Physics

Canonical transformations play fundamental roles in simplifying and solving physical systems. However, their design and implementation can be challenging in the many-particle setting. Viewing canonical transformations from the angle of learnable diffeomorphism reveals a fruitful connection to normalizing flows in machine learning. The key issue is then how to impose physical constraints such as symplecticity, unitarity, and permutation equivariance in the flow transformations. In this talk, I will present the design and application of neural canonical transformations for several physical problems. Symplectic flow identifies independent and nonlinear modes of classical Hamiltonians and natural datasets. Fermi flow variationally solves ab initio many-electron problems at finite temperatures.
Refs:
[1] Shuo-Hui Li, Chen-Xiao Dong, Linfeng Zhang, and Lei Wang, Phys. Rev. X 10, 021020 (2020)
[2]  Hao Xie, Linfeng Zhang, and Lei Wang, J. Mach. Learn. , 1, 38 (2022)

Zoom link:  https://pitp.zoom.us/j/98830940500?pwd=WjdydGY5aS9QQzk5SnI0TE1xMkwrdz09

In this talk, I will present two recent works on electronic lattice models, both of which utilize novel numerical algorithms to achieve a deeper understanding of the many-electron problem. Competing and intertwined orders including inhomogeneous patterns of spin and charge are observed in many correlated electron materials, such as high-temperature superconductors. In arXiv:2202.11741, we introduce a new development of constrained-path auxiliary-field quantum Monte Carlo (AFMQC) method and study the interplay between thermal and quantum fluctuations in the two-dimensional Hubbard model. We identify a finite-temperature phase transition below which charge ordering sets in. Quantum gas microscopy has developed into a powerful tool to explore strongly correlated quantum systems.  However, discerning phases with off-diagonal long range order requires the ability to extract these correlations from site-resolved measurements. In the second work arXiv:2209.10565, we study the one-dimensional extended Hubbard model using the variational uniform matrix product states algorithm. We show that a multi-scale complexity measure can pinpoint the transition to and from the bond ordered wave phase with an off-diagonal order parameter, sandwiched between diagonal charge and spin density wave phases, using only diagonal descriptors.

Zoom link:  https://pitp.zoom.us/j/97325001971?pwd=QXNmU2I0L3BxQVErMEZWSDF2bGZ0QT09

I will introduce the QAOA and discuss some recent developments. These might include the application of the QAOA to the Sherrington-Kirkpatrick model, landscape independence, and the odd behavior when starting in a good place.

Zoom link:  https://pitp.zoom.us/j/94804346887?pwd=c1hkRHBZZmRHS1RpM1BqU0R6TCtEdz09

Sofia Gonzalez Garcia, Perimeter Institute & University of Waterloo

Tensor Networks in a Nutshell

This seminar will be an introductory 'class' to Tensor Networks, so I will assume no previous knowledge on the subject. I aim to provide motivation for this powerful ansatz as well as some of its applications. I will introduce the main architectures (MPS, PEPS and MERA) and their characteristics. Throughout the seminar I will try to include part of the material I have produced for a 2017 PSI course taught by Guifre Vidal. 

If time permits I will also briefly introduce my research on the subject, which is on 2D tensor networks contraction and its accuracy convergence.