Symmetry-protected topological order in magnetization plateau states of quantum spin chains

TL;DR

This paper demonstrates that certain magnetization plateau states in one-dimensional antiferromagnetic spin chains are symmetry-protected topological phases, confirmed through field theory analysis, numerical entanglement spectra, and matrix product state methods.

Contribution

It identifies conditions under which magnetization plateau states are symmetry-protected topological phases, linking field theory, numerical, and rigorous matrix product state analyses.

Findings

Magnetization plateau states with S-m in odd integers are SPT phases.

Entanglement spectra show twofold degeneracy under these conditions.

Numerical and matrix product state analyses confirm the theoretical predictions.

Abstract

A symmetry-protected topologically ordered phase is a short-range entangled state, for which some imposed symmetry prohibits the adiabatic deformation into a trivial state which lacks entanglement. In this paper we argue that magnetization plateau states of one-dimensional antiferromagnets which satisfy the conditions $S-m\in$ odd integer, where $S$ is the spin quantum number and $m$ the magnetization per site, can be identified as symmetry-protected topological states if an inversion symmetry about the link center is present. This assertion is reached by mapping the antiferromagnet into a nonlinear sigma model type effective field theory containing a novel Berry phase term (a total derivative term) with a coefficient proportional to the quantity $S-m$, and then analyzing the topological structure of the ground state wave functional which is inherited from the latter term. A boson-vortex duality transformation is employed to examine the topological stability of the ground state in the absence/presence of a perturbation violating link-center inversion symmetry. Our prediction based on field theories is verified by means of a numerical study of the entanglement spectra of actual spin chains, which we find to exhibit twofold degeneracies when the aforementioned condition is met. We complete this study with a rigorous analysis using matrix product states.