Tensor-entanglement renormalization group approach to 2D quantum systems

Abstract

Traditional mean-field theory is a simple generic approach for understanding various phases. But that approach only applies to symmetry breaking states with short-range entanglement. In this paper, we describe a generic approach for studying 2D quantum phases with long-range entanglement (such as topological phases). Our approach is a variational method that uses tensor product states (also known as projected entangled pair states) as trial wave functions. We use a 2D real space RG algorithm to evaluate expectation values in these wave functions. We demonstrate our algorithm by studying several simple 2D quantum spin models.

4 pages, RevTeX4

References in corpus (4)

• Tensor renormalization group approach to 2D classical lattice models
• Criticality, the area law, and the computational power of PEPS
• Entanglement renormalization and topological order
• A mean field approach for string condensed states

Cited by in corpus (5)

• Quantum Monte Carlo simulations of fidelity at magnetic quantum phase transitions
• Magnetization Plateau of Classical Ising Model on Shastry-Sutherland Lattice
• Assessing the accuracy of projected entangled-pair states on infinite lattices
• Numerical Study of Spin-1/2 XXZ Model on Square Lattice from Tensor Product States
• Tensor-product representations for string-net condensed states