Entanglement spectrum and entangled modes of highly excited states in random XX spin chains

TL;DR

This paper investigates the entanglement properties of highly excited states in disordered XX spin chains using the RSRG-X method, validating its accuracy in strong disorder and analyzing its limitations at higher temperatures.

Contribution

The study provides a detailed entanglement analysis of excited states in disordered XX chains and assesses the accuracy of the RSRG-X method across different disorder regimes.

Findings

RSRG-X accurately predicts entanglement features in strong disorder.

Error in RSRG-X increases with weaker disorder and higher temperature.

Entanglement modes and energies align with theoretical predictions in the strong disorder limit.

Abstract

We examine the real space renormalization group method of finding \textit{excited eigenstate} (RSRG-X) of the XX spin-1/2 chain, from entanglement perspectives. Eigenmodes of entanglement Hamiltonian, especially the maximally entangled mode and corresponding entanglement energies are studied and compared with predictions of RSRG-X. Our numerical results demonstrate the accuracy of the RSRG-X method in the strong disorder limit, and quantify its error when applied to weak disorder regime. Overall, our results validate the RSRG-X method qualitatively, but also show that its accuracy decreases with increasing temperature.