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

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 Néel 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.

arXiv comment8 pages, 7 figures

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Cited by in corpus (10)

• Progress on stochastic analytic continuation of quantum Monte Carlo data
• Unlocking the general relationship between energy and entanglement spectra via the wormhole effect
• Demonstrating the wormhole mechanism of the entanglement spectrum via a perturbed boundary
• Relevant long-range interaction of the entanglement Hamiltonian emerges from a short-range gapped system
• Measuring the Boundary Gapless State and Criticality via Disorder Operator
• Accessing Excitation of Many-body Systems via Single-Mode Approximation within Quantum Monte Carlo Simulations
• Angular-time evolution for the Affleck-Kennedy-Lieb-Tasaki chain and its edge-state dynamics
• Worldline deconfinement and emergent long-range interaction in the entanglement Hamiltonian and in the entanglement spectrum
• Detecting underlying symmetry-protected topological phases via strange correlators and edge engineering
• Spontaneous continuous-symmetry breaking and tower of states in a comb chain