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

TL;DR

This paper derives the probability distribution of entanglement entropy across a cut in a 1D spin chain at an infinite randomness fixed point, revealing a specific large deviation form and implications for numerical methods.

Contribution

It explicitly calculates the entanglement entropy distribution at an infinite randomness fixed point using RG and numerical simulations, providing new insights into entanglement behavior.

Findings

Distribution follows a large deviation form with a specific function ψ(k)

Numerical RG simulations confirm the theoretical distribution

Entanglement entropy distribution impacts numerical techniques like MPS

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 $p(S|L) \sim L^{-\psi(k)}$, 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 of such a distribution on numerical techniques that rely on entanglement, such as matrix product state (MPS) 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.