Criticality at the Haldane-insulator charge-density-wave quantum phase transition

TL;DR

This paper investigates the quantum phase transition from a Haldane insulator to a charge-density-wave state in a one-dimensional extended Hubbard model with additional ferromagnetic interactions, revealing critical behavior and topological features.

Contribution

It demonstrates the emergence of a symmetry-protected topological Haldane state and characterizes the nature of the phase transition, including its universality class and entanglement properties.

Findings

Identification of the Haldane insulator with characteristic entanglement degeneracy

Observation of a quantum phase transition with tricritical Ising universality

Transition becomes first order above a critical interaction ratio

Abstract

Exploiting the entanglement concept within a matrix-product-state based infinite density-matrix renormalization group approach, we show that the spin-density-wave and bond-order-wave ground states of the one-dimensional half-filled extended Hubbard model give way to a symmetry-protected topological Haldane state in case an additional alternating ferromagnetic spin interaction is added. In the Haldane insulator the lowest entanglement level features a characteristic twofold degeneracy. Increasing the ratio between nearest-neighbor and local Coulomb interaction $V/U$, the enhancement of the entanglement entropy, the variation of the charge, spin and neutral gaps, and the dynamical spin/density response signal a quantum phase transition to a charge-ordered state. Below a critical point, which belongs to the universality class of the tricritical Ising model with central charge 7/10, the model is critical with $c=1/2$ along the transition line. Above this point, the transition between the Haldane insulator and charge-density-wave phases becomes first order.