In this work we investigate the different states of a system of spin-1 bosons in two potential wells connected by tunneling, with spin-dependent interaction. The model utilizes the well-known Bose-Hubbard Hamiltonian, adding a local interaction term
that depends on the modulus of the total spin in a well, favoring a high- or low-spin state for different signs of the coupling constant. We employ the concept of fidelity to detect critical values of parameters for which the ground state undergoes significant changes. The nature of the states is investigated through evaluation of average occupation numbers in the wells and of spin correlations. A more detailed analysis is done for a two-particle system, but a discussion of the three-particle case and some results for larger numbers are also presented.
We establish a new geometric wave function that combined with a variational principle efficiently describes a system of bosons interacting in a one-dimensional trap. By means of a a combination of the exact wave function solution for contact interact
ions and the asymptotic behaviour of the harmonic potential solution we obtain the ground state energy, probability density and profiles of a few boson system in a harmonic trap. We are able to access all regimes, ranging from the strongly attractive to the strongly repulsive one with an original and simple formulation.
We calculate the Wilson ratio of the one-dimensional Fermi gas with spin imbalance. The Wilson ratio of attractively interacting fermions is solely determined by the density stiffness and sound velocity of pairs and of excess fermions for the two-com
ponent Tomonaga-Luttinger liquid (TLL) phase. The ratio exhibits anomalous enhancement at the two critical points due to the sudden change in the density of states. Despite a breakdown of the quasiparticle description in one dimension, two important features of the Fermi liquid are retained, namely the specific heat is linearly proportional to temperature whereas the susceptibility is independent of temperature. In contrast to the phenomenological TLL parameter, the Wilson ratio provides a powerful parameter for testing universal quantum liquids of interacting fermions in one, two and three dimensions.
In this work, combining the Bethe ansatz approach with the variational principle, we calculate the ground state energy of the relative motion of a system of two fermions with spin up and down interacting via a delta-function potential in a 1D harmoni
c trap. Our results show good agreement with the analytical solution of the problem, and provide a starting point for the investigation of more complex few-body systems where no exact theoretical solution is available.
We investigate two solvable models for Bose-Einstein condensates and extract physical information by studying the structure of the solutions of their Bethe ansatz equations. A careful observation of these solutions for the ground state of both models
, as we vary some parameters of the Hamiltonian, suggests a connection between the behavior of the roots of the Bethe ansatz equations and the physical behavior of the models. Then, by the use of standard techniques for approaching quantum phase transition - gap, entanglement and fidelity - we find that the change in the scenery in the roots of the Bethe ansatz equations is directly related to a quantum phase transition, thus providing an alternative method for its detection.
