Spatially Modulated Interaction Induced Bound States and Scattering Resonances

We study the two-body problem with a spatially modulated interaction potential using a two-channel model, in which the inter-channel coupling is provided by an optical standing wave and its strength modulates periodically in space. As the modulation amplitudes increases, there will appear a sequence of bound states. Part of them will cause divergence of the effective scattering length, defined through the phase shift in the asymptotic behavior of scattering states. We also discuss how the local scattering length, defined through short-range behavior of scattering states, modulates spatially in different regimes. These results provide a theoretical guideline for new control technique in cold atom toolbox, in particular, for alkali-earth-(like) atoms where the inelastic loss is small.Comment: 5 pages, 5 figure

Unsupervised Learning of Frustrated Classical Spin Models I: Principle Component Analysis

This work aims at the goal whether the artificial intelligence can recognize phase transition without the prior human knowledge. If this becomes successful, it can be applied to, for instance, analyze data from quantum simulation of unsolved physical models. Toward this goal, we first need to apply the machine learning algorithm to well-understood models and see whether the outputs are consistent with our prior knowledge, which serves as the benchmark of this approach. In this work, we feed the compute with data generated by the classical Monte Carlo simulation for the XY model in frustrated triangular and union jack lattices, which has two order parameters and exhibits two phase transitions. We show that the outputs of the principle component analysis agree very well with our understanding of different orders in different phases, and the temperature dependences of the major components detect the nature and the locations of the phase transitions. Our work offers promise for using machine learning techniques to study sophisticated statistical models, and our results can be further improved by using principle component analysis with kernel tricks and the neural network method.Comment: 8 pages, 11 figure

Topological Sachdev-Ye-Kitaev Model

In this letter we construct a large-N exactly solvable model to study the interplay between interaction and topology, by connecting Sacheve-Ye-Kitaev (SYK) model with constant hopping. The hopping forms a band structure that can exhibit both topological trivial and nontrivial phases. Starting from a topologically trivial insulator with zero Hall conductance, we show that interaction can drive a phase transition to topological nontrivial insulator with quantized non-zero Hall conductance, and a single gapless Dirac fermion emerges when the interaction is fine tuned to the critical point. The finite temperature effect is also considered and we show that the topological phase with stronger interaction is less stable against temperature. Our model provides a concrete example to illustrate interacting topological phases and phase transition, and can shed light on similar problems in physical systems.Comment: 6 pages, 5 figure