Entanglement spectrum and entangled modes of random XX spin chains

TL;DR

This paper investigates the entanglement properties of finite random XX spin-1/2 chains, analyzing the entanglement spectrum and modes using Jordan-Wigner transformation, and compares results with real space renormalization group predictions.

Contribution

It demonstrates the validity and limitations of RSRG for entanglement in disordered spin chains and visualizes effective spins forming long-distance singlet pairs.

Findings

RSRG is valid for strong disorder in entanglement analysis.

Limitations of RSRG appear at weak disorder levels.

Visualization of effective spins forming long-distance singlet pairs.

Abstract

We study in this work the ground state entanglement properties of finite XX spin-1/2 chains with random couplings, using Jordan-Wigner transformation. We divide the system into two parts and study reduced density matrices (RDMs) of its subsystems. Due to the free-fermion nature of the problem, the RDMs take the form of that of a free fermion thermal ensemble. Finding spectrum of the corresponding entanglement Hamiltonian and corresponding eigenvectors, and comparing them with real space renormalization group (RSRG) treatment, we establish the validity of the RSRG approach for entanglement in the limit of strong disorder, but also find its limitations when disorder is weak. In the latter case our work provides a way to visualize the "effective spins" that form long distance singlet pairs.