Frustration, Area Law, and Interference in Quantum Spin Models

We study frustrated quantum systems from a quantum information perspective. Within this approach, we find that highly frustrated systems do not follow any general “area law” of block entanglement, while weakly frustrated ones have area laws similar to those of nonfrustrated systems away from criticality. To calculate the block entanglement in systems with degenerate ground states, typical in frustrated systems, we define a “cooling” procedure of the ground state manifold and propose a frustration degree and a method to quantify constructive and destructive interference effects of entanglement.

Figure 1

Constructive and destructive interference. Left: $E/\overline{E}$ for a square $\mathbb{B}$, so that $v=h$. Right: $E/\overline{E}$ for a horizontal (vertical) boundary, so that $v=0$ ($h=0$). The vertical axes are of $E/\overline{E}$.