Plaquette Renormalization Scheme for Tensor Network States

Abstract

We present a method for contracting a square-lattice tensor network in two dimensions, based on auxiliary tensors accomplishing successive truncations (renormalization) of 8-index tensors for 2 by 2 plaquettes into 4-index tensors. The scheme is variational, and thus the tensors can be optimized by minimizing the energy. Test results for the quantum phase transition of the transverse-field Ising model confirm that even the smallest possible tensors (two values for each tensor index at each renormalization level) produce much better results than the simple product (mean-field) state.

4 pages, 7 figures

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• Lecture Notes of Tensor Network Contractions
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• Spin-1/2 J1-J2 Heisenberg antiferromagnet on a square lattice: a plaquette renormalized tensor network study
• Time evolution as refining, coarse graining and entangling
• Coarse graining of spin net models: dynamics of intertwiners
• Renormalization group contraction of tensor networks in three dimensions
• Ground-state properties of the spin-1/2 antiferromagnetic Heisenberg model on the triangular lattice: A variational study based on entangled-plaquette states
• Variational Monte Carlo simulations using tensor-product projected states
• Partial long-range order in antiferromagnetic Potts models
• Geometric entanglement and quantum phase transitions in two-dimensional quantum lattice models
• Monte Carlo simulations of two-dimensional fermion systems with string-bond states