Entanglement in a first-order quantum phase transition

We analyze the entanglement properties of the ground state for a system of spins half embedded in a magnetic field, mutually interacting antiferromagnetically. Contrary to the ferromagnetic case where a second-order quantum phase transition occurs, a first-order transition is obtained at zero field and the so-called concurrence which measures the two-spin entanglement displays a jump at the transition point.

Figure 1

Ground state energy of each spin sector as a function of the magnetic field for $\gamma =1∕2$ $\left(\lambda =-1\right)$. In the even case $N=6$ (left) all levels degenerate at $h_{\text{susy}}$ $(•),$ whereas in the odd one $N=5$ (right) a cascade is observed from the $S=N∕2$ to the $S=1∕2$ sector.

Figure 2

Rescaled concurrence of the ground state as a function of the magnetic field for various anisotropy parameter $\gamma$ and for $N={10}^3$ spins $\left(\lambda =-1\right)$. Note that for any $\gamma$, one has $C_R=0$ at zero field.

Figure 3

Rescaled concurrence of the ground state $\mid {\psi }_0⟩$ at the SUSY point as a function of the anisotropy parameter $\gamma$ for $N={10}^4$ spins.