Entanglement spectrum of random-singlet quantum critical points

TL;DR

This paper analyzes the entanglement spectrum at the random-singlet quantum critical point in one dimension, revealing unique geometric dependencies and providing analytical and numerical insights into disordered quantum critical systems.

Contribution

It provides the first computation of the disorder-averaged entanglement spectrum at a random-singlet critical point, comparing analytical results with numerical simulations.

Findings

Disorder-averaged entanglement spectrum matches numerical results in the scaling limit.

Entanglement entropy and spectrum depend differently on Hilbert space partition geometry than in conformal critical points.

Results are applicable to both non-interacting and interacting disordered spin chains.

Abstract

The entanglement spectrum, i.e., the full distribution of Schmidt eigenvalues of the reduced density matrix, contains more information than the conventional entanglement entropy and has been studied recently in several many-particle systems. We compute the disorder-averaged entanglement spectrum, in the form of the disorder-averaged moments of the reduced density matrix, for a contiguous block of many spins at the random-singlet quantum critical point in one dimension. The result compares well in the scaling limit with numerical studies on the random XX model and is also expected to describe the (interacting) random Heisenberg model. Our numerical studies on the XX case reveal that the dependence of the entanglement entropy and spectrum on the geometry of the Hilbert space partition is quite different than for conformally invariant critical points.