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

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.

8 pages, 8 figures

References in corpus (5)

• The density-matrix renormalization group
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• DMRG and periodic boundary conditions: a quantum information perspective
• Efficient evaluation of partition functions of frustrated and inhomogeneous spin systems
• Real-space renormalization group approach for the corner Hamiltonian

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