In this paper we review the quenching dynamics of a quantum $XY$ spin-1/2 chain in the presence of a transverse field, when the transverse field or the anisotropic interaction is quenched at a slow but uniform rate. We also extend the results to the cases in which the system starts with any arbitrary initial condition as opposed to the initial fully magnetically aligned state which has been extensively studied earlier. The evolution is non-adiabatic in the time interval when the parameters are close to their critical values, and is adiabatic otherwise. The density of defects produced due to non-adiabatic transitions is calculated by mapping the many-particle system to an equivalent Landau–Zener problem. We show that in one dimension the density of defects in the final state scales as $1/\sqrt{\tau}$ irrespective of the initial condition, where 𝜏 is the quenching time-scale. However, the magnitude of density of defects is found to depend on the initial condition.

We propose a hidden sector fermion dark matter model which follows a dark $SU(2)_H$ symmetry. Fermions in the dark sector also carry a global $U(1)_H$ charge while the gauge bosons and dark scalar do not have any global $U(1)_H$ charge. The lightest fermion in dark sector can serve as a potential dark matter candidate. We investigate whether the proposed dark matter candidate can explain indirect detection results from galactic centre.