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Speaker: Synge Todo (University of Tokyo)
Time & Date: 13:00 – 14:00, February 20, 2023 (JST)
Place: Online (Zoom meeting)
Title: Monte Carlo sampling in tensor-network representation
Abstract:
Many classical and quantum lattice models can be represented as tensor
networks. However, the exact contraction of a tensor network is
generally exponentially expensive, and some approximation is usually
required. In numerical simulations based on the tensor networks,
approximations with the singular value decomposition are widely used.
On the other hand, various contraction methods based on randomized
algorithms have also been proposed. Unfortunately, with a simple
weighted sampling, it is difficult to control the accuracy because the
expected value variance diverges rapidly as the network grows. In this
talk, I propose a new tensor contraction method based on Monte Carlo
sampling. The proposed method combines the stochastic basis
transformation of tensors with the Markov chain Monte Carlo framework.
It can entirely remove the systematic error due to a finite bond
dimension in the approximate tensor-network contraction while
controlling the variance of measurements.
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—
Satoshi Morita (森田 悟史)
The Institute for Solid State Physics, The University of Tokyo
kawashima.issp.u-tokyo.ac.jp/people/morita/
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