Multi-scale Entanglement Renormalization Ansatz in Two Dimensions: Quantum Ising Model

Abstract

We propose a symmetric version of the multi-scale entanglement renormalization Ansatz (MERA) in two spatial dimensions (2D) and use this Ansatz to find an unknown ground state of a 2D quantum system. Results in the simple 2D quantum Ising model on the $8\times 8$ square lattice are found to be very accurate even with the smallest non-trivial truncation parameter.

version to appear in Phys. Rev. Letters

References in corpus (9)

• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Criticality, the area law, and the computational power of PEPS
• The computational complexity of PEPS
• Variational study of hard-core bosons in a 2-D optical lattice using Projected Entangled Pair States (PEPS)
• Stochastic series expansion method for quantum Ising models with arbitrary interactions
• Strings, Projected Entangled Pair States, and variational Monte Carlo methods
• Unifying variational methods for simulating quantum many-body systems
• Simulation of time evolution with the MERA
• Variational treatment of the Shastry-Sutherland antiferromagnet using Projected Entangled Pair States (PEPS)

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