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We propose a physical picture based on the wormhole effect of thepath-integral formulation to explain the mechanism of entanglement spectrum(ES), such that, our picture not only explains the topological state withbulk-edge correspondence of the energy spectrum and ES (the Li and Haldaneconjecture), but is generically applicable to other systems independent oftheir topological properties. We point out it is ultimately the relativestrength of bulk energy gap (multiplied with inverse temperature $\beta=1/T$)with respect to the edge energy gap that determines the behavior of thelow-lying ES of the system. Depending on the circumstances, the ES can resemblethe energy spectrum of the virtual edge, but can also represent that of thevirtual bulk. We design models both in 1D and 2D to successfully demonstratethe bulk-like low-lying ES at finite temperatures, in addition to the edge-likecase conjectured by Li and Haldane at zero temperature. Our results support thegenerality of viewing the ES as the wormhole effect in the path integral andthe different temperature-dependence for the edge and bulk of ES.

Different temperature-dependence for the edge and bulk of entanglement Hamiltonian