Figure 1: Contact of 1D two-component fermions with zero range interaction at zero temperature.
(a) A contour plot of contact as a function of the dimensionless chemical potential 
and magnetic field 
, where 
is the binding energy determined by the 1D scattering length a1D. The notations V, P, F and PP stand for vacuum, fully paired, fully polarized and partially polarized phase, respectively. Red and green curves represent the phase boundaries obtained from thermodynamic Bethe ansatz equations. Vertical dashed lines correspond to two cuts at fixed h=0.8 and 1.4. (b) Contact is continuous across the quantum critical points. For the transition V–P and F–PP, the dimensionless contact 
continuously increases from zero as 
. For the transition P–PP, contact is finite on both sides of the transition point and a kink exists as 
, indicating the discontinuity of the derivative of contact. (c) The derivative of contact with respect to 
becomes divergent as 
in this 1D system at all the transitions V–P, P–PP and F–PP for fixed values of h=0.8 (blue line) and h=1.4 (red line).
