Entanglement spectrum and quantum phase diagram of the long-range XXZ chain

TL;DR

This paper studies the entanglement spectrum of the long-range XXZ model, revealing self-similarity in the critical phase, and uses this to map the quantum phase diagram with tensor-network methods.

Contribution

It uncovers self-similarity in the entanglement spectrum of the long-range XXZ model and links it to phase transitions, advancing understanding of entanglement in long-range quantum systems.

Findings

Self-similarity in the entanglement spectrum within the critical phase

Identification of phase transitions via breakdown of self-similarity

Confirmation of results with tensor-network numerical methods

Abstract

Entanglement is a central feature of many-body quantum systems and plays a unique role in quantum phase transitions. In many cases, the entanglement spectrum, which represents the spectrum of the density matrix of a bipartite system, contains valuable information beyond the sole entanglement entropy. Here we investigate the entanglement spectrum of the long-range XXZ model. We show that within the critical phase it exhibits a remarkable self-similarity. The breakdown of self-similarity and the transition away from a Luttinger liquid is consistent with renormalization group theory. Combining the two, we are able to determine the quantum phase diagram of the model and locate the corresponding phase transitions. Our results are confirmed by numerically-exact calculations using tensor-network techniques. Moreover, we show that the self-similar rescaling extends to the geometrical entanglement as well as the Luttinger parameter in the critical phase. Our results pave the way to further studies of entanglement properties in long-range quantum models.