Charge modulation as fingerprints of phase-string triggered interference

Charge order appears to be an ubiquitous phenomenon in doped Mott insulators, which is currently under intense experimental and theoretical investigations particularly in the high $T_c$ cuprates. This phenomenon is conventionally understood in terms of Hartree-Fock type mean field theory. Here we demonstrate a mechanism for charge modulation which is rooted in the many-particle quantum physics arising in the strong coupling limit. Specifically, we consider the problem of a single hole in a bipartite $t-J$ ladder. As a remnant of the fermion signs, the hopping hole picks up subtle phases pending the fluctuating spins, the so-called phase string effect. We demonstrate the presence of charge modulations in the density matrix renormalization group solutions which disappear when the phase strings are switched off. This form of charge modulation can be understood analytically in a path-integral language, showing that the phase strings give rise to constructive interferences leading to self-localization. When the latter occurs, left- and right-moving propagating modes emerge inside the localization volume and their interference is responsible for the real space charge modulation.Comment: 14 pages, 10 figures. Comments on a followup paper by S. R. White, D. J. Scalapino, and S. A. Kivelson (arXiv:1502.04403) adde

One-bit Supervision for Image Classification: Problem, Solution, and Beyond

This paper presents one-bit supervision, a novel setting of learning with fewer labels, for image classification. Instead of training model using the accurate label of each sample, our setting requires the model to interact with the system by predicting the class label of each sample and learn from the answer whether the guess is correct, which provides one bit (yes or no) of information. An intriguing property of the setting is that the burden of annotation largely alleviates in comparison to offering the accurate label. There are two keys to one-bit supervision, which are (i) improving the guess accuracy and (ii) making good use of the incorrect guesses. To achieve these goals, we propose a multi-stage training paradigm and incorporate negative label suppression into an off-the-shelf semi-supervised learning algorithm. Theoretical analysis shows that one-bit annotation is more efficient than full-bit annotation in most cases and gives the conditions of combining our approach with active learning. Inspired by this, we further integrate the one-bit supervision framework into the self-supervised learning algorithm which yields an even more efficient training schedule. Different from training from scratch, when self-supervised learning is used for initialization, both hard example mining and class balance are verified effective in boosting the learning performance. However, these two frameworks still need full-bit labels in the initial stage. To cast off this burden, we utilize unsupervised domain adaptation to train the initial model and conduct pure one-bit annotations on the target dataset. In multiple benchmarks, the learning efficiency of the proposed approach surpasses that using full-bit, semi-supervised supervision.Comment: ACM TOMM. arXiv admin note: text overlap with arXiv:2009.0616