  Low-lying entanglement spectrum provides the quintessential fingerprint to
identify the highly entangled quantum matter with topological and conformal
field-theoretical properties. However, when the entangling region acquires long
boundary with the environment, such as that between long coupled chains or in
two or higher dimensions, there unfortunately exists no universal yet practical
method to compute the entanglement spectra with affordable computational cost.
Here we propose a new scheme to overcome such difficulty and successfully
extract the low-lying fine entanglement spectrum (ES). We trace out the
environment via quantum Monte Carlo simulation and diagonalize the reduced
density matrix to gain the ES. We demonstrate the strength and reliability of
our method through long coupled spin chains and answer its long-standing
controversy. Our simulation results, with unprecedentedly large system sizes,
establish the practical computation scheme of the entanglement spectrum with a
huge freedom degree of environment.
