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

Abstract

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. Finally, we state that since the wormhole effect amplifies the bulk energy gap by a factor of β, the relative strength of that with respect to the edge energy gap will determine the behavior of low-lying entanglement spectrum of the system.

Many versus one: The disorder operator and entanglement entropy in fermionic quantum matter

“…Due to the n-fold expansion of the configuration space and the nontrivial connectivity between the replicas during the sampling processes, obtaining numerical data of EE with good quality in QMC simulations has remained a very challenging task. Despite the difficulty, we note there are recent progresses in the nonequilibrium incremental algorithm to obtain the S n with high efficiencies and precisions [15,16,18,34] and similar advances in measuring the ES [17,19] in QMC simulations, which effectively solve the difficulties in measuring EE in boson/spin systems in (2+1)D.…”