Criticality and phase classification for quadratic open quantum many-body systems

We study the steady states of translation-invariant open quantum many-body systems governed by Lindblad master equations, where the Hamiltonian is quadratic in the ladder operators, and the Lindblad operators are either linear or quadratic and Hermitian. These systems are called quasi-free and quadratic, respectively. We find that steady states of one-dimensional systems with finite-range interactions necessarily have exponentially decaying Green's functions. For the quasi-free case without quadratic Lindblad operators, we show that fermionic systems with finite-range interactions are non-critical for any number of spatial dimensions and provide bounds on the correlation lengths. Quasi-free bosonic systems can be critical in $D>1$ dimensions. Lastly, we address the question of phase transitions in quadratic systems and find that, without symmetry constraints beyond invariance under single-particle basis and particle-hole transformations, all gapped Liouvillians belong to the same phase.Comment: 13 pages, 2 figures; the employed methods for the solution of quasi-free and quadratic open systems are described in arXiv:2112.0834

Optimized Lie-Trotter-Suzuki decompositions for two and three non-commuting terms

Lie-Trotter-Suzuki decompositions are an efficient way to approximate operator exponentials $\exp(t H)$ when $H$ is a sum of $n$ (non-commuting) terms which, individually, can be exponentiated easily. They are employed in time-evolution algorithms for tensor network states, digital quantum simulation protocols, path integral methods like quantum Monte Carlo, and splitting methods for symplectic integrators in classical Hamiltonian systems. We provide optimized decompositions up to order $t^6$. The leading error term is expanded in nested commutators (Hall bases) and we minimize the 1-norm of the coefficients. For $n=2$ terms, several of the optima we find are close to those in McLachlan, SlAM J. Sci. Comput. 16, 151 (1995). Generally, our results substantially improve over unoptimized decompositions by Forest, Ruth, Yoshida, and Suzuki. We explain why these decompositions are sufficient to efficiently simulate any one- or two-dimensional lattice model with finite-range interactions. This follows by solving a partitioning problem for the interaction graph.Comment: 30 pages, 8 figures, 8 tables; added results, figures, and references, extended discussio

Super-operator structures and no-go theorems for dissipative quantum phase transitions

In the thermodynamic limit, the steady states of open quantum many-body systems can undergo nonequilibrium phase transitions due to a competition between Hamiltonian and dissipative terms. Here, we consider Markovian systems and elucidate structures of the Liouville super-operator that generates the dynamics. In many cases of interest, a non-orthogonal basis transformation can bring the Liouvillian into block-triangular form, making it possible to assess its spectrum. The spectral gap sets the asymptotic decay rate. The super-operator structure can be used to bound gaps from below, showing that, in a large class of systems, dissipative phase transitions are actually impossible and that the convergence to steady states is exponential. Furthermore, when the blocks on the diagonal are Hermitian, the Liouvillian spectra obey Weyl ordering relations. The results are exemplified by various spin models.Comment: 7 page

Word Embedding based Correlation Model for Question/Answer Matching

With the development of community based question answering (Q&A) services, a large scale of Q&A archives have been accumulated and are an important information and knowledge resource on the web. Question and answer matching has been attached much importance to for its ability to reuse knowledge stored in these systems: it can be useful in enhancing user experience with recurrent questions. In this paper, we try to improve the matching accuracy by overcoming the lexical gap between question and answer pairs. A Word Embedding based Correlation (WEC) model is proposed by integrating advantages of both the translation model and word embedding, given a random pair of words, WEC can score their co-occurrence probability in Q&A pairs and it can also leverage the continuity and smoothness of continuous space word representation to deal with new pairs of words that are rare in the training parallel text. An experimental study on Yahoo! Answers dataset and Baidu Zhidao dataset shows this new method's promising potential.Comment: 8 pages, 2 figure

KD-MVS: Knowledge Distillation Based Self-supervised Learning for Multi-view Stereo

Supervised multi-view stereo (MVS) methods have achieved remarkable progress in terms of reconstruction quality, but suffer from the challenge of collecting large-scale ground-truth depth. In this paper, we propose a novel self-supervised training pipeline for MVS based on knowledge distillation, termed KD-MVS, which mainly consists of self-supervised teacher training and distillation-based student training. Specifically, the teacher model is trained in a self-supervised fashion using both photometric and featuremetric consistency. Then we distill the knowledge of the teacher model to the student model through probabilistic knowledge transferring. With the supervision of validated knowledge, the student model is able to outperform its teacher by a large margin. Extensive experiments performed on multiple datasets show our method can even outperform supervised methods