Probability distribution of the entanglement across a cut at an infinite-randomness fixed point

摘要

We calculate the probability distribution of entanglement entropy S across acut of a finite one dimensional spin chain of length L at an infiniterandomness fixed point using Fisher's strong randomness renormalization group(RG). Using the random transverse-field Ising model as an example, thedistribution is shown to take the form $p(S|L) \sim L^{-\psi(k)}$, where $k = S/ \log [L/L_0]$, the large deviation function $\psi(k)$ is found explicitly,and $L_0$ is a nonuniversal microscopic length. We discuss the implications ofsuch a distribution on numerical techniques that rely on entanglement, such asmatrix product state (MPS) based techniques. Our results are verified withnumerical RG simulations, as well as the actual entanglement entropydistribution for the random transverse-field Ising model which we calculate forlarge L via a mapping to Majorana fermions.