Stable Optimization of a Tensor Product Variational State | Zendy

Andrej Gendiar | Zendy; Nobuya Maeshima | Zendy; Tomotoshi Nishino | Zendy

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Stable Optimization of a Tensor Product Variational State

Author(s) -

Andrej Gendiar,

Nobuya Maeshima,

Tomotoshi Nishino

Publication year - 2003

Publication title -

progress of theoretical physics

Language(s) - English

Resource type - Journals

eISSN - 1347-4081

pISSN - 0033-068X

DOI - 10.1143/ptp.110.691

Subject(s) - physics , ising model , tensor product , partition function (quantum field theory) , variational method , mathematics , maximization , stability (learning theory) , tensor (intrinsic definition) , statistical physics , mathematical optimization , quantum mechanics , pure mathematics , computer science , machine learning

We consider a variational problem for three-dimensional (3D) classicallattice models. We construct the trial state as a two-dimensional product oflocal variational weights that contain auxiliary variables. We propose a stablenumerical algorithm for the maximization of the variational partition functionper layer. The numerical stability and efficiency of the new method areexamined through its application to the 3D Ising model.Comment: 9 pages, 5 figures, in LaTex2e style. accepted for publication in Prog. Theor. Phys. 11

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