SciPost Thesis Link

Title:  Summing matrix elements of the Lieb-Liniger model with reinforcement learning
Author:  Teun Zwart
As Contributor:   Teun Zwart
Type: Master's
Field: Physics
  • Condensed Matter Physics - Theory
Approaches: Theoretical, Computational
Degree granting institution:  University of Amsterdam
Supervisor(s): Jean-S├ębastien Caux
Defense date:  2018-07-12


Correlation functions play an important role in physics, but analytical results do not always exist. For Bethe ansatz solvable models the ABACUS algorithm can numerically find Fourier transformed correlation functions known as dynamical structure functions or DSFs. This occurs through the summation of matrix elements in the Lehmann representation of the DSF. This summing is not optimal, in that it does not sum matrix elements in strictly monotonically decreasing order. In this thesis we apply reinforcement learning to the summing of matrix elements, hoping to develop a strategy that leads to more optimal summation than done by ABACUS. We develop a representation of the Lieb-Liniger model suitable for use in machine learning and use Q-learning to learn the summation strategy of the density operator. We find that the algorithm is able to learn to sum in such a way that it gives preference to highly contributing states, but that performance is far inferior to that shown by ABACUS. As a corollary we also use supervised learning to try to optimize the numerical evaluation of Bethe ansatz parameters known as rapidities, but find that any advantage this method has declines considerably with system size. The evaluation time added by the neural network makes this method unfit for finding rapidities.

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