Ground state of Tonks-Girardeau gas under density-dependent gauge potential in a one dimensional harmonic potential

In the present paper we investigate the ground state of Tonks-Girardeau gas under density-dependent gauge potential. With Bose-Fermi mapping method we obtain the exact ground state wavefunction for the system confined in a harmonic potential. Based on the ground state wavefunction, the reduced one body density matrix (ROBDM), natural orbitals and their occupations, and the momentum distributions are obtained. Compared with the case without gauge potential, the present wavefunction and ROBDM have additional phase factors induced by gauge potential. The momentum distribution is the convolution of that without gauge potential to the Fourier transformation of definite integral of gauge potential. It is shown that because of the density-dependent gauge potential the peak of momentum distributions deviate from zero momentum and the Bose gas take finite total momentum. In particular the momentum distribution is no longer symmetric although the total momentum can become zero by adding a constant to the gauge potential.