Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session GG06: V: Machine Learning for Quantum Matter |
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Sponsoring Units: DCOMP Chair: Xingjian Wang, University of Alabama in Huntsville Room: Virtual Room 3 |
Monday, March 20, 2023 12:30PM - 12:42PM |
GG06.00001: Applying the Variational Principle to Quantum Field Theory with Neural-Networks John M Martyn, Di Luo, Khadijeh Najafi Physicists dating back to Feynman have lamented the challenges of applying the variational principle to quantum field theories, most notably evaluating and optimizing expectation values of a quantum field state. In the context of non-relativistic quantum field theories, this approach requires one to parameterize and optimize over the infinitely many $n$-particle wave functions comprising the state's Fock space representation, a seemingly daunting task. In this work, we introduce a variational ansatz to enable the application of the variational principle to 1D bosonic quantum field theories directly in the continuum. Our ansatz is a neural-network quantum state, and uses the Fock space representation to model a quantum field state as a superposition of $n$-particle wave functions, each of which is parameterized by a common neural-network architecture that is both permutation-invariant and able to accept an arbitrary number of arguments. We develop a novel algorithm for variational Monte Carlo in Fock space and employ it on our ansatz to approximate ground states of the Lieb-Liniger model, the Calogero-Sutherland model, and a regularized Klein-Gordon model. Our ansatz can be seen as the neural-network-based analog of continuous matrix product states, which have traditionally been deployed on 1D field theories but struggle on inhomogenous systems and long-range interactions. The utility of our ansatz lies in its flexibility and broad applicability to such systems, providing a powerful new tool for probing quantum field theories. |
Monday, March 20, 2023 12:42PM - 12:54PM |
GG06.00002: Learning Gradient Boosting Ground States for Quantum Many-Body Systems Vladimir Vargas-Calderón, Johan Ríos, Herbert Vinck-Posada In the last few years, within the field of computational physics, there has been an upswing in the use of artificial neural networks (ANNs) as base models to build variational wave functions. These have proven to be very useful in studying quantum many-body physics, where they have successfully described the physics of those systems through the so-called neural quantum states (NQSs). However, these novel methods have focused on using mainly the ANNs, leaving away possible alternatives that can be very useful in studying physical systems. One of those alternatives is gradient boosting (GB), particularly its version with decision trees, usually called gradient-boosted trees (GBT). Due to its characteristics, it has outperformed ANNs in several machine learning competitions. Motivated by the rise of this method in various fields of data science and machine learning in general, we show in this work how the GBT method can be used together with the variational Monte Carlo framework to describe the ground state of quantum many-body systems. Furthermore, we discuss how the nature of the decision trees can be used to efficiently subdivide the Hilbert space of a quantum system and how the symmetries of the physical system under study can be used to refine our method even further. |
Monday, March 20, 2023 12:54PM - 1:06PM |
GG06.00003: Probing interacting topological matter with neural-network quantum states Fan Yang, Dian Wu, Giuseppe Carleo Recently, many-body quantum matter with topological orders has been efficiently represented by neural-network quantum states in the form of restricted Boltzmann machines. We extend its application to 2D topological materials with interactions, including generalized Kitaev honeycomb model in a magnetic field and frustrated bond-random Heisenberg antiferromagnets on a square lattice. The stability of the emergent spin liquid phases is tested by dynamical spin structure factor, flux excitations as well as bipartite fluctuations, an indicator for many-body entanglement. |
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