We systematically investigate and illustrate the complete ground-state phase diagram for a one-dimensional, three-species mixture of a few repulsively interacting bosons trapped harmonically. To numerically obtain the solutions to the many-body Schrödinger equation, we employ the improved Exact Diagonalization method (Anh-Tai et al 2023 SciPost Phys. 15 048), which is capable of treating strongly-correlated few-body systems from first principles in an efficiently truncated Hilbert space. We present our comprehensive results for all possible combinations of intra- and interspecies interactions in the extreme limits that are either the ideal limit (g = 0) or close to the hard-core limit (). These results show the emergence of unique ground-state properties related to correlations, coherence and spatial localization stemming from strongly repulsive interactions.
We systematically investigate and illustrate the complete ground-state phase diagram for a one-dimensional, three-species mixture of a few repulsively interacting bosons trapped harmonically. To numerically obtain the solutions to the many-body Schrödinger equation, we employ the improved Exact Diagonalization method (Anh-Tai et al 2023 SciPost Phys. 15 048), which is capable of treating strongly-correlated few-body systems from first principles in an efficiently truncated Hilbert space. We present our comprehensive results for all possible combinations of intra- and interspecies interactions in the extreme limits that are either the ideal limit (g = 0) or close to the hard-core limit (). These results show the emergence of unique ground-state properties related to correlations, coherence and spatial localization stemming from strongly repulsive interactions.
Abstract We systematically investigate and illustrate the complete ground-state phase diagram for a one-dimensional, three-species mixture of a few repulsively interacting bosons trapped harmonically. To numerically obtain the solutions to the many-body Schrödinger equation, we employ the improved Exact Diagonalization method (Anh-Tai et al 2023 SciPost Phys. 15 048), which is capable of treating strongly-correlated few-body systems from first principles in an efficiently truncated Hilbert space. We present our comprehensive results for all possible combinations of intra- and interspecies interactions in the extreme limits that are either the ideal limit (g = 0) or close to the hard-core limit ( g → ∞ ). These results show the emergence of unique ground-state properties related to correlations, coherence and spatial localization stemming from strongly repulsive interactions.
We present the complete phase diagram for one-dimensional binary mixtures of bosonic ultracold atomic gases in a harmonic trap. We obtain exact results with direct numerical diagonalization for a small number of atoms, which permits us to quantify quantum many-body correlations. The quantum Monte Carlo method is used to calculate energies and density profiles for larger system sizes. We study the system properties for a wide range of interaction parameters. For the extreme values of these parameters, different correlation limits can be identified, where the correlations are either weak or strong. We investigate in detail how the correlations evolve between the limits. For balanced mixtures in the number of atoms in each species, the transition between the different limits involves sophisticated changes in the one- and two-body correlations. Particularly, we quantify the entanglement between the two components by means of the von Neumann entropy. We show that the limits equally exist when the number of atoms is increased for balanced mixtures. Also, the changes in the correlations along the transitions among these limits are qualitatively similar. We also show that, for imbalanced mixtures, the same limits with similar transitions exist. Finally, for strongly imbalanced systems, only two limits survive, i.e., a miscible limit and a phase-separated one, resembling those expected with a mean-field approach.
