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

Trithep Devakul, Satya N. Majumdar, David A. Huse

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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)∼L-ψ(k), where k≡S/lnL/L0, the large deviation function ψ(k) is found explicitly, and L0 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.

Original languageEnglish (US)
Article number104204
JournalPhysical Review B
Volume95
Issue number10
DOIs
StatePublished - Mar 20 2017

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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