Spectral and Entanglement Properties of the Bosonic Haldane Insulator

TL;DR

This paper identifies and characterizes a topologically nontrivial Haldane insulator phase in a one-dimensional extended Bose-Hubbard model, revealing its spectral, entanglement, and dynamical properties through advanced numerical methods.

Contribution

It demonstrates the existence of a Haldane insulator phase stabilized by nearest-neighbor interactions, with detailed analysis of its entanglement spectrum and dynamical structure factors.

Findings

Haldane insulator is stabilized by nearest-neighbor repulsion.

Entanglement spectrum shows fourfold degeneracy.

Dynamical charge structure factor exhibits gapped dispersion.

Abstract

We discuss the existence of a nontrivial topological phase in one-dimensional interacting systems described by the extended Bose-Hubbard model with a mean filling of one boson per site. Performing large-scale density-matrix renormalization group calculations we show that the presence of nearest-neighbor repulsion enriches the ground-state phase diagram of the paradigmatic Bose-Hubbard model by stabilizing a novel gapped insulating state, the so-called Haldane insulator, which, embedded into superfluid, Mott insulator, and density wave phases, is protected by the lattice inversion symmetry. The quantum phase transitions between the different insulating phases were determined from the central charge via the von Neumann entropy. The Haldane phase reveals a characteristic fourfold degeneracy of the entanglement spectrum. We finally demonstrate that the intensity maximum of the dynamical charge structure factor, accessible by Bragg spectroscopy, features the gapped dispersion known from the spin-1 Heisenberg chain.