In this thesis, we study the physical properties of several ultracold few-boson systems depending on the interactions between their constituents. Nowadays, experimentally, it is possible to have great control with high precision over the geometry and the interactions between the particles, making them an excellent setup to test directly the principles of quantum mechanics. A very interesting point is to study the evolution of their properties with the number of particles. The theoretical study of these systems pretends to microscopically understand the current experimental results and give support to new experimental developments.\n\n\t\t\t\t The method that will be used is the exact diagonalization of the Hamiltonian of the system. As we will see, in spite of the attempts to improve it, the method is limited by the fact that, in practice, it is only useful to study few-particle systems. The method has several advantages. First of all, one has access to both the ground and the excited states. In second place, the method is variational and converges to the exact solution as long as the Hilbert space in which we diagonalize is enlarged.\n\t\t\t\t Moreover, since we have access to the states of the system, it is possible to calculate any observable quantity of interest.\n\n\t\t\t\t First, we will study a system of spinless bosons trapped in a two-dimensional harmonic potential. The effect of the trap is to keep the system bound. It will be seen how the presence of a repulsive interaction changes the energy spectrum and other properties of the system. For instance, the density profile, which is usually measurable, and also the two-body distribution function, which is intimately related to the existence of correlations.\n\n\t\t\t\t Afterwards, the focus will be on the particular case of having only two bosons in the system interacting through a strong repulsive force. Inspired by the one-dimensional case where the fermionization phenomenon takes place in the strongly-interacting limit, we will study whether in two dimensions there is a resembling reminiscent effect. In other words, we will analyze if there are properties of the two strongly-interacting bosons in two dimensions that are like the ones of two noninteracting fermions.\n\n\t\t\t\t After that, we will tackle the localization phenomenon in a one-dimensional system that is caused by an external speckle potential that introduces disorder in the system. We will show that the localization is a robust phenomenon against repulsive contact interactions.\n\n\t\t\t\t Finally, we will study the influence of the spin-orbit coupling in a system of bosons with two possible pseudospin components, associated, for instance, to two hyperfine levels, confined in a two-dimensional harmonic trap. We will present an exhaustive analysis of the combined effects of the interaction and the spin-orbit coupling in the spectrum and the properties of the system. In particular we show the existence of a crossover in the ground state of the system susceptible to be experimentally identified.
We present a density-functional theory for the one-dimensional harmonically trapped Bose-Fermi mixture with repulsive contact interactions. The ground-state density distribution of each component is obtained by solving the Kohn-Sham equations numerically based on the local density approximation and the exact solution for the homogeneous system given by Bethe ansatz method. It is shown that for sufficiently strong interaction, a considerable amount of fermions are repelled out of the central region of the trap, exhibiting partial phase separation of Bose and Fermi components. Oscillations emerge in the Bose density curves, reflecting the strong correlation with fermions. For infinitely strong interaction, the ground-state energy of the mixture and the total density are consistent with the scenario that all atoms in the mixture are fully fermionized.
We consider multi-component quantum mixtures (bosonic, fermionic, or mixed) with strongly repulsive contact interactions in a one-dimensional harmonic trap. In the limit of infinitely strong repulsion and zero temperature, using the class-sum method, we study the symmetries of the spatial wave function of the mixture. We find that the ground state of the system has the most symmetric spatial wave function allowed by the type of mixture. This provides an example of the generalized Lieb–Mattis theorem. Furthermore, we show that the symmetry properties of the mixture are embedded in the large-momentum tails of the momentum distribution, which we evaluate both at infinite repulsion by an exact solution and at finite interactions using a numerical DMRG approach. This implies that an experimental measurement of the Tan’s contact would allow to unambiguously determine the symmetry of any kind of multi-component mixture.
We investigate the ground-state properties of two-component Bose gases confined in one-dimensional harmonic traps in the scheme of density-functional theory. The density-functional calculations employ a Bethe-ansatz-based local-density approximation for the correlation energy, which accounts for the correlation effect properly from the weakly interacting regime to the strongly interacting regime. For the binary Bose mixture with spin-independent interaction, the homogeneous reference system is exactly solvable by the Bethe-ansatz method. Within the local-density approximation, we determine the density distribution of each component and study its evolution from Bose distributions to Fermi-like distribution with the increase in interaction. For the binary mixture of Tonks-Girardeau gases with a tunable interspecies repulsion, with a generalized Bose-Fermi transformation we show that the Bose mixture can be mapped into a two-component Fermi gas, which corresponds to exact soluble Yang-Gaudin model for the homogeneous system. Based on the ground-state energy function of the Yang-Gaudin model, the ground-state density distributions are calculated for various interspecies interactions. It is shown that with the increase in interspecies interaction, the system exhibits composite-fermionization crossover.