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

Abstract

We calculate the probability distribution of entanglement entropy $S$ across a cut of a finite one-dimensional spin chain of length $L$ at an infinite-randomness fixed point using Fisher's strong randomness renormalization group (RG). Using the random transverse-field Ising model as an example, the distribution is shown to take the form $p(S|L)\ensuremath{\sim}{L}^{\ensuremath{-}\ensuremath{\psi}(k)}$, where $k\ensuremath{\equiv}S/ln\left[L/{L}_{0}\right]$, the large deviation function $\ensuremath{\psi}(k)$ is found explicitly, and ${L}_{0}$ is a nonuniversal microscopic length. We discuss the implications of such a distribution on numerical techniques that rely on entanglement, such as matrix-product-state-based techniques. Our results are verified with numerical RG simulations, as well as the actual entanglement entropy distribution for the random transverse-field Ising model which we calculate for large $L$ via a mapping to Majorana fermions.