Matrix multiplication

Quantum mechanics

Matrix product state

Ground state

Pure mathematics

Bandwidth (computing)

Decimation

Isometric exercise

Computer science

Mathematical optimization

Hamiltonian (control theory)

Filter (signal processing)

Statistical physics

Computer network

Ansatz

Tensor (intrinsic definition)

Contraction (grammar)

Physics

Mathematics

Ising model

Physical therapy

Internal medicine

Quantum

Medicine

Computer vision

Physical Review Letters

Tensor-network states (TNS) are a promising but numerically challenging tool for simulating two-dimensional (2D) quantum many-body problems. We introduce an isometric restriction of the TNS ansatz that allows for highly efficient contraction of the network. We consider two concrete applications using this ansatz. First, we show that a matrix-product state representation of a 2D quantum state can be iteratively transformed into an isometric 2D TNS. Second, we introduce a 2D version of the time-evolving block decimation algorithm for approximating of the ground state of a Hamiltonian as an isometric TNS---which we demonstrate for the 2D transverse field Ising model.

Isometric Tensor Network States in Two Dimensions