Variational Energy Minimization for Continuous Matrix Product States (Dr. M. Ganahl)

  • Date: Mar 3, 2017
  • Time: 09:05 AM - 10:00 AM (Local Time Germany)
  • Speaker: Dr. Martin Ganahl
  • Perimter Institute for Theoretical Physics Waterloo, Canada
  • Room: Herbert Walther Lecture Hall
  • Host: MPQ & Max Planck Harvard Center
The generalization of Matrix Product States (MPS) to continuous systems, as proposed in Phys. Rev. Lett. 104, 190405(2010), provides a powerful variational ansatz for the ground state of strongly interacting quantum field theories in one spatial dimension.

A continuous MPS (cMPS) approximation to the ground state can be obtained by simulating an Euclidean time evolution. In this talk I will present a cMPS optimization algorithm based instead on energy minimization by gradient methods. I will demonstrate its performance for the case of the Lieb Liniger model (an integrable model of an interacting bosonic field) directly in the thermodynamic limit. The algorithm shows a significant computational speed‐up, up to two orders of magnitude, with respect to simulating an Euclidean time evolution. As a result, much larger cMPS bond dimension D and much higher accuracy can be reached (e.g. D = 256 with moderate computational resources).

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