Unlocking the general relationship between energy and entanglement spectra via the wormhole effect

Understand

Based on the path integral formulation of the reduced density matrix, we develop a scheme to overcome the exponential growth of computational complexity in reliably extracting low-lying entanglement spectrum from quantum Monte Carlo simulations.

• We test the method on the Heisenberg spin ladder with long entangled boundary between two chains and the results support the Li and Haldane's conjecture on entanglement spectrum of topological phase.
• We then explain the conjecture via the wormhole effect in the path integral and show that it can be further generalized for systems beyond gapped topological phases.
• Our further simulation results on the bilayer antiferromagnetic Heisenberg model with 2D entangled boundary across the $(2+1)$D O(3) quantum phase transition clearly demonstrate the correctness of the wormhole picture.