A main task in condensed-matter physics is to recognize, classify, and characterize phases of matter and the corresponding phase transitions, for which machine learning provides a new class of research tools due to the remarkable development in computing power and algorithms. Despite much exploration in this new field, usually different methods and techniques are needed for different scenarios. Here, we present SimCLP: a simple framework for contrastive learning phases of matter, which is inspired by the recent development in contrastive learning of visual representations. We demonstrate the success of this framework on several representative systems, including non-interacting and quantum many-body, conventional and topological. SimCLP is flexible and free of usual burdens such as manual feature engineering and prior knowledge. The only prerequisite is to prepare enough state configurations. Furthermore, it can generate representation vectors and labels and hence help tackle other problems. SimCLP therefore paves an alternative way to the development of a generic tool for identifying unexplored phase transitions.

The out-of-time-ordered (OTO) correlation is a key quantity for quantifying quantum chaoticity and has been recently used in the investigation of quantum holography. Here we use it to study and characterize many-body localization (MBL). We find that a long-time logarithmic variation of the OTO correlation occurs in the MBL phase but is absent in the Anderson localized and ergodic phases. We extract a localization length in the MBL phase, which depends logarithmically on interaction and diverges at a critical interaction. Furthermore, the infinite-time 'thermal' fluctuation of the OTO correlation is zero (finite) in the ergodic (MBL) phase and thus can be considered as an order parameter for the ergodic-MBL transition, through which the transition can be identified and characterized. Specifically, the critical point and the related critical exponents can be calculated.

We have studied the ground state of the half-filled Hubbard model on a honeycomb lattice by performing the cluster dynamical mean field theory calculations with exact diagonalization on the cluster-impurity solver. Through using elaborate numerical analytic continuation, we identify the existence of a 'spin liquid' from the on-site interaction U = 0 to Uc (between 4.6t and 4.85t) with a smooth crossover correspondingly from the charge fluctuation dominating phase into the charge correlation dominating phase. The semi-metallic state exits only at U = 0. We further find that the magnetic phase transition at Uc from the 'spin liquid' to the Néel antiferromagnetic Mott insulating phase is a first-order quantum phase transition. We also show that the charge fluctuation plays a substantial role on keeping the 'spin liquid' phase against the emergence of a magnetic order.

Long Short-Term Memory (LSTM) models are the building blocks of many state-of-the-art algorithms for Natural Language Processing (NLP). But, there are a large number of parameters in an LSTM model. This usually brings out a large amount of memory space needed for operating an LSTM model. Thus, an LSTM model usually requires a large amount of computational resources for training and predicting new data, suffering from computational inefficiencies. Here we propose an alternative LSTM model to reduce the number of parameters significantly by representing the weight parameters based on matrix product operators (MPO), which are used to characterize the local correlation in quantum states in physics. We further experimentally compare the compressed models based the MPO-LSTM model and the pruning method on sequence classification and sequence prediction tasks. The experimental results show that our proposed MPO-based method outperforms the pruning method.