Bulk and edge dynamics of a 2D Affleck-Kennedy-Lieb-Tasaki model

TL;DR

This study investigates the dynamical properties of a 2D AKLT model, revealing localized states, phase transitions, and distinct edge and bulk behaviors using quantum Monte Carlo simulations.

Contribution

It provides new insights into the bulk and edge spin dynamics of the 2D AKLT model, highlighting localized states and phase transition characteristics.

Findings

Flat band spectrum indicating localized states

Continuous phase transition with gap closing at critical point

Edge gap closing leading to a flat-band-like Luttinger liquid phase

Abstract

We study the dynamical properties of both bulk and edge spins of a two-dimensional Affleck-Kennedy-Lieb-Tasaki (AKLT) model mainly by using the stochastic series expansion quantum Monte Carlo method with stochastic analytic continuation. In the deep AKLT phase, we obtain a spin spectrum with flat band, which is a strong evidence for a localized state. Through the spectrum analysis, we see a clear continuous phase transition from the AKLT phase to the N\'eel phase in the model, and the energy gap becomes closed at the corresponding momentum point. In comparison with linear spin-wave theory, the differences show that there are strong interactions among magnons at high energies. With open boundary condition, the gap of edge spins in the AKLT phase closes at both the $\Gamma$ point and the $\pi$ point interestingly to emerge into a flat-band-like Luttinger liquid phase, which can be explained by symmetry and perturbation approximation. This paper helps us to better understand the completely different dynamical behaviors of bulk and edge spins in the symmetry protected topological phase.