Exact weak bosonic zero modes in a spin/fermion chain

We study an exactly solvable one-dimensional spin-$\frac{1}{2}$ model which can support weak zero modes in its ground state manifold. The spin chain has staggered XXZ-type and ZZ-type spin interaction on neighboring bonds and is thus dubbed the (XXZ,Z) chain. The model is equivalent to an interacting fermionic chain by Jordan-Wigner transformation. We study the phase diagram of the system and work out the conditions and properties of its weak zero modes. In the fermion chain representation, these weak zero modes are given by even-order polynomials of Majorana fermion operators and are thus bosonic. The fermionic chain Hamiltonian contains only fermion hopping and interaction terms and may have potential realization in experiments.Comment: 5 pages, 3 figure

Weakly-supervised Pre-training for 3D Human Pose Estimation via Perspective Knowledge

Modern deep learning-based 3D pose estimation approaches require plenty of 3D pose annotations. However, existing 3D datasets lack diversity, which limits the performance of current methods and their generalization ability. Although existing methods utilize 2D pose annotations to help 3D pose estimation, they mainly focus on extracting 2D structural constraints from 2D poses, ignoring the 3D information hidden in the images. In this paper, we propose a novel method to extract weak 3D information directly from 2D images without 3D pose supervision. Firstly, we utilize 2D pose annotations and perspective prior knowledge to generate the relationship of that keypoint is closer or farther from the camera, called relative depth. We collect a 2D pose dataset (MCPC) and generate relative depth labels. Based on MCPC, we propose a weakly-supervised pre-training (WSP) strategy to distinguish the depth relationship between two points in an image. WSP enables the learning of the relative depth of two keypoints on lots of in-the-wild images, which is more capable of predicting depth and generalization ability for 3D human pose estimation. After fine-tuning on 3D pose datasets, WSP achieves state-of-the-art results on two widely-used benchmarks