Exotic phases of matter in low dimensional lattices: from quantum liquids to kinetic magnetism

Abstract

[eng] In this Thesis we explore exotic phases of matter which arise when different mechanisms compete and favor different ground state configurations. We focus on two classes of low dimensional lattice systems. The first class concerns fluids with both repulsive and attractive interactions, which can result in the appearance of quantum liquid phases. The second class corresponds to systems with geometric frustration, where the minimization of kinetic energy is incompatible with the underlying lattice geometry.

In the first part of this Thesis, we show how quantum liquid phases emerge in ultracold atomic systems loaded into high one-dimensional optical lattices. We study different microscopic systems, including two-component bosonic mixtures, single-component dipolar systems, and single- component systems with two- and three-body interactions. For the bosonic mixture, we investigate Bogoliubov’s theory in the weakly interacting regime and derive an effective dimerized theory in the strongly inter- acting regime. Both theories capture the liquefaction of the mixture and predict a phase transition to a dimerized gas. We perform large-scale, unbiased tensor network simulations, which we contrast with our theoretical predictions, and we find an excellent agreement between them in different regimes of parameters. Moreover, we characterize the different phase transitions with our numerical simulations. Then, we demonstrate that a single- component dipolar system liquefies in the strongly interacting regime due to the presence of superexchange processes. We provide an effective theory that captures the liquefaction and the formation of self-bound Mott insulators. In addition, we provide the two-particle excitation spectrum and observe that its structure provides insights into the many-body phases. Finally, we study the universality of quantum gases and liquids in one dimension and provide a self-consistent theory to solve a quantum fluid with two- and three-body interactions. We demonstrate that quantum gases exhibit universal properties, while quantum liquids do not, since the equation of state depends on microscopic details of the theory. Moreover, we show that the long-distance tails of quantum droplets exhibit a universal decay.

In the second part of this Thesis, we investigate the effects of kinetic frustration on the many-body properties of spin-1/2 fermionic and bosonic systems. Firstly, we study frustrated ladder geometries, such as the zigzag ladder and the square ladder with a perpendicular magnetic flux. For the zigzag ladder, we find that fermionic (bosonic) systems exhibit an effective attractive (repulsive) interaction between holes and spin flips induced solely by kinetic energy and geometric frustration. In the square ladder with a perpendicular magnetic flux, both fermionic and bosonic systems show effective attractive interactions between holes and spin flips. We analyze the

formation of multi-body composites and determine their phase diagram. Moreover, we explore the many-body problem where multi-body composites self-organize to form different many-body phases, including a magnetic polaron gas and a pair density wave. We also discuss various protocols for cold atom experiments that could detect these multi-body composites. Secondly, we examine the impact of kinetic frustration on the magnetic properties of a spin-1/2 fermionic system in a triangular lattice at finite and zero temperature. We demonstrate that the system exhibits a magnetic transition as it is doped away from half-filling. Specifically, the system becomes antiferromagnetic (ferromagnetic) when doped below (above) half-filling. At finite temperature, we observe the system’s tendency to form magnetic orders by inspecting the behavior of the magnetic susceptibility. Next, we explore the formation of magnetic many-body phases at low temperatures, including the magnetic polaron gas the antiferromagnetic spin bag phase. The former is characterized by the formation of magnetization plateaus and the latter by binding of holes. Finally, we provide the temperature dependence of the charge-spin-spin correlation function.

[cat] En aquesta Tesi explorem fases exòtiques de la matèria que apareixen quan diferents mecanismes competeixen i afavoreixen diferents configuracions de l’estat fonamental. Ens centrem en dues classes de sistemes reticulars de baixa dimensió. La primera classe correspon a fluids amb interaccions tant repulsives com atractives, que poden provocar l'aparició de fases líquides quàntiques. La segona classe correspon a sistemes amb frustració geomètrica, on la minimització de l'energia cinètica és incompatible amb la geometria de la xarxa.

A la primera part d’aquesta Tesi, mostrem com emergeixen fases líquides quàntiques en sistemes atòmics ultrafreds carregats en xarxes òptiques unidimensionals. Estudiem diferents sistemes microscòpics incloent: barreges bosòniques de dues components, sistemes dipolars d’una component i sistemes d’una component amb interaccions a dos i tres cossos. Desenvolupem diferents teories que capturen la liqüefacció per als diferents sistemes esmentats i a més, realitzem simulacions de xarxes tensorials a gran escala que contrastem amb les nostres prediccions teòriques i trobem una excel·lent concordança entre elles en diferents règims de paràmetres.

A la segona part d’aquesta Tesi, explorem els efectes de la frustració cinètica en les propietats de molts cossos de sistemes d’espín-1/2 fermiònics i bosònics. En primer lloc, investiguem geometries d’escala frustrada, incloent-hi l’escala en ziga-zaga i l’escala quadrada amb un flux magnètic perpendicular. Per a l’escala en ziga- zaga, trobem que els sistemes fermiònics (bosònics) presenten una interacció efectiva atractiva (repulsiva) entre els forats i els espins voltejats, induïda únicament per l’energia cinètica i la frustració geomètrica. A l’escala quadrada amb un flux magnètic perpendicular, tant els sistemes fermiònics com els bosònics presenten interaccions atractives efectives entre els forats i els espins voltejats. En segon lloc, estudiem l’impacte de la frustració cinètica sobre les propietats magnètiques d’un sistema fermiònic d’espín-1/2 en una xarxa triangular a temperatura finita i zero. Demostrem que el sistema exhibeix una transició magnètica en funció del dopatge. Concretament, el sistema es torna antiferromagnètic (ferromagnètic) quan es dopa per sota (per sobre) de quan està mig ple.