Negativity Spectrum in the Random Singlet Phase

TL;DR

This paper investigates the negativity spectrum in the random singlet phase of disordered quantum systems, deriving universal scaling laws for negativity moments and revealing non-trivial relations between negativity measures after disorder averaging.

Contribution

It provides the first analytic formulas for negativity spectrum scaling in the random singlet phase using strong disorder renormalization group techniques.

Findings

Derived universal scaling formulas for negativity moments.

Validated predictions with numerical SDRG and exact XX chain computations.

Discovered that negativity and logarithmic negativity are not trivially related after disorder averaging.

Abstract

Entanglement features of the ground state of disordered quantum matter are often captured by an infinite randomness fixed point that, for a variety of models, is the random singlet phase. Although a copious number of studies covers bipartite entanglement in pure states, at present, less is known for mixed states and tripartite settings. Our goal is to gain insights in this direction by studying the negativity spectrum in the random singlet phase. Through the strong disorder renormalization group technique, we derive analytic formulas for the universal scaling of the disorder averaged moments of the partially transposed reduced density matrix. Our analytic predictions are checked against a numerical implementation of the strong disorder renormalization group and against exact computations for the XX spin chain (a model in which free fermion techniques apply). Importantly, our results show that the negativity and logarithmic negativity are not trivially related after the average over the disorder.