Real-space entanglement spectrum of quantum Hall systems

We study the real-space entanglement spectrum for fractional quantum Hall systems, which maintains locality along the spatial cut, and provide evidence that it possesses a scaling property. We also consider the closely related particle entanglement spectrum and carry out the Schmidt decomposition of the Laughlin state analytically at large size.

Figure 1

Low-lying RSP ES of the $\nu =1$ filled LLL, for $N=30$ particles, and $N_A=15$. Lower inset: lowest levels. Upper inset: low-lying ES vs $N_A$ for $N=16$.

Figure 2

Similar to Fig. 1, but for the $\nu =1/3$ Laughlin state with $N=12$, $N_A=6$, and upper inset shows minimum $\xi$ only.

Figure 3

Same as Fig. 2 but for the Coulomb interaction.

Figure 4

Low-lying ES for the PP in the $\nu =1/3$ Laughlin state, for $N=12$ particles, including all $N_A$ values, vs $L^A$, not $L_z^A$.