Reduced one-body density matrix of Tonks–Girardeau gas at finite temperature

With thermal Bose-Fermi mapping method, we investigate the Tonks-Girardeau gas at finite temperature. It is shown that at low temperature, the Tonks gas displays the Fermi-like density profiles, and with the increase in temperature, the Tonks gas distributes in wider region. The reduced one-body density matrix is diagonal dominant in the whole temperature region, and the off-diagonal elements shall vanish rapidly with the deviation from the diagonal part at high temperature.