PIRSA:17040034

Applying DMRG to Non-relativistic Continuous Systems in 1D and 3D

Stoudenmire, M. (2017). Applying DMRG to Non-relativistic Continuous Systems in 1D and 3D. Perimeter Institute. https://pirsa.org/17040034

Stoudenmire, Miles. Applying DMRG to Non-relativistic Continuous Systems in 1D and 3D. Perimeter Institute, Apr. 18, 2017, https://pirsa.org/17040034 

          @misc{ pirsa_PIRSA:17040034,
            doi = {10.48660/17040034},
            url = {https://pirsa.org/17040034},
            author = {Stoudenmire, Miles},
            keywords = {Condensed Matter, Quantum Fields and Strings, Quantum Gravity, Quantum Information},
            language = {en},
            title = {Applying DMRG to Non-relativistic Continuous Systems in 1D and 3D},
            publisher = {Perimeter Institute},
            year = {2017},
            month = {apr},
            note = {PIRSA:17040034 see, \url{https://pirsa.org}}
          }

Miles Stoudenmire Flatiron Institute

Talk numberPIRSA:17040034
DOI10.48660/17040034
Collection
Talk Type Conference
Subject

Abstract

The density matrix renormalization group works very well for one-dimensional (1D) lattice systems, and can naively be adapted for non-relativistic continuum systems in 1D by discretizing real space using a grid. I will discuss challenges inherent in this approach and successful applications. Recently, the success of the grid approach for 1D motivated us to extend the approach to 3D by treating the transverse directions with a basis set. This hybrid grid/basis-set approach allows DMRG to scale much better for long molecules and we obtain state-of-the-art results with modest computing resources. A key component of the approach is a powerful algorithm for compressing long-range interactions into a matrix product operator which I will present in some detail.