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 $p(S|L)\sim L^{-\psi (k)}$, 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.

6 pages, 4 figures

References in corpus (9)

• The density-matrix renormalization group in the age of matrix product states
• Scaling of Entanglement Entropy in the Random Singlet Phase
• Quantum criticality of hot random spin chains
• Entanglement spectrum of random-singlet quantum critical points
• Entanglement entropy at infinite randomness fixed points in higher dimensions
• Entanglement Entropy in the Two-Dimensional Random Transverse Field Ising Model
• Increasing of entanglement entropy from pure to random quantum critical chains
• Finite-size scaling of the entanglement entropy of the quantum Ising chain with homogeneous, periodically modulated and random couplings
• Statistics of the Number of Zero Crossings : from Random Polynomials to Diffusion Equation

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• Entanglement across extended random defects in the XX spin chain