Anyonic Haldane insulator in one dimension

TL;DR

This paper numerically demonstrates a topological Haldane phase in a one-dimensional extended Hubbard model, applicable to both bosons and anyons, protected by combined symmetries, with implications for experimental detection.

Contribution

It reveals the existence of a topological Haldane insulator phase for anyons in 1D Hubbard models, extending previous bosonic results and analyzing symmetry protections.

Findings

Haldane insulator exists for anyons despite broken reflection symmetry

Protected by combined spatial-inversion and time-reversal symmetries

Asymmetry in dynamical density structure factor could aid experimental detection

Abstract

We demonstrate numerically the existence of a nontrivial topological Haldane phase for the one-dimensional extended ($U$-$V$) Hubbard model with a mean density of one particle per site, not only for bosons but also for anyons, despite a broken reflection parity symmetry. The Haldane insulator, surrounded by superfluid, Mott insulator and density-wave phases in the $V$-$U$ parameter plane, is protected by combined (modified) spatial-inversion and time-reversal symmetries, which is verified within our matrix-product-state based infinite density-matrix renormalization group scheme by analyzing generalized transfer matrices. With regard to an experimental verification of the anyonic Haldane insulator state the calculated asymmetry of the dynamical density structure factor should be of particular importance.