Spurious Long-range Entanglement and Replica Correlation Length

Understand

Topological entanglement entropy has been regarded as a smoking-gun signature of topological order in two dimensions, capturing the total quantum dimension of the topological particle content.

• An extrapolation method on cylinders has been used frequently to measure the topological entanglement entropy.
• Here, we show that a class of short-range entangled 2D states, when put on an infinite cylinder of circumference $L$, exhibits the entanglement R\'enyi entropy of any integer index $\alpha \ge 2$ that obeys $S_\alpha = a L - \gamma$ where $a, \gamma > 0 $.
• Under the extrapolation method, the subleading term $\gamma$ would be identified as the topological entanglement entropy, which is spurious.