Entanglement spectrum of one-dimensional extended Bose-Hubbard models

TL;DR

This paper investigates the entanglement spectrum of a 1D extended Bose-Hubbard model, revealing how block symmetry and partition dependence relate to quantum phases and correlations, offering new insights into many-body entanglement properties.

Contribution

It introduces a novel analysis of the entanglement spectrum's block structure and partition dependence in the extended Bose-Hubbard model, linking spectral degeneracies to physical phases.

Findings

Block symmetry explains spectral double degeneracy in Haldane-insulator.

Partition dependence correlates with density-density correlations.

Spectral degeneracy exhibits periodic behavior in superfluid and supersolid phases.

Abstract

The entanglement spectrum provides crucial information about correlated quantum systems. We show that the study of the block-like nature of the reduced density matrix in number sectors and the partition dependence of the spectrum in finite systems leads to interesting unexpected insights, which we illustrate for the case of a 1D extended Hubbard model. We show that block symmetry provides an intuitive understanding of the spectral double degeneracy of the Haldane-insulator, revealing as well partial double degeneracy for the Mott-insulator. Moreover, surprisingly, the partition dependence of the spectral degeneracy in the Haldane- and Mott-insulator is directly linked to the, in principle unrelated, density-density correlations, and presents an intriguing periodic behavior in superfluid and supersolid phases.