictly two dimensional environment, while in the presence of substrates the situation changes; on weakly attractive substrates the formation of a liquid phase is indeed possible, while on stronger substrates, that are closer approximations of the two dimensional system, we can’t observe any liquid. We find out however that the corrugation a the substrate helps the stabilization of a liquid phase, and can lead to phase coexistence of different fluid phases even on a substrate as strong as graphite. When performing Quantum Monte Carlo simulations it is crucial to have good trial wave functions. Designing good wave functions on the other hand in a hard task, especially when we study Fermi liquids at high density. In order to study strongly correlated systems more accurate and sophisticated wave functions were designed. Including backflow transformations has proven to significantly increase the quality of trial wave functions for Fermi liquids, especially at high density, but some results still show a poor quantitative agreement with experimental data for example for the spin polarization of 3He. We introduce a new class of trial wave functions for strongly correlate Fermi systems. These wave functions are based on iterated backflow transformations and on the introduction of correlations between backflow coordinates. While exact results are usually not available in Quantum Monte Carlo simulations of Fermi system our iterative backflow procedure allows to define a set of increasingly accurate wave functions that can be used to obtain both a strict upper bound and a strict lower bound to the exact ground state energy, and have an estimate of the exact energy. We used these wave functions to study two dimensional 3 He at freezing. We could obtain variational energy estimates that are significantly lower than the ones available in literature; moreover the upper and lower bound we could obtain for 3 He allowed us to give an estimate for the ground state energy that is in good agreement with exact data obtained with the Transient Estimate technique. Having seen the good results that can be obtained using these wave functions we used them to simulate another system, three dimensional 4He; we studied this system in different conditions, at negative pressure, at equilibrium and at freezing; in all cases we could obtain variational energies that are lower than the ones obtained using Shadow Wave Functions, and the upper and lower bounds for the energy are consistent with exact Diffusion Monte Carlo data. The good results we obtained in the study of a Bose system suggest that the iterative backflow transformations could find applications that can go well beyond the simulations of strongly correlated fermions.
Moroni, Saverio
Ruggeri, Michele
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/4854
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