We investigate the topological properties of a two-chain quantum ladder with uneven legs,i.e.,the two chains differ in their periods by a factor of 2.Such an uneven ladder presents rich band structures classified by t...We investigate the topological properties of a two-chain quantum ladder with uneven legs,i.e.,the two chains differ in their periods by a factor of 2.Such an uneven ladder presents rich band structures classified by the closure of either direct or indirect bandgaps.It also provides opportunities to explore fundamental concepts concerning band topology and edge modes,including the difference of intracellular and intercellular Zak phases,and the role of the inversion symmetry(IS).We calculate the Zak phases of the two kinds and find excellent agreement with the dipole moment and extra charge accumulation.We also find that configurations with IS feature a pair of degenerate two-side edge modes emerging as the closure of the direct bandgap,while configurations without IS feature one-side edge modes emerging as not only the closure of both direct and indirect bandgaps but also within the band continuum.Furthermore,by projecting to the two sublattices,we find that the effective Bloch Hamiltonian corresponds to that of a generalized Su–Schrieffer–Heeger model or the Rice–Mele model whose hopping amplitudes depend on the quasimomentum.In this way,the topological phases can be efficiently extracted through winding numbers.We propose that uneven ladders can be realized by spin-dependent optical lattices and their rich topological characteristics can be examined by near future experiments.展开更多
Generative Models have been shown to be extremely useful in learning features from unlabeled data. In particular, variational autoencoders are capable of modeling highly complex natural distributions such as images, w...Generative Models have been shown to be extremely useful in learning features from unlabeled data. In particular, variational autoencoders are capable of modeling highly complex natural distributions such as images, while extracting natural and human-understandable features without labels. In this paper we combine two highly useful classes of models, variational ladder autoencoders, and MMD variational autoencoders, to model face images. In particular, we show that we can disentangle highly meaningful and interpretable features. Furthermore, we are able to perform arithmetic operations on faces and modify faces to add or remove high level features.展开更多
基金supported by the Natural Science Foundation of Zhejiang Province,China (Grant Nos.LR22A040001 and LY21A040004)the National Natural Science Foundation of China (Grant Nos.12074342 and 11835011)。
文摘We investigate the topological properties of a two-chain quantum ladder with uneven legs,i.e.,the two chains differ in their periods by a factor of 2.Such an uneven ladder presents rich band structures classified by the closure of either direct or indirect bandgaps.It also provides opportunities to explore fundamental concepts concerning band topology and edge modes,including the difference of intracellular and intercellular Zak phases,and the role of the inversion symmetry(IS).We calculate the Zak phases of the two kinds and find excellent agreement with the dipole moment and extra charge accumulation.We also find that configurations with IS feature a pair of degenerate two-side edge modes emerging as the closure of the direct bandgap,while configurations without IS feature one-side edge modes emerging as not only the closure of both direct and indirect bandgaps but also within the band continuum.Furthermore,by projecting to the two sublattices,we find that the effective Bloch Hamiltonian corresponds to that of a generalized Su–Schrieffer–Heeger model or the Rice–Mele model whose hopping amplitudes depend on the quasimomentum.In this way,the topological phases can be efficiently extracted through winding numbers.We propose that uneven ladders can be realized by spin-dependent optical lattices and their rich topological characteristics can be examined by near future experiments.
文摘Generative Models have been shown to be extremely useful in learning features from unlabeled data. In particular, variational autoencoders are capable of modeling highly complex natural distributions such as images, while extracting natural and human-understandable features without labels. In this paper we combine two highly useful classes of models, variational ladder autoencoders, and MMD variational autoencoders, to model face images. In particular, we show that we can disentangle highly meaningful and interpretable features. Furthermore, we are able to perform arithmetic operations on faces and modify faces to add or remove high level features.
