Andreev-Bashkin drag plays a very important role in multiple areas such as superfluid mixtures, super-conductors, and dense nuclear matter. Here we point out that the drag phenomenon can be also important in the physics of solitons, ubiquitous objects arising in a wide array of fields ranging from tsunami waves and fiber-optic communication to biological systems. So far, fruitful studies have been conducted in ultracold atomic systems where nontrivial soliton dynamics occurred due to intercomponent density-density interaction. In this work we show that current-current coupling between components (Andreev-Bashkin drag) can lead to a substantially different kind of effect, unsupported by density-density interactions, such as a drag-induced dark soliton generation. This also points out that soliton dynamics can be used as a tool to experimentally study the dissipationless drag effect.

We demonstrate microscopically the existence of a new superfluid state of matter in a three-component Bose mixture trapped in an optical lattice. The superfluid transport involving coflow of all three components is arrested in that state, while counterflows between any pair of components are dissipationless. The presence of three components allows for three different types of counterflows with only two independent superfluid degrees of freedom.

Dissipationless flows in single-component superfluids have a significant degree of universality. In 4He, the dissipationless mass flow occurs with a superfluid velocity determined by the gradient of the superfluid phase. However, in interacting superfluid mixtures, principally new effects appear. In this Letter, we demonstrate a new kind of dissipationless phenomenon arising in mixtures of interacting bosons in optical lattices. We point out that for a particular class of optical lattices, bosons condense in a state where one of the components’ superflow results in dissipationless mass flow of the other component, in a direction different from either of the components’ superfluid velocities. The free-energy density of these systems contains a vector productlike interaction of superfluid velocities, producing the dissipationless noncollinear entrainment. The effect represents a superfluid counterpart of the Spin Hall effect.

Recent progress in optically trapped ultracold atomic gases is now making it possible to access microscopic observables in doped Mott insulators, which are the parent states of high-temperature superconductors. This makes it possible to address longstanding questions about the temperature scales at which attraction between charge carriers are present, and their mechanism. Controllable theoretical results for this problem are not available at low temperature due to the sign problem. In this work, we make important progress with this problem by employing worm-algorithm Monte Carlo, which allows us to obtain completely unbiased results for two charge carriers in a Mott insulator. Our method gives access to lower temperatures than what is currently possible in experiments, and provides evidence for attraction between dopants at a temperature scale that is now feasible in ultracold atomic systems. We also report on spin correlations in the presence of charge carriers, which are directly comparable to experiments.

Strongly interacting many-body quantum systems constitute some of the most challenging problems in physics, and exact analytical solutions are rare. In this thesis, we will investigate the models of two such systems numerically using the unbiased worm-algorithm Monte Carlo method.

The first model is the t-J model, which describes strongly correlated lattice electrons and is thought to capture the essential physics of high-temperature superconductors. Of particular interest to us is the emergent magnetic polaron studied in the first two papers. The microscopic pairing mechanism between these quasiparticles remains one of the most outstanding open questions in condensed matter physics.

The second model is an extended multi-component Bose--Hubbard model, which describes lattice bosons of multiple species. This model is essential to the third paper, in which we demonstrate a novel superfluid phenomenon in the form of a dissipationless drag effect that couples the different superfluid components of a superfluid mixture in a noncollinear fashion. Dissipationless drag is a fundamental effect present in a diverse set of physical systems. In the fourth paper, we further use the Bose--Hubbard model to study other new superfluid phenomena that arise when the number of superfluid components is increased.

A general introduction to the research field is first given in the thesis, after which some prerequisites are refreshed. Then essential concepts are introduced, and the numerical method is outlined and benchmarked. Following that is a summary of the research carried out.

Kvantfysikaliska system med många starkt interagerande partiklar utgör några av de svåraste problemen inom fysiken och exakta analytiska lösningar är därför sällsynta. I denna avhandling studeras två sådana system med hjälp av en kontrollerbar numerisk metod vid namn mask-Monte Carlo.

Den första modellen som studeras är t-J modellen vilken beskriver starkt korrelerade gitterelektroner och som förväntas skildra de väsentliga egenskaperna hos högtemperatursupraledare. Av särskilt intresse för denna avhandling är emergensen av magnetiska polaroner vilka studeras i de två första artiklarna. Den mikroskopiska parbildningsmekanismen mellan dessa kvasipartiklar kvarstår som ett ännu olöst problem inom den kondenserade materiens fysik.

Den andra modellen som studeras är en utökning av den multikomponenta Bose-Hubbard-modellen och beskriver flera olika arter av gitterbosoner. Denna modell används i den tredje artikeln för att påvisa ett nytt fenomen där drag-växelverkan kopplar två blandbara superfluida komponenter på ett icke-kolinjärt vis. Det bör påpekas att konventionell dissipationslös drag-växelverkan är ett fenomen som återfinns i en mångfald av fysikaliska system. Med hjälp av Bose-Hubbard-modellen studeras i den fjärde artikeln fenomen som uppstår när antalet superfluida komponenter ökas.

I avhandlingen ges först en allmän introduktion till de forskningsfält som berörs, därefter följer ett kapitel i vilket förkunskaper inom området gås igenom. Efter detta introduceras en handfull nödvändiga koncept varpå den numeriska metoden beskrivs och vissa av dess resultat verifieras. Därefter följer slutligen en sammanfattning av forskningen som bedrivits.

Polarons are elementary quasi-particles characterizing several interacting many-body quantum systems. The authors present an unbiased Quantum Monte Carlo simulation of a magnetic polaron in a t-J model at low-temperature, and find excellent agreement with a recent experimental realization in the framework of cold-atoms systems. Polarons are among the most elementary quasiparticles of interacting quantum matter, consisting of a charge carrier dressed by an excited background. In Mott insulators, they take the form of a dopant surrounded by a distorted spin-background. Despite the fundamental importance of polarons for the electronic structure of strongly correlated systems, access to their internal structure was only recently realized in experiments, while controllable theoretical results are still lacking due to the sign problem. Here we report unbiased high-precision data obtained from worm-algorithm Monte Carlo that reveal the real-space structure of a polaron in thet-Jmodel deep inside the region where the sign problem becomes significant. These results are directly comparable to recent quantum gas microscopy experiments, but give access to significantly lower temperatures.

We demonstrate microscopically the existence of a new superfluid state of matter in a three-component Bose mixture trapped in an optical lattice. In that state, the superfluid transport involving co-flow of all three components is arrested, while counter-flows between any pair of components are dissipationless. Due to the presence of the third component, the types of counterpropagating components are allowed to fluctuate.