Monte Carlo study of quantum phase transitions at zero temperature

TL;DR

This thesis applies quantum Monte Carlo methods to study ultracold quantum systems, including Rydberg atoms, Yukawa particles, and para-hydrogen, revealing their phase diagrams and quantum-classical behavior at various temperatures.

Contribution

It introduces detailed quantum Monte Carlo techniques for various interactions and models, including new analytic expressions for Ewald summation and phase diagrams for Rydberg atom systems.

Findings

Phase diagram of Rydberg atoms mapped at different densities and temperatures

Quantum Monte Carlo results for Yukawa potential systems

Insights into para-hydrogen behavior at zero and finite temperatures

Abstract

In this Ph.D. thesis quantum Monte Carlo methods are applied to investigate the properties of a number of ultracold quantum systems. In Chapter 1 we discuss the analytical approaches and approximations used in the subsequent Chapters; also we describe the general concepts of the two-particle scattering problem as a tool to construct Jastrow terms in trial wave functions. Chapter 2 explains in details the Quantum Monte Carlo methods employed in our calculations from the theoretical and practical points of view. In Chapter 3 we explain the Ewald summation technique, applied to a power-law 1/|r|k interaction potential, and a generic approach to obtain the Ewald terms. The obtained expressions of this analytic work are implemented into simulations of different physically relevant systems (Rydberg atoms and Yukawa particles). Chapter 5 is devoted to the modelling of a system, governed by the model potential between Rydberg atoms $1/r^6$. The phase diagram of the system is obtained for a relevant range of densities and temperatures, combining quantum simulations at low temperature and classical treatment at higher temperature. A special attention is paid to the classical description of this system, composed of Rydberg atoms, and its comparison to the quantum system. In Chapter 4 we present the simulation of a system with the Yukawa interaction potential. The following Chapter 6 presents the results of the Quantum Monte Carlo simulations of molecular para-hydrogen at zero and finite temperatures, performed in our Group. Conclusions are drawn in Chapter 7.