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Product Wave Function Renormalization Group: construction from the matrix product point of view

Kouji Ueda·Tomotoshi Nishino·Kouichi Okunishi·Yasuhiro Hieida·Rene Derian·Andrej Gendiar
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Abstract

We present a construction of a matrix product state (MPS) that approximates the largest-eigenvalue eigenvector of a transfer matrix T, for the purpose of rapidly performing the infinite system density matrix renormalization group (DMRG) method applied to two-dimensional classical lattice models. We use the fact that the largest-eigenvalue eigenvector of T can be approximated by a state vector created from the upper or lower half of a finite size cluster. Decomposition of the obtained state vector into the MPS gives a way of extending the MPS, at the system size increment process in the infinite system DMRG algorithm. As a result, we successfully give the physical interpretation of the product wave function renormalization group (PWFRG) method, and obtain its appropriate initial condition.

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Kouji Ueda, Tomotoshi Nishino, Kouichi Okunishi, Yasuhiro Hieida, Rene Derian, Andrej Gendiar. 2005-09-13. Product Wave Function Renormalization Group: construction from the matrix product point of view. https://doi.org/10.1143/jpsj.75.014003

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