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The study of the competition or coexistence of different ground states in many-body systems is an exciting and actual topic of research, both experimentally and theoretically. Quantum fluctuations of a given phase can suppress or enhance…
A finite-temperature many-body perturbation theory is presented that expands in power series the electronic grand potential, chemical potential, internal energy, and entropy on an equal footing. Sum-over-states and sum-over-orbitals…
We explore the Coleman-Weinberg phase transition in regions outside the validity of perturbation theory. For this purpose we study a Euclidean field theory with two scalars and discrete symmetry in four dimensions. The phase diagram is…
The phase transition patterns displayed by a model of two coupled complex scalar fields are studied at finite temperature and chemical potential. Possible phenomena like symmetry persistence and inverse symmetry breaking at high…
We establish a new non-equilibrium scaling regime in the short time evolution of one-dimensional interacting open quantum systems subject to a generic heating mechanism. This dynamical regime is characterized by uncompensated phonon…
We introduce a novel construction of a contour deformation within the framework of Loop-Tree Duality for the numerical computation of loop integrals featuring threshold singularities in momentum space. The functional form of our contour…
Phase behavior of the Yukawa hard-sphere polydisperse mixture with high degree of polydispersity is studied using high temperature approximation (HTA) and mean spherical approximation (MSA). We have extended and applied the scheme developed…
The Hopf algebra of undecorated rooted trees has tamed the combinatorics of perturbative contributions, to anomalous dimensions in Yukawa theory and scalar $\phi^3$ theory, from all nestings and chainings of a primitive self-energy…
A brief review of various numerical techniques used in loop quantum cosmology and results is presented. These include the way extensive numerical simulations shed insights on the resolution of classical singularities, resulting in the key…
We introduce a new analytical method for studying the open quantum systems problem of a discrete system weakly coupled to an environment of harmonic oscillators. Our approach is based on a phase space representation of the density matrix…
The analysis of phase transitions in cosmological spacetimes shows that their existence requires a time-dependent apparent horizon radius, which in turn implies an equation of state different from that of a dark energy fluid. This condition…
Thermodynamics of two-dimensional Yukawa (screened Coulomb or Debye-H\"uckel) systems is studied systematically using molecular dynamics (MD) simulations. Simulations cover very broad parameter range spanning from weakly coupled gaseous…
The preparation of thermal equilibrium states is important for the simulation of condensed-matter and cosmology systems using a quantum computer. We present a method to prepare such mixed states with unitary operators, and demonstrate this…
Long-range quantum systems, in which the interactions decay as $1/r^{\alpha}$, are of increasing interest due to the variety of experimental set-ups in which they naturally appear. Motivated by this, we study fundamental properties of…
Cosmology appears as the most promising way to test and constrain quantum gravity theories. Loop quantum gravity is among the most advanced attempts to perform a non-perturbative quantization of general relativity. Its cosmological…
With combined hopping parameter and strong coupling expansions, we calculate a dimensionally reduced Polyakov-loop effective theory valid for heavy quarks at nonzero temperature and arbitrary chemical potential. We numerically compute the…
We devote our studies to the subject of weakly nonintegrable dynamics of systems with a macroscopic number of degrees of freedom. Our main points of interest are the relations between the timescales of thermalization and the timescales of…
We study the finite temperature crossovers in the vicinity of a zero temperature quantum phase transition. The universal crossover functions are observables of a continuum quantum field theory. Particular attention is focussed on the high…
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…
Numerical techniques to efficiently model out-of-equilibrium dynamics in interacting quantum many-body systems are key for advancing our capability to harness and understand complex quantum matter. Here we propose a new numerical approach…