Properties of ground state and quench dynamics of one-dimensional contact repulsive single-spin flipped Fermi gases

Based on the exact solution method, the ground state and quench dynamics properties of one-dimensionalsingle-spin flipped Fermi gas with repulsion interaction are studied. With the Bethe wave function, the single-body correlation function and two-body correlation function of the ground state and those between differenteigen-states can be reduced into a summation of simple functions, thereby greatly reducing the computationaldifficulty. For the system in the ground state, the single-body correlation functions and two-body correlationfunctions as well as momentum distributions for spin-up particles are investigated in real space with differentinteraction strengths. As the interaction strength increases, the number of nodes in the single-body correlationfunction remains unchanged, while the amplitude of oscillation decreases. Meanwhile, the number of peaks inthe two-body correlation function increases by one due to interaction, indicating that the spin-down particlebehaves as a spin-up particle. The momentum distribution becomes more smooth around Fermi surface with theinteraction strength increasing. The interaction quench dynamics is investigated. The system is prepared in theground state of ideal Fermi gas, and then the interaction strength is quenched to a finite positive value. Thesystem evolves under time-dependent Schrodinger equation. The overlap between the initial state and eigen-state of post-quench interaction strength is expressed in the form of continued multiplication. The square of themodulus of this overlap, which represents the occupation probability, is calculated. We find that the occupationprobabilities of the ground state and doubly degenerated excited state always have the first and the secondlargest value for an arbitrary interaction strength, respectively, which means that the difference in eigenenergybetween these two states gives the primary period of oscillation. For relatively large particle number (),the primary period always does not change under different interaction strengths. It is found that in the case ofinteraction quenching, the momentum distribution and the correlation function show periodic oscillations. Whenthe interaction strength is adjusted to a relatively small value, the oscillation periodicity is well-defined and theoscillation amplitude is small. The system can be approximated by a two-level model. When the interactionstrength increases to a very large value, the oscillation periodicity worsens and the amplitude increases, but aprimary period remains unchanged. Although the overall deviation is far from the initial state, it is very close tothe initial state at time t=mL(2) /(2 pi h). This is because the difference between most energy eigenvalues isalmost an integral multiple of energy unit 2 x (2 pi/ L)(2) .