Simulation of two dimensional quantum systems on an infinite lattice revisited: corner transfer matrix for tensor contraction

Abstract

An extension of the projected entangled-pair states (PEPS) algorithm to infinite systems, known as the iPEPS algorithm, was recently proposed to compute the ground state of quantum systems on an infinite two-dimensional lattice. Here we investigate a modification of the iPEPS algorithm, where the environment is computed using the corner transfer matrix renormalization group (CTMRG) method, instead of using one-dimensional transfer matrix methods as in the original proposal. We describe a variant of the CTMRG that addresses different directions of the lattice independently, and use it combined with imaginary time evolution to compute the ground state of the two-dimensional quantum Ising model. Near criticality, the modified iPEPS algorithm is seen to provide a better estimation of the order parameter and correlators.

5 pages, 5 figures, 1 table, revised version, accepted in PRB

References in corpus (11)

• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Tensor renormalization group approach to 2D classical lattice models
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• The iTEBD algorithm beyond unitary evolution
• Scaling of entanglement support for Matrix Product States
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Ground state fidelity from tensor network representations
• First order phase transition in the anisotropic quantum orbital compass model
• Variational treatment of the Shastry-Sutherland antiferromagnet using Projected Entangled Pair States (PEPS)
• Quantum phase transitions in a two-dimensional quantum XYX model: Ground-state fidelity and entanglement

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